├── .idea ├── .gitignore ├── misc.xml ├── vcs.xml ├── inspectionProfiles │ └── profiles_settings.xml ├── modules.xml └── euler.iml ├── 029.py ├── 010.py ├── 071.py ├── 016.py ├── 006.py ├── 028.py ├── 048.py ├── 001.py ├── 097.py ├── 301.py ├── 020.py ├── 068.py ├── 100.py ├── 013.py ├── 117.py ├── 173.py ├── 063.py ├── 132.py ├── 056.py ├── 065.py ├── 003.py ├── 052.py ├── 120.py ├── 131.py ├── 700.py ├── 002.py ├── 025.py ├── 004.py ├── 009.py ├── 069.py ├── 007.py ├── 057.py ├── 113.py ├── 129.py ├── 187.py ├── 089.py ├── 124.py ├── 138.py ├── 034.py ├── 041.py ├── 099.py ├── 188.py ├── 123.py ├── 030.py ├── 114.py ├── 101.py ├── 106.py ├── 135.py ├── 067.py ├── 136.py ├── 684.py ├── 038.py ├── 033.py ├── 086.py ├── 119.py ├── 145.py ├── 032.py ├── 045.py ├── 076.py ├── 091.py ├── 203.py ├── 055.py ├── 686.py ├── 058.py ├── 049.py ├── 062.py ├── 019.py ├── 053.py ├── 024.py ├── 125.py ├── data ├── ep17.csv ├── ep18.txt ├── ep79.txt ├── ep08.txt ├── ep11.txt ├── ep13.txt ├── pe096.txt ├── ep67.txt ├── ep42.txt ├── ep89.txt ├── ep99.txt └── ep81.txt ├── 046.py ├── 059.py ├── 088.py ├── 070.py ├── 008.py ├── 587.py ├── 206.py ├── 115.py ├── 012.py ├── 021.py ├── 042.py ├── 118.py ├── 231.py ├── 137.py ├── 014.py ├── 023.py ├── 090.py ├── 112.py ├── 243.py ├── 022.py ├── 080.py ├── 087.py ├── 015.py ├── 134.py ├── 204.py ├── 104.py ├── 179.py ├── 075.py ├── 079.py ├── 094.py ├── 027.py ├── 072.py ├── 085.py ├── 026.py ├── 064.py ├── 510.py ├── 036.py ├── 144.py ├── 047.py ├── 719.py ├── 078.py ├── 081.py ├── 050.py ├── 044.py ├── 083.py ├── 005.py ├── 040.py ├── 082.py ├── 107.py ├── 116.py ├── 035.py ├── 043.py ├── 808.py ├── 077.py ├── 031.py ├── 051.py ├── 018.py ├── 102.py ├── 108.py ├── 110.py ├── 122.py ├── 066.py ├── 357.py ├── 143.py ├── 095.py ├── 140.py ├── 121.py ├── 060.py ├── 074.py ├── 103.py ├── 037.py ├── 105.py ├── 017.py ├── 039.py ├── 073.py ├── 160.py ├── 727.py ├── 540.py ├── 092.py ├── 061.py ├── 098.py ├── 011.py ├── 675.py ├── 093.py ├── 205.py ├── 084.py ├── README.md ├── 054.py └── 096.py /.idea/.gitignore: -------------------------------------------------------------------------------- 1 | 2 | # Default ignored files 3 | /workspace.xml -------------------------------------------------------------------------------- /029.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | r = range(2,101) 4 | print len({a**b for a in r for b in r}) 5 | -------------------------------------------------------------------------------- /010.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | from sympy import sieve 4 | print sum(list(sieve.primerange(1,2e6))) 5 | -------------------------------------------------------------------------------- /071.py: -------------------------------------------------------------------------------- 1 | # time cost = 408 ns ± 1.89 ns 2 | 3 | def main(D=10**6): 4 | k = int((D-5)/7) 5 | return 2+3*k 6 | -------------------------------------------------------------------------------- /016.py: -------------------------------------------------------------------------------- 1 | # time cost = 51.6 µs ± 629 ns 2 | 3 | def main(): 4 | ans = sum(map(int,str(2**1000))) 5 | return ans 6 | -------------------------------------------------------------------------------- /006.py: -------------------------------------------------------------------------------- 1 | # time cost = 569 ns ± 45.8 ns 2 | 3 | def main(n=100): 4 | ans = n*(n-1)*(n+1)*(3*n+2)/12 5 | return int(ans) 6 | -------------------------------------------------------------------------------- /028.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.47 µs ± 2.67 ns 2 | 3 | def main(n=500): 4 | res = 16*n**3/3 + 10*n**2 + 26*n/3 + 1 5 | return int(res) 6 | -------------------------------------------------------------------------------- /048.py: -------------------------------------------------------------------------------- 1 | # time cost = 9.14 ms ± 71.6 µs 2 | 3 | def main(): 4 | res = sum([x**x for x in range(1,1001)]) 5 | return (res % 10**10) 6 | -------------------------------------------------------------------------------- /001.py: -------------------------------------------------------------------------------- 1 | # time cost = 123 µs ± 15.4 µs 2 | 3 | def main(): 4 | ans = sum([x for x in range(1,1000) if x%3==0 or x%5==0]) 5 | return ans 6 | -------------------------------------------------------------------------------- /097.py: -------------------------------------------------------------------------------- 1 | # ans = 8739992577, time cost = 5.15 µs 2 | 3 | def main(): 4 | res = (28433*pow(2,7830457,10**10)+1)%(10**10) 5 | return res 6 | -------------------------------------------------------------------------------- /301.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.51 µs ± 31.6 ns 2 | 3 | def main(N=30): 4 | a,b = 1,2 5 | for _ in range(N): 6 | a,b = b,a+b 7 | return a 8 | -------------------------------------------------------------------------------- /020.py: -------------------------------------------------------------------------------- 1 | # time cost = 27.2 µs ± 149 ns 2 | 3 | from math import factorial as fac 4 | 5 | def main(): 6 | ans = sum(map(int,str(fac(100)))) 7 | return ans 8 | -------------------------------------------------------------------------------- /068.py: -------------------------------------------------------------------------------- 1 | # this problem can be solved with pen and paper, no programming is required. 2 | # see https://www.cnblogs.com/metaquant/p/11957802.html for an explanation 3 | -------------------------------------------------------------------------------- /100.py: -------------------------------------------------------------------------------- 1 | # time cost = 5.73 µs ± 59.8 ns 2 | 3 | def main(N=10**12): 4 | b,t = 15,21 5 | while t < N: 6 | b,t = 2*t+3*b-2,3*t+4*b-3 7 | return b 8 | -------------------------------------------------------------------------------- /013.py: -------------------------------------------------------------------------------- 1 | # time cost = 159 µs ± 858 ns 2 | 3 | def main(): 4 | large_sum = sum(map(int,open('data/ep13.txt'))) 5 | ans = str(large_sum)[:10] 6 | return ans 7 | -------------------------------------------------------------------------------- /117.py: -------------------------------------------------------------------------------- 1 | # time cost = 16.9 µs ± 82.7 ns 2 | 3 | def main(n=50): 4 | arr = [1,2,4,8] 5 | for _ in range(n-4): 6 | arr.append(sum(arr[-4:])) 7 | return arr[-1] 8 | -------------------------------------------------------------------------------- /173.py: -------------------------------------------------------------------------------- 1 | # time cost = 45.8 µs ± 293 ns 2 | 3 | def main(N=10**6): 4 | side = N//4 5 | u = int(side**0.5) + 1 6 | res = sum((side//i-i for i in range(1,u))) 7 | return res 8 | -------------------------------------------------------------------------------- /063.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.8 µs ± 29.8 ns 2 | 3 | from math import log10 4 | 5 | def main(): 6 | c = 0 7 | for n in range(1,10): 8 | c += int(1/(1-log10(n))) 9 | return c 10 | -------------------------------------------------------------------------------- /.idea/misc.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | -------------------------------------------------------------------------------- /.idea/vcs.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | -------------------------------------------------------------------------------- /132.py: -------------------------------------------------------------------------------- 1 | # time cost = 242 ms ± 488 µs 2 | 3 | from sympy import primerange 4 | 5 | def main(N=10**9,k=40): 6 | primes = [p for p in primerange(7,200000) if pow(10,N,p)==1] 7 | return sum(primes[:k]) 8 | -------------------------------------------------------------------------------- /056.py: -------------------------------------------------------------------------------- 1 | # time cost = 190 ms ± 515 µs 2 | 3 | def main(): 4 | str_sum = lambda y : sum([int(x) for x in str(y)]) 5 | res = max([str_sum(a**b) for a in range(1,100) for b in range(1,100)]) 6 | return res 7 | -------------------------------------------------------------------------------- /065.py: -------------------------------------------------------------------------------- 1 | # time cost = 30.8 µs ± 113 ns 2 | 3 | def main(N=100): 4 | m,n = 1,2 5 | for i in range(2,N+1): 6 | a = 2 * i//3 if i%3==0 else 1 7 | m,n = n,m+a*n 8 | return sum(map(int,str(n))) 9 | -------------------------------------------------------------------------------- /003.py: -------------------------------------------------------------------------------- 1 | # time cost = 238 µs ± 789 ns 2 | 3 | def main(n=600851475143): 4 | i = 2 5 | while i * i < n: 6 | while n%i == 0: 7 | n /= i 8 | i += 2 if i>2 else 1 9 | return n 10 | -------------------------------------------------------------------------------- /052.py: -------------------------------------------------------------------------------- 1 | # time cost = 314 ms ± 5.06 ms 2 | 3 | from itertools import count 4 | 5 | def main(): 6 | for x in count(10,1): 7 | if all(set(str(k*x))==set(str(x)) for k in range(6,1,-1)): 8 | return x 9 | -------------------------------------------------------------------------------- /120.py: -------------------------------------------------------------------------------- 1 | # time cost = 617 µs ± 1.28 µs 2 | 3 | def main(): 4 | even = [a**2-2*a for a in range(3,1001) if a%2==0] 5 | odd = [a**2-a for a in range(3,1001) if a%2==1] 6 | ans = sum(even) + sum(odd) 7 | return ans 8 | -------------------------------------------------------------------------------- /131.py: -------------------------------------------------------------------------------- 1 | # time cost = 8.71 ms ± 878 µs 2 | 3 | from sympy import isprime 4 | 5 | def main(N=576): 6 | c = 0 7 | for i in range(1,N+1): 8 | if isprime(3*i**2+3*i+1): 9 | c += 1 10 | return c 11 | -------------------------------------------------------------------------------- /.idea/inspectionProfiles/profiles_settings.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 6 | -------------------------------------------------------------------------------- /700.py: -------------------------------------------------------------------------------- 1 | # time cost = 12.8 µs ± 176 ns 2 | 3 | def main(): 4 | c = 1504170715041707 5 | nc = 8912517754604 6 | res = c + nc 7 | while nc > 0: 8 | c,nc = nc,(-c)%nc 9 | res += nc 10 | return res 11 | -------------------------------------------------------------------------------- /002.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.75 µs ± 75.2 ns 2 | 3 | def main(N=4e6): 4 | a,b = 2,8 5 | arr = [a,b] 6 | while True: 7 | a,b = b,4*b+a 8 | arr.append(b) 9 | if b > N: 10 | return sum(arr[:-1]) 11 | -------------------------------------------------------------------------------- /025.py: -------------------------------------------------------------------------------- 1 | # time cost = 40.2 ms ± 412 µs 2 | 3 | def main(N=1000): 4 | a,b,n = 1,1,1 5 | while True: 6 | n += 1 7 | a,b = b,a+b 8 | if len(str(a)) == N: 9 | return n 10 | -------------------------------------------------------------------------------- /004.py: -------------------------------------------------------------------------------- 1 | # time cost = 169 ms ± 402 µs 2 | 3 | def main(): 4 | r = range(999,99,-1) 5 | is_palindrome = lambda x : str(x) == str(x)[::-1] 6 | ans = max([i*j for i in r for j in r if (i*j)%11==0 and is_palindrome(i*j)]) 7 | return ans 8 | -------------------------------------------------------------------------------- /009.py: -------------------------------------------------------------------------------- 1 | # time cost = 146 µs ± 791 ns 2 | 3 | def main(p=1000): 4 | for a in range(1,p//3): 5 | n,d = p**2-2*p*a,2*p-2*a 6 | if n % d == 0: 7 | b = n/d 8 | c = p-a-b 9 | return int(a*b*c) 10 | -------------------------------------------------------------------------------- /069.py: -------------------------------------------------------------------------------- 1 | # time cost = 6.91 ms ± 154 µs 2 | 3 | from sympy import prime 4 | 5 | def main(N=10**6): 6 | i,prod,arr = 1,1,[] 7 | while prod <= N: 8 | prod *= prime(i) 9 | arr.append(prod) 10 | i += 1 11 | return arr[-2] 12 | -------------------------------------------------------------------------------- /007.py: -------------------------------------------------------------------------------- 1 | # time cost = 197 ms ± 1.18 ms 2 | 3 | from sympy import primerange 4 | from math import log,ceil 5 | 6 | def main(n=10001): 7 | upper_bound = ceil((log(n)+log(log(n))) * n) 8 | primes = list(primerange(1,upper_bound)) 9 | return primes[n-1] 10 | -------------------------------------------------------------------------------- /057.py: -------------------------------------------------------------------------------- 1 | # time cost = 885 µs ± 9.93 µs 2 | 3 | from math import log10 4 | 5 | def main(N=1000): 6 | c,n,d = 0,1,1 7 | for i in range(N): 8 | n,d = 2 * d + n,d + n 9 | if int(log10(n)) > int(log10(d)): 10 | c += 1 11 | return c 12 | -------------------------------------------------------------------------------- /113.py: -------------------------------------------------------------------------------- 1 | # time cost = 8.51 µs ± 116 ns 2 | 3 | from math import factorial as fac 4 | 5 | def comb_num(n,k): 6 | num = fac(n)//(fac(n-k)*fac(k)) 7 | return num 8 | 9 | def main(d=100): 10 | res = comb_num(d+9,9)+comb_num(d+10,10)-10*d-2 11 | return res 12 | -------------------------------------------------------------------------------- /129.py: -------------------------------------------------------------------------------- 1 | # time cost = 642 µs ± 2.22 µs 2 | 3 | from sympy.ntheory import n_order 4 | 5 | def main(N=10**6): 6 | n = N + 1 7 | while True: 8 | if n % 5 != 0 and n_order(10,9*n)>N: 9 | return n 10 | else: 11 | n = n + 2 12 | -------------------------------------------------------------------------------- /187.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.51 s ± 5.57 ms 2 | 3 | from sympy import primerange,primepi 4 | 5 | def main(N=10**8): 6 | c = 0 7 | u = int(N**0.5) 8 | primes = primerange(1,u+1) 9 | for n,p in enumerate(primes): 10 | c += primepi((N-1)//p)-n 11 | return c 12 | -------------------------------------------------------------------------------- /089.py: -------------------------------------------------------------------------------- 1 | # time cost = 565 µs ± 11.4 µs 2 | 3 | import re 4 | 5 | def main(): 6 | with open('data/ep89.txt') as f: 7 | romans = f.read() 8 | new = re.sub("DCCCC|LXXXX|VIIII|CCCC|XXXX|IIII", '**',romans) 9 | savings = len(romans) - len(new) 10 | return savings 11 | -------------------------------------------------------------------------------- /124.py: -------------------------------------------------------------------------------- 1 | # time cost = 153 ms ± 1.19 ms 2 | 3 | def main(n=10**5,k=10**4): 4 | arr = [[1,i] for i in range(n+1)] 5 | for i in range(2,n+1): 6 | if arr[i][0] == 1: 7 | for j in range(i,n+1,i): 8 | arr[j][0] *= i 9 | return sorted(arr)[k][1] 10 | -------------------------------------------------------------------------------- /.idea/modules.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | -------------------------------------------------------------------------------- /138.py: -------------------------------------------------------------------------------- 1 | # time cost = 6.96 µs ± 23.6 ns 2 | 3 | def main(N=12): 4 | n,res = 0,0 5 | x,y = 38,17 6 | while n < N: 7 | b1,b2 = 2*x+4,2*x-4 8 | if b1%5 == 0 or b2%5==0: 9 | res += y 10 | n += 1 11 | x,y = 9*x+20*y,4*x+9*y 12 | return res 13 | -------------------------------------------------------------------------------- /034.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.22 s ± 3.31 ms 2 | 3 | from math import factorial 4 | 5 | def main(): 6 | fac_dict = {str(n):factorial(n) for n in range(10)} 7 | res = 0 8 | for i in range(10,2177282): 9 | if sum([fac_dict[x] for x in str(i)]) == i: 10 | res += i 11 | return res 12 | -------------------------------------------------------------------------------- /041.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.92 ms ± 111 µs 2 | 3 | from sympy import prevprime 4 | 5 | def main(): 6 | start = 7654321 7 | while True: 8 | prevp = prevprime(start) 9 | if set(str(prevp)) == set('1234567'): 10 | return prevp 11 | else: 12 | start = prevp 13 | -------------------------------------------------------------------------------- /099.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.51 ms ± 24.9 µs 2 | 3 | from math import log10 4 | 5 | def main(): 6 | with open('data/ep99.txt') as f: 7 | pairs = [list(map(int,s.split(','))) for s in f.readlines()] 8 | log_pairs = [x[1]*log10(x[0]) for x in pairs] 9 | return log_pairs.index(max(log_pairs))+1 10 | -------------------------------------------------------------------------------- /188.py: -------------------------------------------------------------------------------- 1 | # time cost = 31.9 µs ± 78.6 ns 2 | 3 | from sympy.ntheory import totient 4 | 5 | def main(b=1777,e=1855,m=10**8): 6 | res,phis = 1,[m] 7 | while m != 1: 8 | m = totient(m) 9 | phis.append(m) 10 | for phi in reversed(phis): 11 | res = pow(b,res,phi) 12 | return res 13 | -------------------------------------------------------------------------------- /123.py: -------------------------------------------------------------------------------- 1 | # time cost = 358 ms ± 3.45 ms 2 | 3 | from sympy import nextprime 4 | 5 | def main(N=10**10): 6 | n,p = 7037,71059 7 | while True: 8 | np = nextprime(p,2) 9 | n = n + 2 10 | r = 2*n*np 11 | if r > N: 12 | return n 13 | else: 14 | p = np 15 | -------------------------------------------------------------------------------- /030.py: -------------------------------------------------------------------------------- 1 | # time cost = 761 ms ± 19.2 ms 2 | 3 | def main(): 4 | power_dict = {i:i**5 for i in range(0,10)} 5 | res = [] 6 | for i in range(10,6*9**5): 7 | sum_of_digits = sum([power_dict[int(x)] for x in str(i)]) 8 | if i == sum_of_digits: 9 | res.append(i) 10 | return sum(res) 11 | -------------------------------------------------------------------------------- /114.py: -------------------------------------------------------------------------------- 1 | # time cost = 186 ns ± 1.67 ns 2 | 3 | from functools import lru_cache 4 | 5 | @lru_cache(maxsize=None) 6 | def f(n,m): 7 | if n < m: 8 | return 1 9 | elif n == m: 10 | return 2 11 | else: 12 | return 2*f(n-1,m)-f(n-2,m)+f(n-m-1,m) 13 | 14 | def main(): 15 | return f(50,3) 16 | -------------------------------------------------------------------------------- /101.py: -------------------------------------------------------------------------------- 1 | # time cost = 22.6 µs ± 87 ns 2 | 3 | def main(): 4 | res = 0 5 | tdp = lambda x: (x**11+1)//(x+1) 6 | arr = [tdp(x) for x in range(1,11)] 7 | diff = lambda arr:[x-y for x,y in zip(arr[1:],arr[:-1])] 8 | for _ in range(10): 9 | res += sum(arr) 10 | arr = diff(arr) 11 | return res 12 | -------------------------------------------------------------------------------- /106.py: -------------------------------------------------------------------------------- 1 | # time cost = 6.35 µs ± 191 ns 2 | 3 | from math import factorial as fac 4 | 5 | def comb_num(n,k): 6 | num = fac(n)//(fac(n-k)*fac(k)) 7 | return num 8 | 9 | def main(N=12): 10 | res = 0 11 | for i in range(1,N//2+1): 12 | res += comb_num(N,2*i)*(comb_num(2*i,i)//2-comb_num(2*i,i)//(i+1)) 13 | return res 14 | -------------------------------------------------------------------------------- /135.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.21 s ± 5.8 ms 2 | 3 | from collections import defaultdict 4 | 5 | def main(N=10**6): 6 | res = defaultdict(int) 7 | for a in range(2,N+1): 8 | u = min(a,(N+a**2)//(4*a)+1) 9 | for d in range(a//4+1,u): 10 | res[a*(4*d-a)] += 1 11 | return len([k for k,v in res.items() if v==10]) 12 | -------------------------------------------------------------------------------- /067.py: -------------------------------------------------------------------------------- 1 | # time cost = 3.18ms 2 | 3 | with open('euler/ep67.txt') as f: 4 | table = [list(map(int,s.split())) for s in f.readlines()] 5 | 6 | def main(): 7 | for row in range(len(table)-1, 0, -1): 8 | for col in range(0, row): 9 | table[row-1][col] += max(table[row][col], table[row][col+1]) 10 | return table[0][0] 11 | -------------------------------------------------------------------------------- /136.py: -------------------------------------------------------------------------------- 1 | # time cost = 1min 30s ± 4.84 s 2 | 3 | from collections import defaultdict 4 | 5 | def main(N=5*10**7): 6 | res = defaultdict(int) 7 | for a in range(2,N+1): 8 | u = min(a,(N+a**2)//(4*a)+1) 9 | for d in range(a//4+1,u): 10 | res[a*(4*d-a)] += 1 11 | return len([k for k,v in res.items() if v==1]) 12 | -------------------------------------------------------------------------------- /684.py: -------------------------------------------------------------------------------- 1 | # time cost = 271 µs ± 3.42 µs 2 | 3 | def s(k,r,m=10**9+7): 4 | res = ((r+1)*(r+2)//2+5)*pow(10,k,m)-9*k-6-r 5 | return res 6 | 7 | def main(n=90): 8 | fib = [0,1] 9 | for _ in range(n-1): 10 | fib.append(sum(fib[-2:])) 11 | res = [s(*divmod(fib[i],9)) for i in range(2,n+1)] 12 | return sum(res)%(10**9+7) 13 | -------------------------------------------------------------------------------- /038.py: -------------------------------------------------------------------------------- 1 | # time cost = 360 µs ± 3.8 µs 2 | 3 | def is_pandgital(x): 4 | digits_set = set(str(x)) 5 | if digits_set == set(str(123456789)): 6 | return True 7 | return False 8 | 9 | def main(): 10 | for p in range(9487,9233,-1): 11 | ans = int(str(p) + str(p*2)) 12 | if is_pandgital(ans): 13 | return ans 14 | -------------------------------------------------------------------------------- /033.py: -------------------------------------------------------------------------------- 1 | # ans = 100, time cost = 33.7 µs 2 | 3 | from math import gcd 4 | 5 | def main(): 6 | nom,den = 1,1 7 | for i in range(1,10): 8 | for d in range(1,i): 9 | for n in range(1,d): 10 | if d*(10*n+i) == n*(10*i+d): 11 | nom *= n 12 | den *= d 13 | return den//gcd(nom,den) 14 | -------------------------------------------------------------------------------- /086.py: -------------------------------------------------------------------------------- 1 | # time cost = 3.85 s ± 3.71 ms 2 | 3 | def main(N=10**6): 4 | c,length = 0,2 5 | while c < N: 6 | length = length + 1 7 | for wph in range(3,2*length): 8 | sq = (length**2 + wph**2)**0.5 9 | if sq % 1 == 0: 10 | c += (wph//2) if length>wph else (length-(wph+1)//2+1) 11 | return length 12 | -------------------------------------------------------------------------------- /119.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.68 ms ± 16.7 µs per 2 | 3 | def main(k=30): 4 | arr = [] 5 | for b in range(2,100): 6 | for p in range(2,10): 7 | n = b ** p 8 | if n > 10: 9 | ds = sum([int(x) for x in str(n)]) 10 | if ds == b: 11 | arr.append(n) 12 | return sorted(arr)[k-1] 13 | -------------------------------------------------------------------------------- /145.py: -------------------------------------------------------------------------------- 1 | # time cost = 4.89 µs ± 19 ns 2 | 3 | def reversible_numbers(d): 4 | r = d % 4 5 | if r == 0 or r == 2: 6 | return 20*30**(d//2-1) 7 | elif r == 3: 8 | return 100*(500)**((d-3)//4) 9 | else: 10 | return 0 11 | 12 | def main(): 13 | ans = sum([reversible_numbers(x) for x in range(2,10)]) 14 | return ans 15 | -------------------------------------------------------------------------------- /032.py: -------------------------------------------------------------------------------- 1 | # time cost = 49.6 ms ± 443 µs 2 | 3 | def main(): 4 | res = set() 5 | for i in range(1,100): 6 | start = 1234 if i <=9 else 123 7 | for j in range(start,10000//i): 8 | s = str(i) + str(j) + str(i*j) 9 | if len(s) == 9 and set(s) == set('123456789'): 10 | res.add(i*j) 11 | return sum(res) 12 | -------------------------------------------------------------------------------- /045.py: -------------------------------------------------------------------------------- 1 | # time cost = 18.1 ms ± 30.1 µs 2 | 3 | from math import sqrt 4 | 5 | def is_pantagon(x): 6 | if (sqrt(24*x+1)+1) % 6 == 0: 7 | return True 8 | return False 9 | 10 | def main(): 11 | i = 144 12 | while True: 13 | h = i*(2*i-1) 14 | if is_pantagon(h): 15 | return h 16 | else: 17 | i += 1 18 | -------------------------------------------------------------------------------- /076.py: -------------------------------------------------------------------------------- 1 | # time cost = 2ms 2 | 3 | from functools import lru_cache 4 | 5 | @lru_cache(maxsize=2048) 6 | def partition(i,j): 7 | if i == 1 or j == 1: 8 | return 1 9 | elif i <= j: 10 | return partition(i,i-1)+1 11 | else: 12 | return partition(i,j-1) + partition(i-j,j) 13 | 14 | def main(N=100): 15 | return partition(N,N-1) 16 | -------------------------------------------------------------------------------- /091.py: -------------------------------------------------------------------------------- 1 | # time cost = 3.28 ms ± 59.5 µs 2 | 3 | from math import gcd 4 | 5 | def main(N=50): 6 | count = 0 7 | for x in range(1,N+1): 8 | for y in range(1,N+1): 9 | g = gcd(x,y) 10 | low = max(-g*x/y,(y-N)*g/x) 11 | up = min(g*(N-x)/y,g*y/x) 12 | count += (int(up)-int(low)) 13 | return count + 3*50**2 14 | -------------------------------------------------------------------------------- /203.py: -------------------------------------------------------------------------------- 1 | # time cost = 465 µs ± 3.78 µs 2 | 3 | def main(n=51): 4 | squares = [4,9,25,49] 5 | res = set() 6 | pt = [1,1] 7 | for r in range(n-2): 8 | pt = [x+y for x,y in zip(pt+[0],[0]+pt)] 9 | for comb in pt[:(r+3)//2+2]: 10 | if all([comb%s for s in squares]) != 0: 11 | res.add(comb) 12 | return sum(res) 13 | -------------------------------------------------------------------------------- /055.py: -------------------------------------------------------------------------------- 1 | # time cost = 64.8 ms ± 229 µs 2 | 3 | def is_lychrel(x): 4 | is_palindrome = lambda x : str(x) == str(x)[::-1] 5 | for _ in range(50): 6 | x += int(str(x)[::-1]) 7 | if is_palindrome(x): 8 | return False 9 | return True 10 | 11 | def main(): 12 | ans = len([x for x in range(1,10000) if is_lychrel(x)]) 13 | return ans 14 | -------------------------------------------------------------------------------- /686.py: -------------------------------------------------------------------------------- 1 | # time cost = 428 ms ± 4.64 ms 2 | 3 | from numba import njit 4 | 5 | @njit 6 | def nth_start_with(target=123,N=678910): 7 | n,power,k = 0,2,1 8 | while n= 10**3: 11 | power = power / 10.0 12 | if int(power) == target: 13 | n = n + 1 14 | k = k + 1 15 | return k 16 | -------------------------------------------------------------------------------- /058.py: -------------------------------------------------------------------------------- 1 | # time cost = 276 ms ± 1.39 ms 2 | 3 | from itertools import count 4 | from sympy import isprime 5 | 6 | def main(): 7 | k = 0 8 | for i in count(3,2): 9 | a = i**2 - (i-1) 10 | b = a - (i-1) 11 | c = b - (i-1) 12 | k += len([x for x in [a,b,c] if isprime(x)]) 13 | n = 2 * i - 1 14 | if k/n < 0.1: 15 | return i 16 | -------------------------------------------------------------------------------- /049.py: -------------------------------------------------------------------------------- 1 | # time cost = 3.8 ms ± 549 µs 2 | 3 | from sympy import isprime,primerange 4 | 5 | def main(): 6 | primes = primerange(1000,10000) 7 | for p in primes: 8 | if p != 1487: 9 | a = p + 3330 10 | b = p + 6660 11 | if isprime(a) and isprime(b) and set(str(p))==set(str(a))==set(str(b)): 12 | return str(p) + str(a) + str(b) 13 | -------------------------------------------------------------------------------- /062.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.65 s ± 7.11 ms 2 | 3 | from itertools import count 4 | 5 | perm = lambda x : "".join(sorted(str(x))) 6 | 7 | def cubic_perm(res): 8 | for i in count(5,1): 9 | c = perm(i**3) 10 | if len([x for x in res if x==c]) == 5: 11 | return i**3 12 | 13 | def main(): 14 | res = [perm(i**3) for i in range(5,10001)] 15 | return cubic_perm(res) 16 | -------------------------------------------------------------------------------- /019.py: -------------------------------------------------------------------------------- 1 | # time cost = 6.46 ms ± 10.9 µs 2 | 3 | import datetime as dt 4 | 5 | def count_sundays(): 6 | delta = dt.timedelta(days=1) 7 | start_date = dt.datetime(1901, 1, 1) 8 | end_date = dt.datetime(2000, 12, 31) 9 | count = 0 10 | while start_date <= end_date: 11 | if start_date.day==1 and start_date.isoweekday()==7: count+=1 12 | start_date += delta 13 | return count 14 | -------------------------------------------------------------------------------- /053.py: -------------------------------------------------------------------------------- 1 | # time cost = 997 µs ± 5.72 µs 2 | 3 | from math import factorial as fac 4 | 5 | def comb_num(n,k): 6 | num = fac(n)/(fac(n-k)*fac(k)) 7 | return num 8 | 9 | def main(): 10 | count = 0 11 | for n in range(23,101): 12 | for r in range(1,n//2): 13 | if comb_num(n,r) > 10**6: 14 | count += (n - 2*r + 1) 15 | break 16 | return count 17 | -------------------------------------------------------------------------------- /024.py: -------------------------------------------------------------------------------- 1 | # time cost = 280 ns ± 1.51 ns 2 | 3 | from math import factorial as fac 4 | from functools import lru_cache 5 | 6 | @lru_cache(maxsize=128) 7 | def nth_lexi_perm(n,s): 8 | if len(s) == 1: 9 | return s 10 | else: 11 | q,r = divmod(n,fac(len(s)-1)) 12 | return (s[q] + nth_lexi_perm(r,s[:q]+s[q+1:])) 13 | 14 | def main(n=10**6,s='0123456789'): 15 | return nth_lexi_perm(n-1,s) 16 | -------------------------------------------------------------------------------- /125.py: -------------------------------------------------------------------------------- 1 | # time cost = 224 ms ± 1.35 ms 2 | 3 | def is_palindromic(n): 4 | n = str(n) 5 | return n == n[::-1] 6 | 7 | def main(N=10**8): 8 | psos = set() 9 | u = int((N/2)**0.5) 10 | for i in range(1,u): 11 | sos = i*i 12 | while sos < N: 13 | i += 1 14 | sos += i*i 15 | if is_palindromic(sos): 16 | psos.add(sos) 17 | return sum(psos) 18 | -------------------------------------------------------------------------------- /data/ep17.csv: -------------------------------------------------------------------------------- 1 | 1,one 2 | 2,two 3 | 3,three 4 | 4,four 5 | 5,five 6 | 6,six 7 | 7,seven 8 | 8,eight 9 | 9,nine 10 | 10,ten 11 | 11,eleven 12 | 12,twelve 13 | 13,thirteen 14 | 14,fourteen 15 | 15,fifteen 16 | 16,sixteen 17 | 17,seventeen 18 | 18,eighteen 19 | 19,nineteen 20 | 20,twenty 21 | 30,thirty 22 | 40,forty 23 | 50,fifty 24 | 60,sixty 25 | 70,seventy 26 | 80,eighty 27 | 90,ninety 28 | 100,onehundred 29 | 1000,onethousand 30 | -------------------------------------------------------------------------------- /data/ep18.txt: -------------------------------------------------------------------------------- 1 | 75 2 | 95 64 3 | 17 47 82 4 | 18 35 87 10 5 | 20 04 82 47 65 6 | 19 01 23 75 03 34 7 | 88 02 77 73 07 63 67 8 | 99 65 04 28 06 16 70 92 9 | 41 41 26 56 83 40 80 70 33 10 | 41 48 72 33 47 32 37 16 94 29 11 | 53 71 44 65 25 43 91 52 97 51 14 12 | 70 11 33 28 77 73 17 78 39 68 17 57 13 | 91 71 52 38 17 14 91 43 58 50 27 29 48 14 | 63 66 04 68 89 53 67 30 73 16 69 87 40 31 15 | 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 -------------------------------------------------------------------------------- /046.py: -------------------------------------------------------------------------------- 1 | # time cost = 19.7 ms ± 199 µs 2 | 3 | from math import sqrt 4 | from sympy import isprime 5 | 6 | def nonexist(x): 7 | limit = int(sqrt((x-1)/2)) 8 | for i in range(1,limit+1): 9 | if isprime(x-2*i**2): 10 | return False 11 | return True 12 | 13 | def main(): 14 | i = 35 15 | while True: 16 | if not isprime(i) and nonexist(i): 17 | return i 18 | i += 2 19 | -------------------------------------------------------------------------------- /059.py: -------------------------------------------------------------------------------- 1 | # time cost = 668 µs ± 3.63 µs 2 | 3 | from collections import Counter 4 | 5 | def main(): 6 | with open('data/ep59.txt') as f: 7 | cipher = list(map(int,f.read().split(','))) 8 | space_ascii = ord(' ') 9 | key = [Counter(cipher[i::3]).most_common(1)[0][0] ^ space_ascii for i in range(3)] 10 | cycles = len(cipher)//3 11 | res = sum([x^y for x,y in zip(cipher,key*cycles)]) 12 | return res 13 | -------------------------------------------------------------------------------- /088.py: -------------------------------------------------------------------------------- 1 | # time cost = 163 ms ± 1.13 ms 2 | 3 | def main(): 4 | 5 | def update_min_n_arr(p,s,f,start): 6 | k = p - s + f 7 | if k < 12001: 8 | min_n_arr[k] = min(min_n_arr[k],p) 9 | for i in range(start,12000//p*2): 10 | update_min_n_arr(p*i,s+i,f+1,i) 11 | 12 | min_n_arr = [24000]*12001 13 | update_min_n_arr(1,1,1,2) 14 | return sum(set(min_n_arr[2:])) 15 | -------------------------------------------------------------------------------- /070.py: -------------------------------------------------------------------------------- 1 | # time cost = 47.4 ms ± 847 µs 2 | 3 | from sympy import primerange 4 | 5 | def main(): 6 | is_permutation = lambda x,y : "".join(sorted(str(x))) == "".join(sorted(str(y))) 7 | primes = list(primerange(2000,4000)) 8 | dt = {(x*y,(x-1)*(y-1)):((x*y)/((x-1)*(y-1))) for x in primes for y in primes if x*y<10**7} 9 | for n,phi_n in sorted(dt,key=dt.get): 10 | if is_permutation(n,phi_n): 11 | return n 12 | -------------------------------------------------------------------------------- /008.py: -------------------------------------------------------------------------------- 1 | # time cost = 4.71 ms ± 3.86 µs 2 | 3 | from functools import reduce 4 | 5 | def main(): 6 | with open('euler/ep08.txt','r') as f: 7 | data = '' 8 | for line in f.readlines(): 9 | data = data + line.strip() 10 | res = [] 11 | for i in range(988): 12 | sub = [int(x) for x in data[i:i+13]] 13 | prod = reduce(lambda x,y:x*y, sub) 14 | res.append(prod) 15 | return max(res) 16 | -------------------------------------------------------------------------------- /587.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.92 ms ± 98.5 µs 2 | 3 | from math import sqrt,asin,pi 4 | 5 | def t(n): 6 | res = (n**2+n-sqrt(2)*n**1.5)/(n**2+1) 7 | return res 8 | 9 | def area(t,n): 10 | res = 1/(2*n) - asin(1-t)/2 + (1-t)*(1-1/n)/2 11 | return res 12 | 13 | def main(N=0.001): 14 | i = 100 15 | while True: 16 | if area(t(i),i)/(1-pi/4) < N: 17 | return i 18 | else: 19 | i = i + 1 20 | -------------------------------------------------------------------------------- /data/ep79.txt: -------------------------------------------------------------------------------- 1 | 319 2 | 680 3 | 180 4 | 690 5 | 129 6 | 620 7 | 762 8 | 689 9 | 762 10 | 318 11 | 368 12 | 710 13 | 720 14 | 710 15 | 629 16 | 168 17 | 160 18 | 689 19 | 716 20 | 731 21 | 736 22 | 729 23 | 316 24 | 729 25 | 729 26 | 710 27 | 769 28 | 290 29 | 719 30 | 680 31 | 318 32 | 389 33 | 162 34 | 289 35 | 162 36 | 718 37 | 729 38 | 319 39 | 790 40 | 680 41 | 890 42 | 362 43 | 319 44 | 760 45 | 316 46 | 729 47 | 380 48 | 319 49 | 728 50 | 716 51 | -------------------------------------------------------------------------------- /206.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.58 ms ± 17.4 µs 2 | 3 | def is_concealed_square(number): 4 | seq = ['1', '2', '3', '4', '5', '6', '7', '8', '9','0'] 5 | digits = [x for x in str(number)] 6 | if len(digits) == 19 and digits[0::2] == seq: 7 | return True 8 | return False 9 | 10 | def main(n=1389026620): 11 | while True: 12 | if is_concealed_square(n**2): 13 | return n 14 | else: 15 | n = n - 10 16 | -------------------------------------------------------------------------------- /115.py: -------------------------------------------------------------------------------- 1 | # time cost = 19.8 µs ± 80.8 ns 2 | 3 | from functools import lru_cache 4 | 5 | @lru_cache(maxsize=None) 6 | def f(n,m): 7 | if n < m: 8 | return 1 9 | elif n == m: 10 | return 2 11 | else: 12 | return 2*f(n-1,m)-f(n-2,m)+f(n-m-1,m) 13 | 14 | def main(N=10**6): 15 | n = 51 16 | while True: 17 | w = f(n,50) 18 | if w > N: 19 | return n 20 | else: 21 | n += 1 22 | -------------------------------------------------------------------------------- /012.py: -------------------------------------------------------------------------------- 1 | # time cost = 127 ms ± 1.09 ms 2 | 3 | from sympy import factorint 4 | 5 | def number_of_divisor(n): 6 | d = factorint(n) 7 | res = 1 8 | for i in d: 9 | res *= (d[i]+1) if i%2==1 else d[i] 10 | return res 11 | 12 | def main(): 13 | n = 7 14 | nd,nnd = number_of_divisor(n),number_of_divisor(n+1) 15 | while nd*nnd <= 500: 16 | n += 1 17 | nd,nnd = nnd,number_of_divisor(n+1) 18 | return n*(n+1)//2 19 | -------------------------------------------------------------------------------- /021.py: -------------------------------------------------------------------------------- 1 | # time cost = 206 ms ± 2.44 ms 2 | 3 | from sympy import factorint 4 | 5 | def sum_of_divisors(n): 6 | divs = factorint(n) 7 | res = 1 8 | for p in divs: 9 | res *= (p**(divs[p]+1)-1)//(p-1) 10 | return res-n 11 | 12 | def main(n=10000): 13 | arr = [] 14 | for i in range(2,n+1): 15 | a = sum_of_divisors(i) 16 | if a != i and sum_of_divisors(a) == i: 17 | arr.append(i) 18 | return sum(arr) 19 | -------------------------------------------------------------------------------- /042.py: -------------------------------------------------------------------------------- 1 | # time cost = 5.08 ms ± 8.23 µs 2 | 3 | from math import sqrt 4 | 5 | def alphabet(word): 6 | alpha = lambda s : ord(s) - ord('A') + 1 7 | res = sum([alpha(x) for x in word]) 8 | return res 9 | 10 | def main(): 11 | with open('euler/ep42.txt','r') as f: 12 | data = f.read().replace('"',"").split(',') 13 | word_value = [alphabet(x) for x in data] 14 | res = [x for x in word_value if sqrt(1+8*x)%2==1] 15 | return len(res) 16 | -------------------------------------------------------------------------------- /118.py: -------------------------------------------------------------------------------- 1 | # time cost = 10.4 s ± 291 ms 2 | 3 | from itertools import permutations,product 4 | from sympy import isprime 5 | from sympy.utilities.iterables import multiset_partitions 6 | 7 | def main(): 8 | cnt = 0 9 | for pt in multiset_partitions([str(x) for x in range(1,10)]): 10 | for perm in product(*(permutations(x) for x in pt)): 11 | if all(isprime(int("".join(x))) for x in perm): 12 | cnt += 1 13 | return cnt 14 | -------------------------------------------------------------------------------- /231.py: -------------------------------------------------------------------------------- 1 | # time cost = 29.6s 2 | 3 | from sympy import primerange 4 | 5 | def legendre(n, p): 6 | exponent = 0 7 | while n > 0: 8 | n //= p 9 | exponent += n 10 | return exponent 11 | 12 | def main(n=2000_0000, k=1500_0000): 13 | total_sum = 0 14 | 15 | for p in primerange(1,n): 16 | exponent = legendre(n, p) - legendre(k, p) - legendre(n - k, p) 17 | total_sum += exponent * p 18 | 19 | return total_sum 20 | -------------------------------------------------------------------------------- /137.py: -------------------------------------------------------------------------------- 1 | # time cost = 13.2 µs ± 128 ns 2 | 3 | def main(N=15): 4 | arr = [] 5 | x1,y1,x2,y2,x3,y3 = -1,1,1,1,4,2 6 | u,v = 9,4 7 | while True: 8 | x1,y1 = -u+5*v,-v+u 9 | x2,y2 = u+5*v,v+u 10 | x3,y3 = 4*u+10*v,4*v+2*u 11 | target = [(x-1)//5 for x in [x1,x2,x3] if (x-1)%5==0] 12 | arr += target 13 | if len(arr) == N: 14 | return arr[-1] 15 | else: 16 | u,v = 9*u+20*v,4*u+9*v 17 | -------------------------------------------------------------------------------- /014.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.26 s ± 105 ms 2 | 3 | def main(N=10**6): 4 | d = {} 5 | for x in range(2,N): 6 | i,n = x,0 7 | while x != 1: 8 | if x < i: 9 | n = n + d[x] 10 | break 11 | elif x % 2 == 0: 12 | x = x // 2 13 | n += 1 14 | else: 15 | x = (3*x+1) // 2 16 | n += 2 17 | d[i] = n 18 | return max(d,key=d.get) 19 | -------------------------------------------------------------------------------- /023.py: -------------------------------------------------------------------------------- 1 | # time cost = 798 ms ± 1.93 ms 2 | 3 | def sigma(n): 4 | res = 0 5 | for i in range(1,int(n**0.5)+1): 6 | if n % i == 0: 7 | res += (i + n//i) if i**2 != n else i 8 | return res-n 9 | 10 | def main(): 11 | limit = 28123 12 | res,abn = 0,set() 13 | for i in range(1,limit+1): 14 | if sigma(i)>i: 15 | abn.add(i) 16 | if not any((i-x in abn) for x in abn): 17 | res += i 18 | return res 19 | -------------------------------------------------------------------------------- /090.py: -------------------------------------------------------------------------------- 1 | # timec cost = 456 ms ± 2.91 ms 2 | 3 | from itertools import combinations 4 | 5 | def main(): 6 | counter = 0 7 | sq = {1,4,6,16,25,36,46,64,81} 8 | cube_number = list(range(9)) + [6] 9 | comb = list(combinations(cube_number,6)) 10 | for i in comb: 11 | for j in comb: 12 | numbers = {e for x in i for y in j for e in (10*x+y,10*y+x)} 13 | if sq <= numbers: 14 | counter += 1 15 | return counter//2 16 | -------------------------------------------------------------------------------- /112.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.79 s ± 10.9 ms 2 | 3 | from itertools import count 4 | 5 | def is_bouncy_number(n): 6 | sort = sorted(str(n)) 7 | lst = list(str(n)) 8 | if sort == lst or sort == lst[::-1]: 9 | return False 10 | else: 11 | return True 12 | 13 | def main(pert=0.99): 14 | n = 0 15 | for i in count(100,1): 16 | if is_bouncy_number(i): 17 | n = n + 1 18 | if n/i >= pert: 19 | return i 20 | -------------------------------------------------------------------------------- /243.py: -------------------------------------------------------------------------------- 1 | # time cost = 49.4 ms ± 395 µs 2 | 3 | from sympy import prime 4 | from fractions import Fraction as f 5 | from math import prod 6 | 7 | def main(a=15499,b=94744): 8 | fy = lambda n:prod([prime(i) for i in range(1,n+1)]) 9 | fx = lambda n:prod([prime(i)-1 for i in range(1,n+1)]) 10 | n = 1 11 | while True: 12 | if f(fy(n),fx(n)) > f(b,a): 13 | break 14 | n = n + 1 15 | k = int(a/(a*fy(n)-b*fx(n)))+1 16 | return k * fy(n) 17 | -------------------------------------------------------------------------------- /022.py: -------------------------------------------------------------------------------- 1 | # time cost = 246 ms ± 608 µs 2 | 3 | def alphabet(word): 4 | alpha = lambda s : ord(s) - ord('A') + 1 5 | res = sum([alpha(x) for x in word]) 6 | return res 7 | 8 | def main(): 9 | with open('data/ep22.txt','r') as f: 10 | names = f.read().replace('"',"").split(',') 11 | sorted_names = sorted(names) 12 | name_score = lambda word : alphabet(word) * (sorted_names.index(word)+1) 13 | ans = sum([name_score(word) for word in names]) 14 | return ans 15 | -------------------------------------------------------------------------------- /080.py: -------------------------------------------------------------------------------- 1 | # time cost = 42.1 ms ± 549 µs 2 | 3 | def jarvis_sqrt_sum(n,prec=100): 4 | a,b = 5*n,5 5 | while len(str(b)) <= prec+3: 6 | if a >= b: 7 | a,b = a-b,b+10 8 | else: 9 | a,b = a*100,(b-b%10)*10+b%10 10 | return sum([int(x) for x in str(b)[:prec]]) 11 | 12 | def main(): 13 | numbers = set(range(2,100))-{x**2 for x in range(2,10)} 14 | ans = 0 15 | for i in numbers: 16 | ans += jarvis_sqrt_sum(i) 17 | return ans 18 | -------------------------------------------------------------------------------- /087.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.77 s ± 5.66 ms 2 | 3 | from itertools import product 4 | from sympy import primerange 5 | 6 | def main(N=5*10**7): 7 | ans = set() 8 | square_limit = int(N**(1/2))+1 9 | cube_limit = int(N**(1/3))+1 10 | fourth_power_limit = int(N**(1/4))+1 11 | for i,j,k in product(primerange(1,square_limit),primerange(1,cube_limit),primerange(1,fourth_power_limit)): 12 | p = i**2 + j**3 + k**4 13 | ans.add(p) 14 | return len({x for x in ans if x 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 12 | -------------------------------------------------------------------------------- /104.py: -------------------------------------------------------------------------------- 1 | # time cost = 456 ms ± 4.23 ms 2 | 3 | from math import log10 4 | 5 | def fib_top_digits(k): 6 | phi = (1+5**0.5)/2 7 | d = k*log10(phi) - 0.5*log10(5) 8 | res = int(pow(10,d-int(d)+8)) 9 | return res 10 | 11 | def main(N=10**9): 12 | is_pandigital = lambda n:set(str(n)) == set('123456789') 13 | a,b,k = 1,1,2 14 | while True: 15 | a,b = b,(a+b)%N 16 | k = k + 1 17 | if is_pandigital(b) and is_pandigital(fib_top_digits(k)): 18 | return k 19 | -------------------------------------------------------------------------------- /179.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.16 s ± 7.57 ms 2 | 3 | import numpy as np 4 | from numba import njit 5 | 6 | @njit 7 | def number_of_divisors(N): 8 | nod = np.array([0,1]+[2]*(N-1)) 9 | u = int(N**0.5) 10 | for i in range(2,u+1): 11 | nod[i*i] += 1 12 | for j in range(i+1,N//i+1): 13 | nod[i*j] += 2 14 | return nod 15 | 16 | def main(N=10**7): 17 | nod = number_of_divisors(N) 18 | diff = np.diff(nod) 19 | res = N - np.count_nonzero(diff) 20 | return res 21 | -------------------------------------------------------------------------------- /075.py: -------------------------------------------------------------------------------- 1 | # time cost = 720 ms ± 18.5 ms 2 | 3 | from math import gcd 4 | from collections import Counter 5 | 6 | def main(N=1500000): 7 | limit,arr = int((N//2)**0.5)+1,[] 8 | for m in range(2,limit): 9 | for n in range(1,m): 10 | if (m+n)%2 == 1 and gcd(m,n) == 1: 11 | p,k = 2*m*(m+n),1 12 | while k*p <= N: 13 | arr.append(k*p) 14 | k += 1 15 | c = Counter(arr) 16 | return len([x for x in c.values() if x==1]) 17 | -------------------------------------------------------------------------------- /079.py: -------------------------------------------------------------------------------- 1 | # time cost = 367 µs ± 2.94 µs 2 | 3 | import networkx as nx 4 | 5 | def get_data_from_file(file_name="data/ep79.txt"): 6 | data = set() 7 | with open(file_name) as f: 8 | for line in f.readlines(): 9 | data.add(line) 10 | return data 11 | 12 | def main(): 13 | data = get_data_from_file() 14 | G = nx.DiGraph() 15 | for i in data: 16 | G.add_edges_from([(i[0],i[1]),(i[1],i[2])]) 17 | ans = list(nx.all_topological_sorts(G))[0] 18 | return int(''.join(ans)) 19 | -------------------------------------------------------------------------------- /094.py: -------------------------------------------------------------------------------- 1 | # time cost = 25.1 µs ± 56.2 ns 2 | 3 | def main(U=10**9): 4 | x,y = 7,4 5 | p_sum = 0 6 | while True: 7 | a1,a2 = (2*x+1)/3,(2*x-1)/3 8 | s1,s2 = (a1+1)*y/2,(a2-1)*y/2 9 | p1,p2 = (3*a1+1),(3*a2-1) 10 | if (p1<=U) and (a1%1==0) and (s1%1==0): 11 | p_sum += p1 12 | if (p2<=U) and (a2%1==0) and (s2%1==0): 13 | p_sum += p2 14 | if (p1>U) and (p2>U): 15 | return p_sum 16 | else: 17 | x,y = 2*x+3*y,x+2*y 18 | -------------------------------------------------------------------------------- /027.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.34 s ± 48 ms 2 | 3 | from sympy import isprime 4 | 5 | def primes_number(a,b): 6 | f = lambda n,a,b : n**2 + a*n + b 7 | n = 0 8 | while True: 9 | if isprime(f(n,a,b)): 10 | n = n + 1 11 | else: 12 | return n 13 | 14 | def main(): 15 | res = {} 16 | for a in range(-999,1000,2): 17 | for b in [x for x in range(-1000,1001) if isprime(x)]: 18 | res[primes_number(a,b)] = (a,b) 19 | a,b = res[max(res)] 20 | return a*b 21 | -------------------------------------------------------------------------------- /072.py: -------------------------------------------------------------------------------- 1 | # time cost = 225 ns ± 0.296 ns 2 | 3 | from functools import lru_cache 4 | 5 | def number_theory_block(f,n,i=1): 6 | ans = 0 7 | while i <= n: 8 | j = n//(n//i) 9 | ans += (j-i+1)*f(n//i) 10 | i = j + 1 11 | return ans 12 | 13 | @lru_cache(maxsize=2048) 14 | def sum_of_euler_phi(n): 15 | if n == 1: 16 | return 1 17 | else: 18 | return n*(n+1)//2 - number_theory_block(sum_of_euler_phi,n,2) 19 | 20 | def main(N=10**6): 21 | return sum_of_euler_phi(N)-1 22 | -------------------------------------------------------------------------------- /085.py: -------------------------------------------------------------------------------- 1 | # time cost = 194 µs ± 1.03 µs 2 | 3 | from itertools import count 4 | 5 | def main(N=2*10**6): 6 | for dist in count(1,1): 7 | c1,c2 = N-dist,N+dist 8 | limit = int(((8*c2**0.5+1)**0.5-1)/2) + 1 9 | for y in range(1,limit): 10 | t = y*(y+1) 11 | x1 = (-t+(t**2+16*c1*t)**0.5)/(2*t) 12 | x2 = (-t+(t**2+16*c2*t)**0.5)/(2*t) 13 | if x1.is_integer(): 14 | return x1 * y 15 | if x2.is_integer(): 16 | return x2 * y 17 | -------------------------------------------------------------------------------- /026.py: -------------------------------------------------------------------------------- 1 | # time cost = 11.7 ms ± 188 µs 2 | 3 | from math import gcd 4 | from sympy import isprime 5 | 6 | def repeat_num(n): 7 | rem = [1] 8 | while True: 9 | rem.append(10*rem[-1]%n) 10 | if rem[-1] == 0: 11 | return 0 12 | elif rem[-1] in rem[:-1]: 13 | return (len(rem)-1) 14 | 15 | def main(n=1000): 16 | for i in range(n,1,-1): 17 | if gcd(10,i) == 1 and isprime(i): 18 | rep_num = repeat_num(i) 19 | if rep_num == i-1: 20 | return i 21 | -------------------------------------------------------------------------------- /064.py: -------------------------------------------------------------------------------- 1 | # time cost = 285 ms ± 3.41 ms 2 | 3 | def square_root_period(n): 4 | a0 = int(n**0.5) 5 | if a0**2 == n: 6 | return 0 7 | else: 8 | a,m,d,arr = a0,0,1,[a0] 9 | while arr[-1] != 2*a0: 10 | m = d*a - m 11 | d = (n - m**2)//d 12 | a = int((a0+m)/d) 13 | arr.append(a) 14 | return len(arr)-1 15 | 16 | def main(N=10000): 17 | c = 0 18 | for i in range(1,N+1): 19 | if square_root_period(i) % 2 == 1: 20 | c += 1 21 | return c 22 | -------------------------------------------------------------------------------- /510.py: -------------------------------------------------------------------------------- 1 | # time cost = 15.9 ms ± 254 µs 2 | 3 | from math import gcd 4 | 5 | def triplets(u,v): 6 | rc = (u*v)**2 7 | ra = ((u+v)*u)**2 8 | rb = ((u+v)*v)**2 9 | return rc,ra,rb 10 | 11 | def main(n=10**9): 12 | res = 0 13 | u = int(((1+4*n**0.5)**0.5-1)/2) 14 | for j in range(1,u+1): 15 | for i in range(1,j+1): 16 | k = 1 17 | if gcd(i,j) == 1: 18 | rc,ra,rb = triplets(i,j) 19 | k = n // rb 20 | res += k*(k+1)*(rc+ra+rb)//2 21 | return res 22 | -------------------------------------------------------------------------------- /036.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.5 ms ± 13 µs 2 | 3 | def make_palindrome(x): 4 | s = str(x) 5 | p1 = s + s[::-1] 6 | p2 = s + s[:-1][::-1] 7 | return int(p1),int(p2) 8 | 9 | def main(): 10 | is_palindrome = lambda x : x[-1]!=0 and x == x[::-1] 11 | res = 0 12 | for i in range(1,1000): 13 | p1,p2 = make_palindrome(i) 14 | p1_base2,p2_base2 = bin(p1)[2:],bin(p2)[2:] 15 | if is_palindrome(p1_base2): 16 | res = res + p1 17 | if is_palindrome(p2_base2): 18 | res = res + p2 19 | return res 20 | -------------------------------------------------------------------------------- /144.py: -------------------------------------------------------------------------------- 1 | # time cost = 420 µs ± 322 ns 2 | 3 | def next_point(x0,y0,x1,y1): 4 | i = (y1-y0)/(x1-x0) 5 | n = y1/(4*x1) 6 | r = (-i+2*n+i*n**2)/(1+2*i*n-n**2) 7 | m = y1-r*x1 8 | x_new = (-2*r*m)/(4+r**2)-x1 9 | y_new = r * x_new + m 10 | return x_new,y_new 11 | 12 | def main(): 13 | n = 1 14 | x0,y0,x1,y1 = 0,10.1,1.4,-9.6 15 | while True: 16 | x_new,y_new = next_point(x0,y0,x1,y1) 17 | if abs(x_new)<=0.01 and y_new>0: 18 | return n 19 | else: 20 | x0,y0,x1,y1 = x1,y1,x_new,y_new 21 | n += 1 22 | -------------------------------------------------------------------------------- /047.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.07 s ± 3.09 ms 2 | 3 | from sympy import primefactors,nextprime 4 | 5 | def first_int(arr): 6 | f = lambda x : len(primefactors(x)) 7 | for i in range(len(arr)-3): 8 | if f(arr[i])==4 and f(arr[i+1])==4 and f(arr[i+2])==4 and f(arr[i+3])==4: 9 | return arr[i] 10 | return False 11 | 12 | def main(): 13 | p = 211 14 | while True: 15 | nextp = nextprime(p) 16 | if (nextp - p) > 4: 17 | ans = first_int(range(p+1,nextp)) 18 | if ans != False: 19 | return ans 20 | p = nextp 21 | -------------------------------------------------------------------------------- /719.py: -------------------------------------------------------------------------------- 1 | from functools import lru_cache 2 | 3 | def ndigits(n): 4 | res = len(str(n)) 5 | return res 6 | 7 | @lru_cache(maxsize=2048) 8 | def f(n,s): 9 | if n <= s: 10 | return n == s 11 | else: 12 | for i in range(1,ndigits(n)): 13 | if f(n % (10**i),s-n//(10**i)): 14 | return True 15 | return False 16 | 17 | def main(N=10**12): 18 | res = 0 19 | for i in range(1,int(N**0.5)+1): 20 | if i%9 == 0 or i%9==1: 21 | sq = i**2 22 | if f(sq,i): 23 | res += sq 24 | return res 25 | -------------------------------------------------------------------------------- /078.py: -------------------------------------------------------------------------------- 1 | # time cost = 14.1 s ± 66.9 ms 2 | 3 | def partion_function(n): 4 | pn = [1,1] 5 | for i in range(2,n+1): 6 | k,acc = 1,0 7 | g1 = lambda k : i - k*(3*k-1)//2 8 | g2 = lambda k : i - k*(3*k+1)//2 9 | f = lambda x : pn[x] if x >= 0 else 0 10 | while g1(k) >= 0: 11 | acc += (-1)**(k+1)*(f(g1(k))+f(g2(k))) 12 | k += 1 13 | pn.append(acc) 14 | return pn 15 | 16 | def main(N=10**6): 17 | pn = partion_function(55400) 18 | for i in range(61,len(pn)): 19 | if pn[i] % N == 0: 20 | return i 21 | -------------------------------------------------------------------------------- /081.py: -------------------------------------------------------------------------------- 1 | # time cost = 8.01 ms 2 | 3 | from functools import lru_cache 4 | 5 | with open('data/ep81.txt') as f: 6 | table = [list(map(int,s.split(','))) for s in f.readlines()] 7 | 8 | @lru_cache(maxsize=2048) 9 | def min_path_sum(r,c): 10 | if r == 0 and c == 0: 11 | return table[0][0] 12 | elif r == 0 and c >= 1: 13 | return sum(table[r][:c+1]) 14 | elif c == 0 and r >= 1: 15 | return sum(x[0] for x in table[:r+1]) 16 | else: 17 | return table[r][c] + min(min_path_sum(r-1,c),min_path_sum(r,c-1)) 18 | 19 | def main(N=80): 20 | return min_path_sum(N-1,N-1) 21 | -------------------------------------------------------------------------------- /050.py: -------------------------------------------------------------------------------- 1 | # time cost = 6.7 ms ± 709 µs 2 | 3 | from sympy import isprime,primerange,nextprime 4 | 5 | def primesum_below_N(N): 6 | start = 2 7 | arr = [start] 8 | while True: 9 | nextp = nextprime(start) 10 | arr.append(nextp) 11 | if sum(arr)>=N: 12 | return arr[:-1] 13 | start = nextp 14 | 15 | def main(N=10**6): 16 | primes = primesum_below_N(N) 17 | length = len(primes) 18 | for d in range(length-1,0,-1): 19 | for start in range((length-d+1)): 20 | res = sum(primes[start:start+d]) 21 | if isprime(res): 22 | return res 23 | -------------------------------------------------------------------------------- /044.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.55 s ± 10.6 ms 2 | 3 | from math import sqrt 4 | 5 | def is_pantagon(x): 6 | if (sqrt(24*x+1)+1) % 6 == 0: 7 | return True 8 | return False 9 | 10 | def main(): 11 | pantagon = lambda n : n*(3*n-1)/2 12 | pt = [pantagon(n) for n in range(1,2000)] 13 | for i in range(1,2000): 14 | for j in range(0,i): 15 | s1,s2 = pt[i] + 2*pt[j], 2*pt[i] + pt[j] 16 | pk = pt[i] + pt[j] 17 | if is_pantagon(pk): 18 | if is_pantagon(s1): 19 | return pt[i] 20 | if is_pantagon(s2): 21 | return pt[j] 22 | -------------------------------------------------------------------------------- /083.py: -------------------------------------------------------------------------------- 1 | # time cost = 98.2 ms ± 580 µs 2 | 3 | import networkx as nx 4 | 5 | def main(): 6 | with open('data/pe083.txt') as f: 7 | matrix = [[int(x) for x in row.split(',')] for row in f.readlines()] 8 | G = nx.DiGraph() 9 | for i in range(n): 10 | for j in range(m): 11 | neighbors = [(i+x, j+y) for x, y in [(-1,0), (0,-1), (1,0), (0,1)] if 0 <= i+x < n and 0 <= j+y < m] 12 | for ix, jy in neighbors: 13 | G.add_edge((i, j), (ix, jy), weight = matrix[ix][jy]) 14 | path_length = nx.dijkstra_path_length(G, source=(0,0), target=(n-1,m-1)) 15 | return path_length + matrix[0][0] 16 | -------------------------------------------------------------------------------- /005.py: -------------------------------------------------------------------------------- 1 | # approach 1, time complexity = O(n^2) 2 | 3 | from math import gcd 4 | from functools import reduce 5 | 6 | def lcm(n): 7 | def lcm(a, b): 8 | return (a * b) // gcd(a, b) 9 | return reduce(lcm, range(1,n+1)) 10 | 11 | # approach 2, time complexity = O(nlog(n)) 12 | 13 | from sympy import primerange 14 | from math import sqrt,log,floor 15 | 16 | def main(n=20): 17 | primes = list(primerange(1,n)) 18 | i,ans = 0,1 19 | while primes[i] < sqrt(n): 20 | e = floor(log(n)/log(primes[i])) 21 | ans *= (primes[i])**e 22 | i += 1 23 | for p in primes[i:]: 24 | ans *= p 25 | return ans 26 | -------------------------------------------------------------------------------- /040.py: -------------------------------------------------------------------------------- 1 | # time cost = 36.2 µs ± 433 ns 2 | 3 | def get_k_pub(n): 4 | previous_bound = lambda k : 10**k*(k-1/9)+1/9 5 | k = 1 6 | while previous_bound(k)= 10: 14 | k,pub = get_k_pub(n) 15 | m = (n-pub) // k 16 | r = (n-pub) % k 17 | t = 10**(k-1) + m + 1 18 | dn = int(str(t)[r-1]) 19 | return dn 20 | 21 | def main(): 22 | n = [10**x for x in range(7)] 23 | ans = 1 24 | for i in n: 25 | ans *= get_digit(i) 26 | return ans 27 | -------------------------------------------------------------------------------- /082.py: -------------------------------------------------------------------------------- 1 | # time cost = 7.4 ms ± 81.7 µs 2 | 3 | def min_path_sum(matrix): 4 | n = len(matrix) 5 | cost = [matrix[i][0] for i in range(n)] 6 | for column in range(1,n): 7 | cost[0] += matrix[0][column] 8 | for row in range(1,n): 9 | cost[row] = min(cost[row], cost[row-1]) + matrix[row][column] 10 | for row in range(n-2, -1, -1): 11 | cost[row] = min(cost[row], cost[row+1] + matrix[row][column]) 12 | return min(cost) 13 | 14 | def main(): 15 | with open('data/pe082.txt') as f: 16 | matrix = [[int(x) for x in row.split(',')] for row in f.readlines()] 17 | return min_path_sum(matrix) 18 | -------------------------------------------------------------------------------- /107.py: -------------------------------------------------------------------------------- 1 | # time cost = 5.9 ms ± 75.7 µs 2 | 3 | import numpy as np 4 | import networkx as nx 5 | 6 | def convert_matrix_to_graph(): 7 | with open('data/pe107.txt') as f: 8 | network = [] 9 | for line in f.readlines(): 10 | line = line.replace('-','0').strip() 11 | network.append([int(x) for x in line.split(',')]) 12 | g = nx.from_numpy_array(np.array(network)) 13 | return g 14 | 15 | def main(): 16 | g = convert_matrix_to_graph() 17 | mst = nx.minimum_spanning_tree(g) 18 | g_weights = g.size(weight='weight') 19 | mst_weights = t.size(weight='weight') 20 | return g_weights-mst_weights 21 | -------------------------------------------------------------------------------- /116.py: -------------------------------------------------------------------------------- 1 | # approach 1, time cost = 583 ns ± 2.65 ns 2 | 3 | from functools import lru_cache 4 | 5 | @lru_cache(maxsize=None) 6 | def f(n,m): 7 | if n < m: 8 | return 1 9 | else: 10 | return f(n-m,m)+f(n-1,m) 11 | 12 | def main(n=50): 13 | return f(n,2)+f(n,3)+f(n,4)-3 14 | 15 | # approach 2, time cost = 426 µs ± 3.03 µs 16 | 17 | from scipy.special import comb 18 | 19 | def replaced_ways(n,m): 20 | w = 0 21 | for k in range(1,n//m+1): 22 | t = k + n - k*m 23 | w += comb(t,k) 24 | return w 25 | 26 | def main(n=50,length=[2,3,4]): 27 | ways = [replaced_ways(n,x) for x in length] 28 | return sum(ways) 29 | -------------------------------------------------------------------------------- /035.py: -------------------------------------------------------------------------------- 1 | # time cost = 119 ms ± 4.07 ms 2 | 3 | from sympy import sieve,isprime 4 | 5 | def rotate_set(num): 6 | s = str(num) 7 | res = {num} 8 | for i in range(len(s)): 9 | new = s[1:] + s[0] 10 | res.add(int(new)) 11 | s = new 12 | return res 13 | 14 | def main(): 15 | primes = set(sieve.primerange(100,1e6)) 16 | digitset = {'1','3','7','9'} 17 | res_set = {i for i in primes if set(str(i))<=digitset} 18 | for ele in res_set: 19 | x = rotate_set(ele) 20 | for i in x: 21 | if isprime(i) == False: 22 | res_set = res_set-x 23 | break 24 | return len(res_set)+13 25 | -------------------------------------------------------------------------------- /043.py: -------------------------------------------------------------------------------- 1 | # time cost = 5.29 s ± 7.2 ms 2 | 3 | from itertools import permutations 4 | 5 | def main(): 6 | res,ans = [],0 7 | for i in permutations(range(10),10): 8 | d_by_three = (i[2]+i[3]+i[4])%3==0 9 | d_by_seven = (10*i[4]+i[5]-i[6]*2)%7==0 10 | d_by_eleven = (i[5]-i[6]+i[7])%11==0 11 | d_by_thirteen = (100*i[6]+10*i[7]+i[8])%13==0 12 | d_by_seventeen = (100*i[7]+10*i[8]+i[9])%17==0 13 | cond = d_by_three and d_by_seven and d_by_eleven and d_by_thirteen and d_by_seventeen 14 | if i[0]!=0 and i[5]==5 and i[3]%2==0 and cond: 15 | ans += sum([x*10**y for x,y in zip(i,range(9,-1,-1))]) 16 | return ans 17 | -------------------------------------------------------------------------------- /808.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.85 s ± 86.9 ms 2 | 3 | import numpy as np 4 | 5 | def prime_sieve(n): 6 | sieve = np.ones(n//3+(n%6==2), dtype=bool) 7 | sieve[0] = False 8 | for i in range(int(n**0.5)//3+1): 9 | if sieve[i]: 10 | k=3*i+1|1 11 | sieve[((k*k)//3)::2*k] = False 12 | sieve[(k*k+4*k-2*k*(i&1))//3::2*k] = False 13 | return np.r_[2,3,((3*np.nonzero(sieve)[0]+1)|1)] 14 | 15 | def main(n=32000000): 16 | res = 0 17 | p_squares = set(p*p for p in prime_sieve(n)) 18 | for p in p_squares: 19 | rp = int(str(p)[::-1]) 20 | if p != rp and rp in p_squares: 21 | res += p 22 | return res 23 | -------------------------------------------------------------------------------- /077.py: -------------------------------------------------------------------------------- 1 | # time cost = 1 ms 2 | 3 | from sympy import primepi 4 | from functools import lru_cache 5 | 6 | primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79] 7 | 8 | @lru_cache(maxsize=2048) 9 | def ways(x,y): 10 | if x == 0: 11 | return 1 12 | elif x == 1: 13 | return 0 14 | elif y == 1: 15 | return 0 if x%2==1 else 1 16 | elif x < primes[y-1]: 17 | return ways(x,y-1) 18 | else: 19 | return ways(x,y-1) + ways(x-primes[y-1],y) 20 | 21 | def main(N=5000): 22 | i = 11 23 | while True: 24 | w = ways(i,primepi(i)) 25 | if w > N: 26 | return i 27 | else: 28 | i += 1 29 | -------------------------------------------------------------------------------- /031.py: -------------------------------------------------------------------------------- 1 | # top-down method, time cost = 88.6 ns ± 0.468 ns 2 | 3 | from functools import lru_cache 4 | 5 | @lru_cache(maxsize=128) 6 | def ways(x,y=8): 7 | coins = [1, 2, 5, 10, 20, 50, 100, 200] 8 | if x == 1 or y == 1: 9 | return 1 10 | elif x < coins[y-1]: 11 | return ways(x,y-1) 12 | else: 13 | return ways(x,y-1) + ways(x-coins[y-1],y) 14 | 15 | # bottom up method, time cost = 221 µs ± 686 ns 16 | 17 | def dp(target=200): 18 | coins = [1, 2, 5, 10, 20, 50, 100, 200] 19 | d = {i:1 for i in range(target+1)} 20 | for j in range(1,len(coins)): 21 | for i in range(coins[j],target+1): 22 | d[i] = d[i] + d[i-coins[j]] 23 | return d[target] 24 | -------------------------------------------------------------------------------- /051.py: -------------------------------------------------------------------------------- 1 | # time cost = 355 ms ± 1.51 ms 2 | 3 | from sympy import nextprime,isprime 4 | from collections import Counter 5 | 6 | def is_replacable_prime(n): 7 | s = str(n) 8 | count = Counter(s) 9 | num,d = count.most_common(1)[0] 10 | if d == 3 and num in set('012'): 11 | k = 1 12 | for j in range(int(num)+1,10): 13 | new = s.replace(num,str(j)) 14 | if isprime(int(new)): 15 | k += 1 16 | if k == 8: 17 | return True 18 | return False 19 | 20 | def main(): 21 | n = 1111 22 | while True: 23 | p = nextprime(n) 24 | if is_replacable_prime(p): 25 | return p 26 | else: 27 | n = p 28 | -------------------------------------------------------------------------------- /018.py: -------------------------------------------------------------------------------- 1 | with open('data/ep18.txt') as f: 2 | table = [list(map(int,s.split())) for s in f.readlines()] 3 | 4 | # approach 1: bottom-up method, time cost = 62.1 µs ± 5.71 µs 5 | 6 | def main(): 7 | for row in range(len(table)-1, 0, -1): 8 | for col in range(0, row): 9 | table[row-1][col] += max(table[row][col], table[row][col+1]) 10 | return table[0][0] 11 | 12 | # approach 2: top-down method, time cost = 131 ns ± 8.97 ns 13 | 14 | from functools import lru_cache 15 | 16 | @lru_cache(maxsize=128) 17 | def mps(r=0,c=0): 18 | if r == len(table)-2: 19 | return table[r][c] + max(table[r+1][c],table[r+1][c+1]) 20 | else: 21 | return table[r][c] + max(mps(r+1,c),mps(r+1,c+1)) 22 | -------------------------------------------------------------------------------- /102.py: -------------------------------------------------------------------------------- 1 | # time cost = 9.9 ms ± 310 µs 2 | 3 | def area_of_triangle(xa,ya,xb,yb,xc,yc): 4 | area = abs((xa-xc)*(yb-ya)-(xa-xb)*(yc-ya)) / 2 5 | return area 6 | 7 | def main(): 8 | counter = 0 9 | with open('ep102.txt') as f: 10 | coords = [x.strip().split(',') for x in f.readlines()] 11 | for coord in coords: 12 | xa,ya,xb,yb,xc,yc = [int(x) for x in coord] 13 | abc = area_of_triangle(xa,ya,xb,yb,xc,yc) 14 | aob = area_of_triangle(xa,ya,0,0,xb,yb) 15 | aoc = area_of_triangle(xa,ya,0,0,xc,yc) 16 | boc = area_of_triangle(xb,yb,0,0,xc,yc) 17 | if abc == aob + aoc + boc: 18 | counter += 1 19 | return counter 20 | -------------------------------------------------------------------------------- /108.py: -------------------------------------------------------------------------------- 1 | # time cost = 151 µs ± 2.16 µs 2 | 3 | from sympy import factorint 4 | from functools import reduce 5 | from operator import mul,add 6 | 7 | def prime_product(factors): 8 | primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47] 9 | powers = sorted(reduce(add,[[(k-1)//2]*v for k,v in factors.items()]),reverse=True) 10 | bases = primes[:len(powers)] 11 | res = reduce(mul,[b**p for b,p in zip(bases,powers)]) 12 | return res 13 | 14 | def main(N=1000): 15 | n = 2*N - 1 16 | primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47] 17 | while True: 18 | factors = factorint(n) 19 | if all(x in [3,5,7] for x in factors.keys()): 20 | return prime_product(factors) 21 | n += 2 22 | -------------------------------------------------------------------------------- /110.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.41 s ± 9.52 ms 2 | 3 | from sympy import factorint 4 | from functools import reduce 5 | from operator import mul,add 6 | 7 | def prime_product(factors): 8 | primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47] 9 | powers = sorted(reduce(add,[[(k-1)//2]*v for k,v in factors.items()]),reverse=True) 10 | bases = primes[:len(powers)] 11 | res = reduce(mul,[b**p for b,p in zip(bases,powers)]) 12 | return res 13 | 14 | def main(N=4*10**6): 15 | n = 2*N - 1 16 | primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47] 17 | while True: 18 | factors = factorint(n) 19 | if all(x in [3,5,7] for x in factors.keys()): 20 | return prime_product(factors) 21 | n += 2 22 | -------------------------------------------------------------------------------- /122.py: -------------------------------------------------------------------------------- 1 | # time cost = 15.1 µs ± 12.6 ns 2 | 3 | from sympy import isprime 4 | from functools import lru_cache 5 | 6 | def p(n): 7 | for i in range(1,int(n**0.5)+1): 8 | if n % i == 0 and isprime(i): 9 | return i 10 | 11 | def sigma(n): 12 | arr = [23,43,59,77,83,107,149,163,165,179] 13 | if n in arr: 14 | return 1 15 | else: 16 | return 0 17 | 18 | @lru_cache(maxsize=None) 19 | def m(k): 20 | if k == 1: 21 | return 0 22 | elif k == 2: 23 | return 1 24 | elif isprime(k): 25 | return m(k-1)+1-sigma(k) 26 | else: 27 | return min(m(k-1)+1,m(p(k))+m(k//p(k)))-sigma(k) 28 | 29 | def main(N=200): 30 | res = [m(k) for k in range(1,N+1)] 31 | return sum(res) 32 | -------------------------------------------------------------------------------- /066.py: -------------------------------------------------------------------------------- 1 | # time cost = 17.2 ms ± 50.2 µs 2 | 3 | def pell_equation(D): 4 | a0 = int(D**0.5) 5 | a1 = int(2*a0/(D-a0**2)) 6 | seq,P,Q = [a0,a1],[a0,a1*a0+1],[1,a1] 7 | m,d = a0,D-a0**2 8 | while seq[-1] != 2*a0: 9 | m = d*seq[-1]-m 10 | d = (D-m**2)//d 11 | seq.append(int((a0+m)/d)) 12 | P.append(seq[-1]*P[-1]+P[-2]) 13 | Q.append(seq[-1]*Q[-1]+Q[-2]) 14 | if (len(seq)-1) % 2 == 0: 15 | return (P[-2],Q[-2]) 16 | else: 17 | return (P[-2]**2+Q[-2]**2*D,2*P[-2]*Q[-2]) 18 | 19 | def main(N=1000): 20 | dt = {} 21 | for i in range(8,N+1): 22 | if int(i**0.5)**2 == i: 23 | continue 24 | else: 25 | dt[i] = pell_equation(i)[0] 26 | return max(dt,key=dt.get) 27 | -------------------------------------------------------------------------------- /357.py: -------------------------------------------------------------------------------- 1 | # time cost = 32.9 s ± 120 ms 2 | 3 | from sympy import isprime 4 | import numpy as np 5 | 6 | def prime_sieve(n): 7 | sieve = np.ones(n//3+(n%6==2), dtype=np.bool) 8 | sieve[0] = False 9 | for i in range(int(n**0.5)//3+1): 10 | if sieve[i]: 11 | k=3*i+1|1 12 | sieve[((k*k)//3)::2*k] = False 13 | sieve[(k*k+4*k-2*k*(i&1))//3::2*k] = False 14 | return np.r_[2,3,((3*np.nonzero(sieve)[0]+1)|1)] 15 | 16 | def is_valid(n): 17 | u = int(n**0.5) + 1 18 | for i in range(2,u): 19 | if n % i == 0: 20 | if not isprime(i+n//i): 21 | return False 22 | return True 23 | 24 | def main(N=10**8): 25 | arr = prime_sieve(N) - 1 26 | return arr[np.vectorize(is_valid)(arr)].sum() 27 | -------------------------------------------------------------------------------- /143.py: -------------------------------------------------------------------------------- 1 | # time cost = 253 ms ± 5.44 ms 2 | 3 | from math import gcd 4 | from collections import defaultdict 5 | 6 | def generate_pairs(N=120000): 7 | pairs = defaultdict(set) 8 | for i in range(2,346): 9 | for j in range(1,i): 10 | if gcd(i,j) == 1 and (i-j)%3 != 0: 11 | q,r = 2*i*j+j**2,i**2-j**2 12 | q,r = max(q,r),min(q,r) 13 | for k in range(1,N//q+1): 14 | pairs[k*q].add(k*r) 15 | return pairs 16 | 17 | def main(N=120000): 18 | res = set() 19 | pairs = generate_pairs() 20 | for k,v in pairs.items(): 21 | for q in v: 22 | if q in pairs: 23 | for r in (v & pairs[q]): 24 | res.add(k+q+r) 25 | return sum({x for x in res if x<=N}) 26 | -------------------------------------------------------------------------------- /095.py: -------------------------------------------------------------------------------- 1 | # time cost = 16.2 s ± 343 ms 2 | 3 | import numpy as np 4 | 5 | def div_sum_dict(N=10**6): 6 | arr = np.zeros(N,dtype=int) 7 | k = 1 8 | for i in range(N//2): 9 | arr[i+k::k] += k 10 | k += 1 11 | res = {i+1:arr[i] for i in range(N)} 12 | return res 13 | 14 | divsum = div_sum_dict() 15 | 16 | def amicable_chain(start): 17 | arr = [start] 18 | while True: 19 | n = divsum.get(start) 20 | if n == arr[0]: 21 | return arr 22 | elif n == 1 or n > 10**6 or n in arr: 23 | return None 24 | else: 25 | arr.append(n) 26 | start = n 27 | 28 | def main(): 29 | res = [amicable_chain(i) for i in range(10000,10**6)] 30 | return min(max([x for x in res if x!=None],key=len)) 31 | -------------------------------------------------------------------------------- /140.py: -------------------------------------------------------------------------------- 1 | # time cost = 8.72 ms ± 64.4 µs 2 | 3 | import numpy as np 4 | from sympy.solvers.diophantine.diophantine import diop_DN 5 | 6 | def pelleq_solution_generator(d,n): 7 | u,v = diop_DN(d,1)[0] 8 | uv_zero = np.mat([[u],[v]]) 9 | uv_mat = np.mat([[u,d*v],[v,u]]) 10 | xy_mat = [np.mat([[x,d*y],[y,x]]) for x,y in diop_DN(d,n)] 11 | new_mat = np.identity(2,dtype=int) 12 | while True: 13 | yield [np.abs(x @ new_mat @ uv_zero) for x in xy_mat] 14 | new_mat = new_mat @ uv_mat 15 | 16 | def main(N=30): 17 | arr = [2] 18 | for sol in pelleq_solution_generator(5,44): 19 | for ans in sol: 20 | if ans[0,0] % 5 == 2: 21 | arr.append((ans[0,0]-7)//5) 22 | if len(arr) == N: 23 | return sum(arr) 24 | -------------------------------------------------------------------------------- /121.py: -------------------------------------------------------------------------------- 1 | # approach 1, time cost = 490 µs ± 8.63 µs 2 | 3 | import sympy as sp 4 | from math import prod,factorial 5 | 6 | def main(n=15): 7 | x = sp.var('x') 8 | expr = prod([(x+i) for i in range(1,n+1)]) 9 | p = sp.Poly(expr) 10 | res = factorial(n+1)//sum(p.coeffs()[:n//2+1]) 11 | return res 12 | 13 | # approach 2, time cost = 1.01ms 14 | 15 | from fractions import Fraction as f 16 | from functools import lru_cache 17 | from math import factorial 18 | 19 | @lru_cache(maxsize=None) 20 | def prob(n,k): 21 | if k == 0: 22 | return f(1,n+1) 23 | elif n == k: 24 | return f(1,factorial(n+1)) 25 | else: 26 | return prob(n-1,k)*f(n,n+1)+prob(n-1,k-1)*f(1,n+1) 27 | 28 | def main(n=15): 29 | p = sum([prob(n,i) for i in range(n//2+1,n)]) 30 | return 1//p 31 | -------------------------------------------------------------------------------- /060.py: -------------------------------------------------------------------------------- 1 | # time cost = 2.82 s ± 83.9 ms 2 | 3 | from sympy import isprime,primerange 4 | import networkx as nx 5 | from networkx.algorithms.clique import find_cliques 6 | 7 | def is_pair_prime(x,y): 8 | conc = lambda x,y:isprime(int(str(x)+str(y))) 9 | if x == 3: 10 | return conc(x,y) and conc(y,x) 11 | else: 12 | r = x % 3 13 | return y%3==r and conc(x,y) and conc(y,x) 14 | 15 | def main(N=8400): 16 | res = [] 17 | primes = list(primerange(3,N)) 18 | index = 0 19 | for p in primes: 20 | index += 1 21 | for i in primes[index:]: 22 | if is_pair_prime(p,i): 23 | res.append((p,i)) 24 | G = nx.Graph() 25 | G.add_edges_from(res) 26 | ans = [clique for clique in find_cliques(G) if len(clique)==5] 27 | return min(map(sum,ans)) 28 | -------------------------------------------------------------------------------- /074.py: -------------------------------------------------------------------------------- 1 | # time cost = 487 ms ± 2.44 ms 2 | 3 | DT = {169:3,363601:3,1454:3,871:2,45361:2,872:2,45362:2,69:5,78:4,540:2} 4 | 5 | def digit_fact_sum(x): 6 | fac = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880] 7 | res = sum([fac[int(i)] for i in str(x)]) 8 | return res 9 | 10 | def chain_length(n): 11 | arr,m = [],n 12 | global DT 13 | while True: 14 | if n in DT: 15 | length = len(arr) + DT[n] 16 | break 17 | elif n in arr: 18 | length = len(arr) 19 | break 20 | else: 21 | arr.append(n) 22 | n = digit_fact_sum(n) 23 | DT[m] = length 24 | return length 25 | 26 | def main(N=10**6): 27 | c = 0 28 | for i in range(1,N): 29 | if chain_length(i) == 60: 30 | c += 1 31 | return c 32 | -------------------------------------------------------------------------------- /103.py: -------------------------------------------------------------------------------- 1 | # time cost = 421 ms ± 88.1 ms 2 | 3 | from itertools import combinations 4 | 5 | def is_valid(B,tup): 6 | L,S = tup 7 | if len(B) == L: 8 | return sum(B) != S 9 | else: 10 | return (sum(B)-S)*(len(B)-L)>0 11 | 12 | def is_special_sumsets(s): 13 | arr = [(1,x) for x in sorted(s)] 14 | for r in range(2,len(s)): 15 | for i in combinations(sorted(s),r): 16 | for j in arr: 17 | if not is_valid(i,j): 18 | return False 19 | arr.append((len(i),sum(i))) 20 | return True 21 | 22 | def main(arr=[11,18,19,20,22,25],n=7): 23 | optimum = set(arr[len(arr)//2:] + sorted([x+y for x in arr for y in arr])) 24 | for i in combinations(optimum,n): 25 | if is_special_sumsets(i): 26 | return "".join([str(x) for x in i]) 27 | -------------------------------------------------------------------------------- /037.py: -------------------------------------------------------------------------------- 1 | # time cosst = 76.2 ms ± 249 µs 2 | 3 | from sympy import isprime,sieve 4 | 5 | def is_twoside_truncatable_prime(x): 6 | s = str(x) 7 | for i in range(1,len(s)): 8 | if not isprime(int(s[i:])) or not isprime(int(s[:i])): 9 | return False 10 | return True 11 | 12 | def main(): 13 | num,ans = 0,0 14 | for i in sieve.primerange(10,1e6): 15 | if i < 100 and is_twoside_truncatable_prime(i): 16 | num += 1 17 | ans += i 18 | elif i>=100: 19 | s = str(i) 20 | cond1 = (s[0]=='3' or '7') and (s[-1]=='3' or '7') 21 | cond2 = set(s)<={'1','3','7','9'} 22 | if cond1 and cond2 and is_twoside_truncatable_prime(i): 23 | num += 1 24 | ans += i 25 | if num>=11: 26 | return ans 27 | -------------------------------------------------------------------------------- /105.py: -------------------------------------------------------------------------------- 1 | # time cost = 13.7 s ± 736 ms 2 | 3 | from itertools import combinations 4 | 5 | def is_valid(B,tup): 6 | L,S = tup 7 | if len(B) == L: 8 | return sum(B) != S 9 | else: 10 | return (sum(B)-S)*(len(B)-L)>0 11 | 12 | def is_special_sumsets(s): 13 | arr = [(1,x) for x in sorted(s)] 14 | for r in range(2,len(s)): 15 | for i in combinations(sorted(s),r): 16 | for j in arr: 17 | if not is_valid(i,j): 18 | return False 19 | arr.append((len(i),sum(i))) 20 | return True 21 | 22 | def main(): 23 | res = 0 24 | with open('data/pe105.txt') as f: 25 | sets = [[int(x) for x in row.strip().split(',')] for row in f.readlines()] 26 | for s in sets: 27 | if is_special_sumsets(s): 28 | res += sum(s) 29 | return res 30 | -------------------------------------------------------------------------------- /017.py: -------------------------------------------------------------------------------- 1 | # time cost = 4.31 ms ± 58.6 µs 2 | 3 | import pandas as pd 4 | 5 | def num_to_words(n): 6 | if n in words_dict.keys(): 7 | return words_dict[n] 8 | else: 9 | if 21<=n<=100: 10 | ten_digit = n//10*10 11 | digit = n%10 12 | return words_dict[ten_digit] + words_dict[digit] 13 | elif 101<=n<=1000: 14 | hundred_dict = n//100 15 | remainder = n%100 16 | if remainder == 0: 17 | return words_dict[hundred_dict] + 'hundred' 18 | else: 19 | return words_dict[hundred_dict] + 'hundredand' + num_to_words(remainder) 20 | 21 | def main(): 22 | df = pd.read_csv('data/ep17.csv',header=None) 23 | words_dict = df.set_index(0).to_dict()[1] 24 | ans = sum([len(num_to_words(x)) for x in range(1,1001)]) 25 | return ans 26 | -------------------------------------------------------------------------------- /039.py: -------------------------------------------------------------------------------- 1 | # approach1, time cost = 60.1 ms ± 626 µs 2 | 3 | def number_of_solution(p): 4 | num = 0 5 | for a in range(1,p//3): 6 | if (p**2-2*p*a)%(2*p-2*a) == 0: 7 | num += 1 8 | return num 9 | 10 | def main(n=1000): 11 | d = {p:number_of_solution(p) for p in range(2,n+1,2)} 12 | ans = max(d,key=d.get) 13 | return ans 14 | 15 | # approach 2, time cost = 192 µs ± 844 ns 16 | 17 | from math import gcd 18 | from collections import Counter 19 | 20 | def max_number_of_solution(N=1000): 21 | limit,arr = int((N//2)**0.5)+1,[] 22 | for m in range(2,limit): 23 | for n in range(1,m): 24 | if (m+n)%2 == 1 and gcd(m,n) == 1: 25 | p,k = 2*m*(m+n),1 26 | while k*p <= N: 27 | arr.append(k*p) 28 | k += 1 29 | c = Counter(arr) 30 | return c.most_common()[0][0] 31 | -------------------------------------------------------------------------------- /073.py: -------------------------------------------------------------------------------- 1 | # approach 1, time cost = 2.97 s ± 6.42 ms 2 | 3 | def farey_seq(n=12000): 4 | b, d = 3, 11999 5 | ans = 0 6 | while d!=2: 7 | ans += 1 8 | k = int((n + b) / d) 9 | b, d = d, k * d - b 10 | return ans 11 | 12 | 13 | # approach 2, time cost = 101 ns ± 0.171 ns 14 | 15 | from functools import lru_cache 16 | 17 | def number_theory_block(f,n,i=1): 18 | ans = 0 19 | while i <= n: 20 | j = n//(n//i) 21 | ans += (j-i+1)*f(n//i) 22 | i = j + 1 23 | return ans 24 | 25 | def fractions_count(n): 26 | q,r = divmod(n,6) 27 | i = 1 if r == 5 else 0 28 | ans = q*(3*q-2+r)+i 29 | return ans 30 | 31 | @lru_cache(maxsize=2048) 32 | def reduced_fractions_count(n=12000): 33 | if n == 1: 34 | return 0 35 | else: 36 | return fractions_count(n) - number_theory_block(reduced_fractions_count,n,2) 37 | -------------------------------------------------------------------------------- /160.py: -------------------------------------------------------------------------------- 1 | # It has not been completely resolved and needs to be further modified 2 | 3 | from math import prod,log,gcd 4 | from functools import lru_cache 5 | from sympy.ntheory.modular import crt 6 | 7 | def v(n): 8 | u = int(log(n,5)) 9 | return sum([n//(5**i) for i in range(1,u+1)]) 10 | 11 | @lru_cache(maxsize=None) 12 | def A(n,m=3125): 13 | if n < m: 14 | return prod([x for x in range(1,n+1) if gcd(x,5)==1]) 15 | else: 16 | q,r = divmod(n,m) 17 | return ((-1)**q*A(r)) 18 | 19 | @lru_cache(maxsize=None) 20 | def F(n,m=3125): 21 | td = {1: 1, 2: 2, 3: 6, 4: 24, 5: 12, 6: 72, 7: 504, 8: 907, 9: 1913, 10: 1913} 22 | if n <= 10: 23 | return td[n] 24 | else: 25 | q,r = divmod(n,5) 26 | Q,R = divmod(n,m) 27 | return (((F(q))*(A(n)))//(pow(5,v(n)-q-v(q),m)*pow(2,v(n)-v(q),m)))%m 28 | 29 | def main(n=10**12): 30 | res = crt([3125,32],[F(n),0]) 31 | return res[0] 32 | -------------------------------------------------------------------------------- /727.py: -------------------------------------------------------------------------------- 1 | # time cost = 764 ms ± 12.5 ms 2 | 3 | 4 | from math import sqrt,gcd 5 | from itertools import combinations 6 | from functools import reduce 7 | 8 | 9 | def cods(a,b,r): 10 | x = ((a+b)**2+(r+a)**2-(r+b)**2)/(2*a+2*b) 11 | y = sqrt((a+r)**2-x**2) 12 | return x,y 13 | 14 | def inner_point(a,b,c): 15 | xa,ya = 0,0 16 | xb,yb = a+b,0 17 | xc,yc = cods(a,b,c) 18 | x = ((b+c)*xa+(a+c)*xb+(a+b)*xc)/(2*(a+b+c)) 19 | y = ((b+c)*ya+(a+c)*yb+(a+b)*yc)/(2*(a+b+c)) 20 | return x,y 21 | 22 | def soddy_circle_radius(a,b,c): 23 | return (a*b*c)/(a*b+a*c+b*c+2*sqrt(a*b*c*(a+b+c))) 24 | 25 | def dist(a,b,c): 26 | xd,yd = inner_point(a,b,c) 27 | xe,ye = cods(a,b,soddy_circle_radius(a,b,c)) 28 | return sqrt((xd-xe)**2+(yd-ye)**2) 29 | 30 | def ggcd(numbers): 31 | return reduce(gcd,numbers) 32 | 33 | def main(): 34 | res = [x for x in combinations(range(1,101),3) if ggcd(x)==1] 35 | return sum(dist(*x) for x in res)/len(res) 36 | -------------------------------------------------------------------------------- /540.py: -------------------------------------------------------------------------------- 1 | # time cost = 35min 37s 2 | 3 | from sympy import sieve,divisors 4 | 5 | def euler_phi_sieve(n): 6 | arr = list(range(n+1)) 7 | for i in range(2,n+1): 8 | if arr[i] == i: 9 | for j in range(i,n+1,i): 10 | arr[j] -= arr[j]//i 11 | return arr 12 | 13 | def phi(m,n,premob): 14 | res = 0 15 | for i in [x for x in divisors(m) if x<=n]: 16 | res += (premob[i-1]*(n//i)) 17 | return res 18 | 19 | def main(N=3141592653589793): 20 | res = 0 21 | u = int((N/2)**0.5)+1 22 | prephi = euler_phi_sieve(u) 23 | premob = list(sieve.mobiusrange(1,u)) 24 | for m in range(2,u): 25 | if m % 2 == 0: 26 | res += prephi[m] 27 | else: 28 | res += (prephi[m]//2) 29 | for m in range(u,int(N**0.5)+1): 30 | v = int((N-m**2)**0.5) 31 | if m % 2 == 0: 32 | res += phi(m,v,premob) 33 | else: 34 | res += phi(m,v//2,premob) 35 | return res 36 | -------------------------------------------------------------------------------- /092.py: -------------------------------------------------------------------------------- 1 | # time cost = 1.95 ms ± 12.1 µs 2 | 3 | from functools import lru_cache 4 | from math import log10 5 | 6 | def is_happy(n): 7 | 8 | cycle_members = {4, 16, 37, 58, 89, 145, 42, 20} 9 | 10 | def get_next(number): 11 | total_sum = 0 12 | while number > 0: 13 | number, digit = divmod(number, 10) 14 | total_sum += digit ** 2 15 | return total_sum 16 | 17 | while n != 1 and n not in cycle_members: 18 | n = get_next(n) 19 | 20 | return n == 1 21 | 22 | @lru_cache(maxsize=None) 23 | def f(n,k): 24 | if n == k == 0: 25 | return 1 26 | elif n < 0: 27 | return 0 28 | elif n > 0 and k ==0: 29 | return 0 30 | else: 31 | return sum([f(n-i**2,k-1) for i in range(10)]) 32 | 33 | def main(N=10**7): 34 | power = int(log10(N)) 35 | u = 9**2*power 36 | happy_numbers = [i for i in range(1,u+1) if is_happy(i)] 37 | ways = sum([f(x,power) for x in happy_numbers]) 38 | return (N - ways - 1) 39 | -------------------------------------------------------------------------------- /data/ep08.txt: -------------------------------------------------------------------------------- 1 | 73167176531330624919225119674426574742355349194934 2 | 96983520312774506326239578318016984801869478851843 3 | 85861560789112949495459501737958331952853208805511 4 | 12540698747158523863050715693290963295227443043557 5 | 66896648950445244523161731856403098711121722383113 6 | 62229893423380308135336276614282806444486645238749 7 | 30358907296290491560440772390713810515859307960866 8 | 70172427121883998797908792274921901699720888093776 9 | 65727333001053367881220235421809751254540594752243 10 | 52584907711670556013604839586446706324415722155397 11 | 53697817977846174064955149290862569321978468622482 12 | 83972241375657056057490261407972968652414535100474 13 | 82166370484403199890008895243450658541227588666881 14 | 16427171479924442928230863465674813919123162824586 15 | 17866458359124566529476545682848912883142607690042 16 | 24219022671055626321111109370544217506941658960408 17 | 07198403850962455444362981230987879927244284909188 18 | 84580156166097919133875499200524063689912560717606 19 | 05886116467109405077541002256983155200055935729725 20 | 71636269561882670428252483600823257530420752963450 21 | -------------------------------------------------------------------------------- /061.py: -------------------------------------------------------------------------------- 1 | # time cost = 92.1 ms ± 1.28 ms 2 | 3 | from collections import namedtuple 4 | 5 | def poly_numbers(s,n): 6 | Pn = namedtuple('Pn','s v ftd ltd') 7 | v = (n**2*(s-2)-n*(s-4))//2 8 | ftd,ltd = v // 100, v % 100 9 | pn = Pn(s,v,ftd,ltd) 10 | return pn 11 | 12 | def poly_number_graph(): 13 | arr,graph = [],{} 14 | for s in range(3,9): 15 | for n in range(19,141): 16 | pn = poly_numbers(s,n) 17 | if 999 < pn.v < 10000 and pn.ltd>9: 18 | arr.append(pn) 19 | for pn in arr: 20 | res = [] 21 | for apn in arr: 22 | if pn.s != apn.s and pn.ltd == apn.ftd: 23 | res.append(apn) 24 | graph[pn] = res 25 | return graph 26 | 27 | def dfs(graph,types,numbers): 28 | if len(types) == 6 and numbers[-1].ltd == numbers[0].ftd: 29 | print(sum([x.v for x in numbers])) 30 | else: 31 | for pn in graph.get(numbers[-1],[]): 32 | if pn.s not in types: 33 | dfs(graph,types+[pn.s],numbers+[pn]) 34 | 35 | def main(): 36 | graph = poly_number_graph() 37 | for pn in graph: 38 | dfs(graph,[pn.s],[pn]) 39 | -------------------------------------------------------------------------------- /098.py: -------------------------------------------------------------------------------- 1 | # time cost = 60.6 ms ± 372 µs 2 | 3 | def group_by_value(d): 4 | res = {} 5 | for k,v in d.items(): 6 | res[v] = [k] if v not in res.keys() else res[v] + [k] 7 | res = {k:v for k,v in res.items() if len(v)>1} 8 | return res 9 | 10 | def get_word_pairs(): 11 | with open('data/pe098.txt') as f: 12 | words = f.read().replace('"',"").split(',') 13 | d ={x:tuple(sorted(x)) for x in words} 14 | pairs = {k:v for k,v in group_by_value(d).items() if len(k)>2 and len(v)==2} 15 | return pairs 16 | 17 | def get_square_numbers(): 18 | is_all_diff = lambda n: len(set(str(n))) == len(str(n)) 19 | squares = [i**2 for i in range(10,31622) if is_all_diff(i**2)] 20 | sq_dict = {x:len(str(x)) for x in squares} 21 | return group_by_value(sq_dict) 22 | 23 | def main(): 24 | res = [] 25 | squares = get_square_numbers() 26 | pairs = get_word_pairs() 27 | for arr in pairs.values(): 28 | dt = len(arr[0]) 29 | for sq in squares[dt]: 30 | d = {k:v for k,v in zip(arr[0],str(sq))} 31 | num = int("".join([d[x] for x in arr[1]])) 32 | if num in squares[dt]: 33 | res += [sq,num] 34 | return max(res) 35 | -------------------------------------------------------------------------------- /011.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | with open('euler/ep11.txt','r') as f: 4 | data = [map(int, s.split()) for s in f.readlines()] 5 | 6 | def grid_largest_prod(data): 7 | import numpy as np 8 | length = len(data) 9 | res = np.zeros((length,length)) 10 | right = down = down_right = left_down = 0 11 | for i in range(length): 12 | for j in range(length): 13 | right_exist = all([x=0 for x in [i,i-1,i-2,i-3]]) 16 | if right_exist: 17 | right = data[i][j]*data[i+1][j]*data[i+2][j]*data[i+3][j] 18 | if down_exist: 19 | down = data[i][j]*data[i][j+1]*data[i][j+2]*data[i][j+3] 20 | if right_exist and down_exist: 21 | down_right = data[i][j]*data[i+1][j+2]*data[i+2][j+2]*data[i+3][j+3] 22 | if left_exist and down_exist: 23 | left_down = data[i][j]*data[i-1][j+1]*data[i-2][j+2]*data[i-3][j+3] 24 | res[i][j] = max(right,down,down_right,left_down) 25 | max_res = np.max(res) 26 | return max_res 27 | 28 | print grid_largest_prod(data) 29 | -------------------------------------------------------------------------------- /675.py: -------------------------------------------------------------------------------- 1 | from collections import defaultdict 2 | 3 | def smallest_prime_factor_sieve(n): 4 | arr = list(map(lambda x: x if x%2==1 else 2,range(n+1))) 5 | for i in range(3,int(n**0.5)+1,2): 6 | if arr[i] == i: 7 | for j in range(i*i,n+1,i): 8 | if arr[j] == j: 9 | arr[j] = i 10 | return arr 11 | 12 | def prime_factorization_sieve(n): 13 | spf = smallest_prime_factor_sieve(n) 14 | def get_factorization(x): 15 | res = dict() 16 | while x != 1: 17 | p = spf[x] 18 | exp = 1 19 | x = x // p 20 | while spf[x] == p: 21 | exp += 1 22 | x = x // p 23 | res.update({p:exp}) 24 | return res 25 | return [0,1]+[get_factorization(i) for i in range(2,n+1)] 26 | 27 | def sf(factors): 28 | res = 1 29 | for power in factors.values(): 30 | res *= (2*power+1) 31 | return res 32 | 33 | def main(N=10**7): 34 | M = 1000000087 35 | res,ct = 0,defaultdict(int) 36 | factors = prime_factorization_sieve(N) 37 | for i in range(1,N): 38 | for k,v in factors[i+1].items(): 39 | ct[k] += v 40 | res += (sf(ct) % M) 41 | return res%M 42 | -------------------------------------------------------------------------------- /093.py: -------------------------------------------------------------------------------- 1 | # time cost = 12.2 s ± 42 ms 2 | 3 | from itertools import permutations,product,count,combinations 4 | 5 | def eval_arith_expression(dp,op): 6 | arr = [] 7 | expr = (dp[0],op[0],dp[1],op[1],dp[2],op[2],dp[3]) 8 | s1 = "%d%s%d%s%d%s%d" % expr 9 | s2 = "(%d%s%d)%s(%d%s%d)" % expr 10 | s3 = "(%d%s(%d%s%d))%s%d" % expr 11 | s4 = "%d%s((%d%s%d)%s%d)" % expr 12 | s5 = "%d%s(%d%s(%d%s%d))" % expr 13 | for s in [s1,s2,s3,s4,s5]: 14 | try: 15 | arr.append(eval(s)) 16 | except ZeroDivisionError: 17 | pass 18 | return arr 19 | 20 | def consecutive_integers_number(integers): 21 | c = 0 22 | numbers = [] 23 | operators = list(product(["+","-","*","/"],repeat=3)) 24 | digits_perm = list(permutations(integers,4)) 25 | for dp in digits_perm: 26 | for op in operators: 27 | numbers += eval_arith_expression(dp,op) 28 | for i in count(1): 29 | if i in numbers: 30 | c += 1 31 | else: 32 | return c 33 | 34 | def main(): 35 | d = {} 36 | for p in combinations(range(1,10),4): 37 | d[tuple(p)] = consecutive_integers_number(p) 38 | res = max(d,key=d.get) 39 | return "".join([str(x) for x in res]) 40 | -------------------------------------------------------------------------------- /data/ep11.txt: -------------------------------------------------------------------------------- 1 | 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 2 | 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 3 | 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 4 | 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 5 | 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 6 | 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 7 | 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 8 | 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 9 | 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 10 | 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 11 | 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 12 | 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 13 | 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 14 | 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 15 | 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 16 | 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 17 | 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 18 | 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 19 | 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 20 | 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48 -------------------------------------------------------------------------------- /205.py: -------------------------------------------------------------------------------- 1 | # approach 1, time cost = 101 ms ± 484 µs 2 | 3 | from itertools import product 4 | from collections import Counter 5 | 6 | def dice_values_sum_ways(sides,number): 7 | arrangement = product(range(1,sides+1),repeat=number) 8 | sum_of_values = [sum(x) for x in arrangement] 9 | c = Counter(sum_of_values) 10 | return dict(c) 11 | 12 | def main(): 13 | beats = 0 14 | total = (4**9) * (6**6) 15 | pw = dice_values_sum_ways(4,9) 16 | cw = dice_values_sum_ways(6,6) 17 | for k1,v1 in pw.items(): 18 | for k2,v2 in cw.items(): 19 | if k1 > k2: 20 | beats += (v1*v2) 21 | return round(beats/total,7) 22 | 23 | # appraoch 2, time cost = 3.88 ms ± 53.3 µs 24 | 25 | from scipy.special import comb 26 | 27 | def numbers_of_ways(m,n,p): 28 | up = int((p-m)/n)+1 29 | seq = [(-1)**j * comb(m,j) * comb(p-n*j-1,m-1) for j in range(up)] 30 | return sum(seq) 31 | 32 | def prob(): 33 | beats = 0 34 | total = (4**9) * (6**6) 35 | pw = {i:numbers_of_ways(9,4,i) for i in range(9,37)} 36 | cw = {i:numbers_of_ways(6,6,i) for i in range(6,37)} 37 | for k1,v1 in pw.items(): 38 | for k2,v2 in cw.items(): 39 | if k1 > k2: 40 | beats += (v1*v2) 41 | return round(beats/total,7) 42 | -------------------------------------------------------------------------------- /084.py: -------------------------------------------------------------------------------- 1 | # time cost = 3.52 ms ± 9.31 µs 2 | 3 | import numpy as np 4 | 5 | def get_dice_mat(): 6 | n,s = 40,4 7 | freq = {2:1,3:2,4:3,5:4,6:3,7:2,8:1} 8 | prob = {k:v/s**2 for k,v in freq.items()} 9 | mat = np.zeros((n,n)) 10 | for i in range(n): 11 | for j in range(n): 12 | mat[i,j] = prob.get((j-i)%40,0) 13 | return mat 14 | 15 | def get_card_mat(): 16 | n = 40 17 | card_mat = np.zeros((n,n)) 18 | for i in range(n): 19 | if i in [2,17,33]: 20 | card_mat[i,0] = 0.0625 21 | card_mat[i,i] = 0.875 22 | card_mat[i,10] = 0.0625 23 | elif i == 30: 24 | card_mat[i,10] = 1 25 | elif i == 7: 26 | card_mat[i,i] = 0.375 27 | card_mat[i,15] = 0.125 28 | for j in [0,4,5,10,11,12,24,39]: 29 | card_mat[i,j] = 0.0625 30 | elif i == 22: 31 | card_mat[i,i] = 0.375 32 | card_mat[i,25] = 0.125 33 | for j in [0,5,10,11,19,24,28,39]: 34 | card_mat[i,j] = 0.0625 35 | elif i == 36: 36 | card_mat[i,i] = 0.375 37 | card_mat[i,5] = 0.1875 38 | for j in [0,10,11,12,24,33,39]: 39 | card_mat[i,j] = 0.0625 40 | else: 41 | card_mat[i,i] = 1.0 42 | return card_mat 43 | 44 | def get_steady_vector(): 45 | C = get_card_mat() 46 | D = get_dice_mat() 47 | T = D @ C 48 | vec_i = np.array([1]+[0]*39) 49 | while True: 50 | vec_s = vec_i @ T 51 | if np.array_equal(vec_s,vec_i): 52 | return vec_s 53 | else: 54 | vec_i = vec_s 55 | 56 | def main(n=3): 57 | v = get_steady_vector() 58 | rank = (-v).argsort()[:n] 59 | return "".join([str(x) for x in rank]) 60 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | > *Project Euler exists to encourage, challenge, and develop the skills and enjoyment of anyone with an interest in the fascinating world of mathematics.* 2 | 3 | ## 欧拉计划是什么？ 4 | 5 | 欧拉计划(Project Euler)是一个在线解题网站，或者通俗的说是一个是刷题网站，但是相比于力扣先程序员常用的刷题网站，欧拉计划中的题目数学味要更浓，通常需要结合一定的数学与编程知识，写出适当的程序来求解问题。 6 | 7 | 就我个人的经历，欧拉计划是一个锻炼个人算法技能与数学知识的绝佳工具，在解决问题的过程中，你不仅可以了解一些以前不甚了了的数学知识，更可以将这种数学知识与算法设计结合起来，从而得到不断优化的算法。 8 | 9 | 正因为网站上的很多题目需要你花大量的时间来查询文献、学习新的数学知识并编写代码来求解，解答出一道难题通常会给你带来更强烈的满足感，就像很多人常说的，欧拉计划会让人刷题上瘾。 10 | 11 | ## 欧拉计划适合什么人？ 12 | 13 | 欧拉计划更加适合那些对数学感兴趣，尤其是对用编程来解决数学问题感兴趣的同学。就涉及的数学知识而言，欧拉计划中的大部分题目都与数论有关，所有了解一些常用的初等数论知识，如整除性质、数论函数、丢番图方程等等对解答题目会很有帮助。 14 | 15 | 欧拉计划不适合用来做准备程序员面试的刷题练习，因为欧拉计划中题目的难度通常比力扣等刷题网站中的题目要难得多，刷题非常浪费时间。其次，欧拉计划中的题目过于注重数学知识背景，而相对弱化了对编程技巧的训练，和一般公司的招聘要求是背道而驰的。 16 | 17 | 在编程语言方面，欧拉计划没有任何限制，解题时不需要提交代码，只需要提交最终结果就可以了，部分题目甚至可以使用数学技巧直接笔算解决。根据网站的提示，大部分问题应能在普通电脑上在一分钟内得到答案，如果代码的运行时间超过一分钟，则说明你的代码或者算法需要优化。 18 | 19 | ## 如何使用欧拉计划网站？ 20 | 21 | 在进入欧拉计划网站后，我们可以点击上方的Archives栏查看所有题目，在下面的列表中一页会显示五十个题目，我们可以点击列表上方或下方的序号进行翻页，或者输入题号直接到达某个题目。 22 | 23 | 我们可以根据题目的序号(ID)、已解答的人数(Solved By)和难度系数(Difficulty)来对所有题目进行降序或升序排列。一般而言，我们可以根据已解答人数降序排列，这样可以更容易解决的题目会排在前面。其次我们可以根据难度系数选择题目，难度系数低的题目要比难度系数高的题目更易解决，但这个指标的可参考性不如已解答人数指标。 24 | 25 | 我们可以点击Progress栏查看我们的解题进度，包括已经解答出的题目、现在的等级、所获的奖章、发表的文章以及解题的时间线。当我们解答出题目后，可以点击对应这个问题的论坛，查看其它人是如何解决这个问题的。 26 | 27 | ## 为什么要建立欧拉计划中文站？ 28 | 29 | 相对于力扣等刷题网站，欧拉计划的国内的知名度相对较低，一方面可能是因为定位比较小众，另一方面则是因为本土化不够，网站题目是英文，论坛上的讨论是英文，相关的参考文章也基本都是英文，对于英文不好的同学可能接受起来比较困难。 30 | 31 | 我建立[欧拉计划中文站](https://pe.metaquant.org/)，一方面是经常觉得欧拉计划上的题目设计的非常巧妙，解题过程让我充满收获，值得翻译成中文和更多人分享；另一方面，也是对我自己的解题历程、思路和代码做一些记录并与大家交流，如能启发出更好的思路和代码，则更感欣慰。 32 | 33 | 在每篇文章中，我首先将题目翻译成了中文，然后给出了我的解题思路和对应的代码，代码也可以在本仓库中找到。如果对题目翻译、解题思路以及代码有疑惑或者需要指出其中的错误的，可以在仓库中发出issue，我会尽量积极回复。 34 | 35 | ## 我自己的解题历程 36 | 37 | 我在2017年7月20日做出了第一道题，这几年来在工作之余断断续续做出了接近一百多道题目，进度相对比较缓慢。我自身也不太注重刷题的速度，我希望能够对每道题给出最优的解法，不仅效率较高，同时代码结构也能比较优雅。在解题后，我会对解题思路做一个详细的描述，希望阅读的人能够很快的理解我的思路。关于我的解题进度，这幅图片会及时更新： 38 | 39 | ![img](https://projecteuler.net/profile/sorrowise.png) 40 | 41 | 我的主力编程语言是python,而这也是欧拉工程解题语言中最常用的语言之一。python由于其优秀的设计，以及诸如列表推导式，lambda表达式等可口的语法糖，众多易用的外部库，通常只需要很少数量的代码，就可以很优雅的解决一些复杂的问题。如果可能，将来我还会尝试用其它语言，比如说julia，Haskell来解答题目。 42 | -------------------------------------------------------------------------------- /054.py: -------------------------------------------------------------------------------- 1 | # time cost = 42.1 ms ± 157 µs 2 | 3 | from collections import Counter 4 | 5 | class Card: 6 | def __init__(self,vs): 7 | d = {'T':10,'J':11,'Q':12,'K':13,'A':14} 8 | self.s = vs[1] 9 | if vs[0] not in set('TJQKA'): 10 | self.v = int(vs[0]) 11 | else: 12 | self.v = d[vs[0]] 13 | 14 | class Hand: 15 | def __init__(self,cards): 16 | self.values = [x.v for x in cards] 17 | self.suits = [x.s for x in cards] 18 | self.value_counter = Counter(self.values).most_common() 19 | self.fc = self.value_counter[0][1] 20 | self.sc = self.value_counter[1][1] 21 | self.suit_kind = len(set(self.suits)) 22 | self.ranks = sorted([x.v for x in cards],reverse=True) 23 | self.diff = set([self.ranks[:-1][i]-self.ranks[1:][i] for i in range(4)]) 24 | 25 | def categories(self): 26 | if self.suit_kind == 1 and self.diff == {1}: 27 | return ('Straight Flush',9) 28 | elif self.suit_kind == 1: 29 | return ('Flush',6) 30 | elif self.diff == {1}: 31 | return ('Straight',5) 32 | elif self.fc == 4: 33 | return ('Four of a Kind',8) 34 | elif self.fc == 3 and self.sc == 2: 35 | return ('Full House',7) 36 | elif self.fc == 3 and self.sc == 1: 37 | return ('Three of a Kind',4) 38 | elif self.fc == 2 and self.sc == 2: 39 | return ('Two Pairs',3) 40 | elif len(self.value_counter) == 4 and self.fc == 2: 41 | return ('One Pair',2) 42 | else: 43 | return ('High Card',1) 44 | 45 | def is_winner(self,hand): 46 | if self.categories()[1] > hand.categories()[1]: 47 | return True 48 | elif self.categories()[1] < hand.categories()[1]: 49 | return False 50 | elif self.categories()[1] in [8,7,4,3,2]: 51 | return self.value_counter > hand.value_counter 52 | else: 53 | return self.ranks > hand.ranks 54 | 55 | def main(): 56 | count = 0 57 | with open('data/ep54.txt') as f: 58 | hands = [line.split() for line in f] 59 | for hand in hands: 60 | p1_cards = [Card(x) for x in hand[:5]] 61 | p2_cards = [Card(x) for x in hand[5:]] 62 | p1_hand,p2_hand = Hand(p1_cards),Hand(p2_cards) 63 | if p1_hand.is_winner(p2_hand): 64 | count += 1 65 | return count 66 | -------------------------------------------------------------------------------- /096.py: -------------------------------------------------------------------------------- 1 | # time cost = 221 ms ± 2.83 ms 2 | 3 | from itertools import product 4 | 5 | def exact_cover(X, Y): 6 | X = {j: set() for j in X} 7 | for i, row in Y.items(): 8 | for j in row: 9 | X[j].add(i) 10 | return X, Y 11 | 12 | def select(X, Y, r): 13 | cols = [] 14 | for j in Y[r]: 15 | for i in X[j]: 16 | for k in Y[i]: 17 | if k != j: 18 | X[k].remove(i) 19 | cols.append(X.pop(j)) 20 | return cols 21 | 22 | def deselect(X, Y, r, cols): 23 | for j in reversed(Y[r]): 24 | X[j] = cols.pop() 25 | for i in X[j]: 26 | for k in Y[i]: 27 | if k != j: 28 | X[k].add(i) 29 | 30 | def solve(X, Y, solution): 31 | if not X: 32 | yield list(solution) 33 | else: 34 | c = min(X, key=lambda c: len(X[c])) 35 | for r in list(X[c]): 36 | solution.append(r) 37 | cols = select(X, Y, r) 38 | for s in solve(X, Y, solution): 39 | yield s 40 | deselect(X, Y, r, cols) 41 | solution.pop() 42 | 43 | def solve_sudoku(size, grid): 44 | R, C = size 45 | N = R * C 46 | X = ([("rc", rc) for rc in product(range(N), range(N))] + 47 | [("rn", rn) for rn in product(range(N), range(1, N + 1))] + 48 | [("cn", cn) for cn in product(range(N), range(1, N + 1))] + 49 | [("bn", bn) for bn in product(range(N), range(1, N + 1))]) 50 | Y = dict() 51 | for r, c, n in product(range(N), range(N), range(1, N + 1)): 52 | b = (r // R) * R + (c // C) # Box number 53 | Y[(r, c, n)] = [ 54 | ("rc", (r, c)), 55 | ("rn", (r, n)), 56 | ("cn", (c, n)), 57 | ("bn", (b, n))] 58 | X, Y = exact_cover(X, Y) 59 | for i, row in enumerate(grid): 60 | for j, n in enumerate(row): 61 | if n: 62 | select(X, Y, (i, j, n)) 63 | for solution in solve(X, Y, []): 64 | for (r, c, n) in solution: 65 | grid[r][c] = n 66 | yield grid 67 | 68 | def import_grids(): 69 | grids = [] 70 | with open('data/pe096.txt') as f: 71 | data = f.readlines() 72 | for i in range(1,492,10): 73 | grid = [[int(x) for x in row.strip()] for row in data[i:i+9]] 74 | grids.append(grid) 75 | return grids 76 | 77 | def main(): 78 | ans = 0 79 | grids = import_grids() 80 | for grid in grids: 81 | g = list(solve_sudoku((3, 3), grid))[0] 82 | ans += (g[0][0]*100+g[0][1]*10+g[0][2]) 83 | return ans 84 | -------------------------------------------------------------------------------- /data/ep13.txt: -------------------------------------------------------------------------------- 1 | 37107287533902102798797998220837590246510135740250 2 | 46376937677490009712648124896970078050417018260538 3 | 74324986199524741059474233309513058123726617309629 4 | 91942213363574161572522430563301811072406154908250 5 | 23067588207539346171171980310421047513778063246676 6 | 89261670696623633820136378418383684178734361726757 7 | 28112879812849979408065481931592621691275889832738 8 | 44274228917432520321923589422876796487670272189318 9 | 47451445736001306439091167216856844588711603153276 10 | 70386486105843025439939619828917593665686757934951 11 | 62176457141856560629502157223196586755079324193331 12 | 64906352462741904929101432445813822663347944758178 13 | 92575867718337217661963751590579239728245598838407 14 | 58203565325359399008402633568948830189458628227828 15 | 80181199384826282014278194139940567587151170094390 16 | 35398664372827112653829987240784473053190104293586 17 | 86515506006295864861532075273371959191420517255829 18 | 71693888707715466499115593487603532921714970056938 19 | 54370070576826684624621495650076471787294438377604 20 | 53282654108756828443191190634694037855217779295145 21 | 36123272525000296071075082563815656710885258350721 22 | 45876576172410976447339110607218265236877223636045 23 | 17423706905851860660448207621209813287860733969412 24 | 81142660418086830619328460811191061556940512689692 25 | 51934325451728388641918047049293215058642563049483 26 | 62467221648435076201727918039944693004732956340691 27 | 15732444386908125794514089057706229429197107928209 28 | 55037687525678773091862540744969844508330393682126 29 | 18336384825330154686196124348767681297534375946515 30 | 80386287592878490201521685554828717201219257766954 31 | 78182833757993103614740356856449095527097864797581 32 | 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-------------------------------------------------------------------------------- /data/ep89.txt: -------------------------------------------------------------------------------- 1 | MMMMDCLXXII 2 | MMDCCCLXXXIII 3 | MMMDLXVIIII 4 | MMMMDXCV 5 | DCCCLXXII 6 | MMCCCVI 7 | MMMCDLXXXVII 8 | MMMMCCXXI 9 | MMMCCXX 10 | MMMMDCCCLXXIII 11 | MMMCCXXXVII 12 | MMCCCLXXXXIX 13 | MDCCCXXIIII 14 | MMCXCVI 15 | CCXCVIII 16 | MMMCCCXXXII 17 | MDCCXXX 18 | MMMDCCCL 19 | MMMMCCLXXXVI 20 | MMDCCCXCVI 21 | MMMDCII 22 | MMMCCXII 23 | MMMMDCCCCI 24 | MMDCCCXCII 25 | MDCXX 26 | CMLXXXVII 27 | MMMXXI 28 | MMMMCCCXIV 29 | MLXXII 30 | MCCLXXVIIII 31 | MMMMCCXXXXI 32 | MMDCCCLXXII 33 | MMMMXXXI 34 | MMMDCCLXXX 35 | MMDCCCLXXIX 36 | MMMMLXXXV 37 | MCXXI 38 | MDCCCXXXVII 39 | MMCCCLXVII 40 | MCDXXXV 41 | CCXXXIII 42 | CMXX 43 | MMMCLXIV 44 | MCCCLXXXVI 45 | DCCCXCVIII 46 | MMMDCCCCXXXIV 47 | CDXVIIII 48 | MMCCXXXV 49 | MDCCCXXXII 50 | MMMMD 51 | MMDCCLXIX 52 | MMMMCCCLXXXXVI 53 | MMDCCXLII 54 | MMMDCCCVIIII 55 | DCCLXXXIIII 56 | MDCCCCXXXII 57 | MMCXXVII 58 | DCCCXXX 59 | CCLXIX 60 | MMMXI 61 | MMMMCMLXXXXVIII 62 | MMMMDLXXXVII 63 | MMMMDCCCLX 64 | MMCCLIV 65 | CMIX 66 | MMDCCCLXXXIIII 67 | CLXXXII 68 | MMCCCCXXXXV 69 | MMMMDLXXXVIIII 70 | MMMDCCCXXI 71 | MMDCCCCLXXVI 72 | MCCCCLXX 73 | MMCDLVIIII 74 | MMMDCCCLIX 75 | MMMMCCCCXIX 76 | MMMDCCCLXXV 77 | XXXI 78 | CDLXXXIII 79 | MMMCXV 80 | MMDCCLXIII 81 | MMDXXX 82 | MMMMCCCLVII 83 | MMMDCI 84 | MMMMCDLXXXIIII 85 | MMMMCCCXVI 86 | CCCLXXXVIII 87 | MMMMCML 88 | MMMMXXIV 89 | MMMCCCCXXX 90 | DCCX 91 | MMMCCLX 92 | MMDXXXIII 93 | CCCLXIII 94 | MMDCCXIII 95 | MMMCCCXLIV 96 | CLXXXXI 97 | CXVI 98 | MMMMCXXXIII 99 | CLXX 100 | DCCCXVIII 101 | MLXVII 102 | DLXXXX 103 | MMDXXI 104 | MMMMDLXXXXVIII 105 | MXXII 106 | LXI 107 | DCCCCXLIII 108 | MMMMDV 109 | MMMMXXXIV 110 | MDCCCLVIII 111 | MMMCCLXXII 112 | MMMMDCCXXXVI 113 | MMMMLXXXIX 114 | MDCCCLXXXI 115 | MMMMDCCCXV 116 | MMMMCCCCXI 117 | MMMMCCCLIII 118 | MDCCCLXXI 119 | MMCCCCXI 120 | MLXV 121 | MMCDLXII 122 | MMMMDXXXXII 123 | MMMMDCCCXL 124 | MMMMCMLVI 125 | CCLXXXIV 126 | MMMDCCLXXXVI 127 | MMCLII 128 | MMMCCCCXV 129 | MMLXXXIII 130 | MMMV 131 | MMMV 132 | DCCLXII 133 | MMDCCCCXVI 134 | MMDCXLVIII 135 | CCLIIII 136 | CCCXXV 137 | MMDCCLXXXVIIII 138 | MMMMDCLXXVIII 139 | MMMMDCCCXCI 140 | MMMMCCCXX 141 | MMCCXLV 142 | MMMDCCCLXIX 143 | MMCCLXIIII 144 | MMMDCCCXLIX 145 | MMMMCCCLXIX 146 | CMLXXXXI 147 | MCMLXXXIX 148 | MMCDLXI 149 | MMDCLXXVIII 150 | MMMMDCCLXI 151 | MCDXXV 152 | DL 153 | CCCLXXII 154 | MXVIIII 155 | MCCCCLXVIII 156 | CIII 157 | MMMDCCLXXIIII 158 | MMMDVIII 159 | MMMMCCCLXXXXVII 160 | MMDXXVII 161 | MMDCCLXXXXV 162 | MMMMCXLVI 163 | MMMDCCLXXXII 164 | MMMDXXXVI 165 | MCXXII 166 | CLI 167 | DCLXXXIX 168 | MMMCLI 169 | MDCLXIII 170 | MMMMDCCXCVII 171 | MMCCCLXXXV 172 | MMMDCXXVIII 173 | MMMCDLX 174 | MMMCMLII 175 | MMMIV 176 | MMMMDCCCLVIII 177 | MMMDLXXXVIII 178 | MCXXIV 179 | MMMMLXXVI 180 | CLXXIX 181 | MMMCCCCXXVIIII 182 | DCCLXXXV 183 | MMMDCCCVI 184 | LI 185 | CLXXXVI 186 | MMMMCCCLXXVI 187 | MCCCLXVI 188 | CCXXXIX 189 | MMDXXXXI 190 | MMDCCCXLI 191 | DCCCLXXXVIII 192 | MMMMDCCCIV 193 | MDCCCCXV 194 | MMCMVI 195 | MMMMCMLXXXXV 196 | MMDCCLVI 197 | MMMMCCXLVIII 198 | DCCCCIIII 199 | MMCCCCIII 200 | MMMDCCLXXXVIIII 201 | MDCCCLXXXXV 202 | DVII 203 | MMMV 204 | DCXXV 205 | MMDCCCXCV 206 | DCVIII 207 | MMCDLXVI 208 | MCXXVIII 209 | MDCCXCVIII 210 | MMDCLX 211 | MMMDCCLXIV 212 | MMCDLXXVII 213 | MMDLXXXIIII 214 | MMMMCCCXXII 215 | MMMDCCCXLIIII 216 | DCCCCLXVII 217 | MMMCLXXXXIII 218 | MCCXV 219 | MMMMDCXI 220 | MMMMDCLXXXXV 221 | MMMCCCLII 222 | MMCMIX 223 | MMDCCXXV 224 | MMDLXXXVI 225 | MMMMDCXXVIIII 226 | DCCCCXXXVIIII 227 | MMCCXXXIIII 228 | MMDCCLXXVIII 229 | MDCCLXVIIII 230 | MMCCLXXXV 231 | MMMMDCCCLXXXVIII 232 | MMCMXCI 233 | MDXLII 234 | MMMMDCCXIV 235 | MMMMLI 236 | DXXXXIII 237 | MMDCCXI 238 | MMMMCCLXXXIII 239 | MMMDCCCLXXIII 240 | MDCLVII 241 | MMCD 242 | MCCCXXVII 243 | MMMMDCCIIII 244 | MMMDCCXLVI 245 | MMMCLXXXVII 246 | MMMCCVIIII 247 | MCCCCLXXIX 248 | DL 249 | DCCCLXXVI 250 | MMDXCI 251 | MMMMDCCCCXXXVI 252 | MMCII 253 | MMMDCCCXXXXV 254 | MMMCDXLV 255 | MMDCXXXXIV 256 | MMD 257 | MDCCCLXXXX 258 | MMDCXLIII 259 | MMCCXXXII 260 | MMDCXXXXVIIII 261 | DCCCLXXI 262 | MDXCVIIII 263 | MMMMCCLXXVIII 264 | MDCLVIIII 265 | MMMCCCLXXXIX 266 | MDCLXXXV 267 | MDLVIII 268 | MMMMCCVII 269 | MMMMDCXIV 270 | MMMCCCLXIIII 271 | MMIIII 272 | MMMMCCCLXXIII 273 | CCIII 274 | MMMCCLV 275 | MMMDXIII 276 | MMMCCCXC 277 | MMMDCCCXXI 278 | MMMMCCCCXXXII 279 | CCCLVI 280 | MMMCCCLXXXVI 281 | MXVIIII 282 | MMMCCCCXIIII 283 | CLXVII 284 | MMMCCLXX 285 | CCCCLXIV 286 | MMXXXXII 287 | MMMMCCLXXXX 288 | MXL 289 | CCXVI 290 | CCCCLVIIII 291 | MMCCCII 292 | MCCCLVIII 293 | MMMMCCCX 294 | MCDLXXXXIV 295 | MDCCCXIII 296 | MMDCCCXL 297 | MMMMCCCXXIII 298 | DXXXIV 299 | CVI 300 | MMMMDCLXXX 301 | DCCCVII 302 | MMCMLXIIII 303 | MMMDCCCXXXIII 304 | DCCC 305 | MDIII 306 | MMCCCLXVI 307 | MMMCCCCLXXI 308 | MMDCCCCXVIII 309 | CCXXXVII 310 | CCCXXV 311 | MDCCCXII 312 | MMMCMV 313 | MMMMCMXV 314 | MMMMDCXCI 315 | DXXI 316 | MMCCXLVIIII 317 | MMMMCMLII 318 | MDLXXX 319 | MMDCLXVI 320 | CXXI 321 | MMMDCCCLIIII 322 | MMMCXXI 323 | MCCIII 324 | MMDCXXXXI 325 | CCXCII 326 | MMMMDXXXV 327 | MMMCCCLXV 328 | MMMMDLXV 329 | MMMCCCCXXXII 330 | MMMCCCVIII 331 | DCCCCLXXXXII 332 | MMCLXIV 333 | MMMMCXI 334 | MLXXXXVII 335 | MMMCDXXXVIII 336 | MDXXII 337 | MLV 338 | MMMMDLXVI 339 | MMMCXII 340 | XXXIII 341 | MMMMDCCCXXVI 342 | MMMLXVIIII 343 | MMMLX 344 | MMMCDLXVII 345 | MDCCCLVII 346 | MMCXXXVII 347 | MDCCCCXXX 348 | MMDCCCLXIII 349 | MMMMDCXLIX 350 | MMMMCMXLVIII 351 | DCCCLXXVIIII 352 | MDCCCLIII 353 | MMMCMLXI 354 | MMMMCCLXI 355 | MMDCCCLIII 356 | MMMDCCCVI 357 | MMDXXXXIX 358 | MMCLXXXXV 359 | MMDXXX 360 | MMMXIII 361 | DCLXXIX 362 | DCCLXII 363 | MMMMDCCLXVIII 364 | MDCCXXXXIII 365 | CCXXXII 366 | MMMMDCXXV 367 | MMMCCCXXVIII 368 | MDCVIII 369 | MMMCLXXXXIIII 370 | CLXXXI 371 | MDCCCCXXXIII 372 | MMMMDCXXX 373 | MMMDCXXIV 374 | MMMCCXXXVII 375 | MCCCXXXXIIII 376 | CXVIII 377 | MMDCCCCIV 378 | MMMMCDLXXV 379 | MMMDLXIV 380 | MDXCIII 381 | MCCLXXXI 382 | MMMDCCCXXIV 383 | MCXLIII 384 | MMMDCCCI 385 | MCCLXXX 386 | CCXV 387 | MMDCCLXXI 388 | MMDLXXXIII 389 | MMMMDCXVII 390 | MMMCMLXV 391 | MCLXVIII 392 | MMMMCCLXXVI 393 | MMMDCCLXVIIII 394 | MMMMDCCCIX 395 | DLXXXXIX 396 | DCCCXXII 397 | MMMMIII 398 | MMMMCCCLXXVI 399 | DCCCXCIII 400 | DXXXI 401 | MXXXIIII 402 | CCXII 403 | MMMDCCLXXXIIII 404 | MMMCXX 405 | MMMCMXXVII 406 | DCCCXXXX 407 | MMCDXXXVIIII 408 | MMMMDCCXVIII 409 | LV 410 | MMMDCCCCVI 411 | MCCCII 412 | MMCMLXVIIII 413 | MDCCXI 414 | MMMMDLXVII 415 | MMCCCCLXI 416 | MMDCCV 417 | MMMCCCXXXIIII 418 | MMMMDI 419 | MMMDCCCXCV 420 | MMDCCLXXXXI 421 | MMMDXXVI 422 | MMMDCCCLVI 423 | MMDCXXX 424 | MCCCVII 425 | MMMMCCCLXII 426 | MMMMXXV 427 | MMCMXXV 428 | MMLVI 429 | MMDXXX 430 | MMMMCVII 431 | MDC 432 | MCCIII 433 | MMMMDCC 434 | MMCCLXXV 435 | MMDCCCXXXXVI 436 | MMMMCCCLXV 437 | CDXIIII 438 | MLXIIII 439 | CCV 440 | MMMCMXXXI 441 | CCCCLXVI 442 | MDXXXII 443 | MMMMCCCLVIII 444 | MMV 445 | MMMCLII 446 | MCMLI 447 | MMDCCXX 448 | MMMMCCCCXXXVI 449 | MCCLXXXI 450 | MMMCMVI 451 | DCCXXX 452 | MMMMCCCLXV 453 | DCCCXI 454 | MMMMDCCCXIV 455 | CCCXXI 456 | MMDLXXV 457 | CCCCLXXXX 458 | MCCCLXXXXII 459 | MMDCIX 460 | DCCXLIIII 461 | DXIV 462 | MMMMCLII 463 | CDLXI 464 | MMMCXXVII 465 | MMMMDCCCCLXIII 466 | MMMDCLIIII 467 | MCCCCXXXXII 468 | MMCCCLX 469 | CCCCLIII 470 | MDCCLXXVI 471 | MCMXXIII 472 | MMMMDLXXVIII 473 | MMDCCCCLX 474 | MMMCCCLXXXX 475 | MMMCDXXVI 476 | MMMDLVIII 477 | CCCLXI 478 | MMMMDCXXII 479 | MMDCCCXXI 480 | MMDCCXIII 481 | MMMMCLXXXVI 482 | MDCCCCXXVI 483 | MDV 484 | MMDCCCCLXXVI 485 | MMMMCCXXXVII 486 | MMMDCCLXXVIIII 487 | MMMCCCCLXVII 488 | DCCXLI 489 | MMCLXXXVIII 490 | MCCXXXVI 491 | MMDCXLVIII 492 | MMMMCXXXII 493 | MMMMDCCLXVI 494 | MMMMCMLI 495 | MMMMCLXV 496 | MMMMDCCCXCIV 497 | MCCLXXVII 498 | LXXVIIII 499 | DCCLII 500 | MMMCCCXCVI 501 | MMMCLV 502 | MMDCCCXXXXVIII 503 | DCCCXV 504 | MXC 505 | MMDCCLXXXXVII 506 | MMMMCML 507 | MMDCCCLXXVIII 508 | DXXI 509 | MCCCXLI 510 | DCLXXXXI 511 | MMCCCLXXXXVIII 512 | MDCCCCLXXVIII 513 | MMMMDXXV 514 | MMMDCXXXVI 515 | MMMCMXCVII 516 | MMXVIIII 517 | MMMDCCLXXIV 518 | MMMCXXV 519 | DXXXVIII 520 | MMMMCLXVI 521 | MDXII 522 | MMCCCLXX 523 | CCLXXI 524 | DXIV 525 | MMMCLIII 526 | DLII 527 | MMMCCCXLIX 528 | MMCCCCXXVI 529 | MMDCXLIII 530 | MXXXXII 531 | CCCLXXXV 532 | MDCLXXVI 533 | MDCXII 534 | MMMCCCLXXXIII 535 | MMDCCCCLXXXII 536 | MMMMCCCLXXXV 537 | MMDCXXI 538 | DCCCXXX 539 | MMMDCCCCLII 540 | MMMDCCXXII 541 | MMMMCDXCVIII 542 | MMMCCLXVIIII 543 | MMXXV 544 | MMMMCDXIX 545 | MMMMCCCX 546 | MMMCCCCLXVI 547 | MMMMDCLXXVIIII 548 | MMMMDCXXXXIV 549 | MMMCMXII 550 | MMMMXXXIII 551 | MMMMDLXXXII 552 | DCCCLIV 553 | MDXVIIII 554 | MMMCLXXXXV 555 | CCCCXX 556 | MMDIX 557 | MMCMLXXXVIII 558 | DCCXLIII 559 | DCCLX 560 | D 561 | MCCCVII 562 | MMMMCCCLXXXIII 563 | MDCCCLXXIIII 564 | MMMDCCCCLXXXVII 565 | MMMMCCCVII 566 | MMMDCCLXXXXVI 567 | CDXXXIV 568 | MCCLXVIII 569 | MMMMDLX 570 | MMMMDXII 571 | MMMMCCCCLIIII 572 | MCMLXXXXIII 573 | MMMMDCCCIII 574 | MMDCLXXXIII 575 | MDCCCXXXXIV 576 | XXXXVII 577 | MMMDCCCXXXII 578 | MMMDCCCXLII 579 | MCXXXV 580 | MDCXXVIIII 581 | MMMCXXXXIIII 582 | MMMMCDXVII 583 | MMMDXXIII 584 | MMMMCCCCLXI 585 | DCLXXXXVIIII 586 | LXXXXI 587 | CXXXIII 588 | MCDX 589 | MCCLVII 590 | MDCXXXXII 591 | MMMCXXIV 592 | MMMMLXXXX 593 | MMDCCCCXLV 594 | MLXXX 595 | MMDCCCCLX 596 | MCDLIII 597 | MMMCCCLXVII 598 | MMMMCCCLXXIV 599 | MMMDCVIII 600 | DCCCCXXIII 601 | MMXCI 602 | MMDCCIV 603 | MMMMDCCCXXXIV 604 | CCCLXXI 605 | MCCLXXXII 606 | MCMIII 607 | CCXXXI 608 | DCCXXXVIII 609 | MMMMDCCXLVIIII 610 | MMMMCMXXXV 611 | DCCCLXXV 612 | DCCXCI 613 | MMMMDVII 614 | MMMMDCCCLXVIIII 615 | CCCXCV 616 | MMMMDCCXX 617 | MCCCCII 618 | MMMCCCXC 619 | MMMCCCII 620 | MMDCCLXXVII 621 | MMDCLIIII 622 | CCXLIII 623 | MMMDCXVIII 624 | MMMCCCIX 625 | MCXV 626 | MMCCXXV 627 | MLXXIIII 628 | MDCCXXVI 629 | MMMCCCXX 630 | MMDLXX 631 | MMCCCCVI 632 | MMDCCXX 633 | MMMMDCCCCXCV 634 | MDCCCXXXII 635 | MMMMDCCCCXXXX 636 | XCIV 637 | MMCCCCLX 638 | MMXVII 639 | MLXXI 640 | MMMDXXVIII 641 | MDCCCCII 642 | MMMCMLVII 643 | MMCLXXXXVIII 644 | MDCCCCLV 645 | MCCCCLXXIIII 646 | MCCCLII 647 | MCDXLVI 648 | MMMMDXVIII 649 | DCCLXXXIX 650 | MMMDCCLXIV 651 | MDCCCCXLIII 652 | CLXXXXV 653 | MMMMCCXXXVI 654 | MMMDCCCXXI 655 | MMMMCDLXXVII 656 | MCDLIII 657 | MMCCXLVI 658 | DCCCLV 659 | MCDLXX 660 | DCLXXVIII 661 | MMDCXXXIX 662 | MMMMDCLX 663 | MMDCCLI 664 | MMCXXXV 665 | MMMCCXII 666 | MMMMCMLXII 667 | MMMMCCV 668 | MCCCCLXIX 669 | MMMMCCIII 670 | CLXVII 671 | MCCCLXXXXIIII 672 | MMMMDCVIII 673 | MMDCCCLXI 674 | MMLXXIX 675 | CMLXIX 676 | MMDCCCXLVIIII 677 | DCLXII 678 | MMMCCCXLVII 679 | MDCCCXXXV 680 | MMMMDCCXCVI 681 | DCXXX 682 | XXVI 683 | MMLXIX 684 | MMCXI 685 | DCXXXVII 686 | MMMMCCCXXXXVIII 687 | MMMMDCLXI 688 | MMMMDCLXXIIII 689 | MMMMVIII 690 | MMMMDCCCLXII 691 | MDCXCI 692 | MMCCCXXIIII 693 | CCCCXXXXV 694 | MMDCCCXXI 695 | MCVI 696 | MMDCCLXVIII 697 | MMMMCXL 698 | MLXVIII 699 | CMXXVII 700 | CCCLV 701 | MDCCLXXXIX 702 | MMMCCCCLXV 703 | MMDCCLXII 704 | MDLXVI 705 | MMMCCCXVIII 706 | MMMMCCLXXXI 707 | MMCXXVII 708 | MMDCCCLXVIII 709 | MMMCXCII 710 | MMMMDCLVIII 711 | MMMMDCCCXXXXII 712 | MMDCCCCLXXXXVI 713 | MDCCXL 714 | MDCCLVII 715 | MMMMDCCCLXXXVI 716 | DCCXXXIII 717 | MMMMDCCCCLXXXV 718 | MMCCXXXXVIII 719 | MMMCCLXXVIII 720 | MMMDCLXXVIII 721 | DCCCI 722 | MMMMLXXXXVIIII 723 | MMMCCCCLXXII 724 | MMCLXXXVII 725 | CCLXVI 726 | MCDXLIII 727 | MMCXXVIII 728 | MDXIV 729 | CCCXCVIII 730 | CLXXVIII 731 | MMCXXXXVIIII 732 | MMMDCLXXXIV 733 | CMLVIII 734 | MCDLIX 735 | MMMMDCCCXXXII 736 | MMMMDCXXXIIII 737 | MDCXXI 738 | MMMDCXLV 739 | MCLXXVIII 740 | MCDXXII 741 | IV 742 | MCDLXXXXIII 743 | MMMMDCCLXV 744 | CCLI 745 | MMMMDCCCXXXVIII 746 | DCLXII 747 | MCCCLXVII 748 | MMMMDCCCXXXVI 749 | MMDCCXLI 750 | MLXI 751 | MMMCDLXVIII 752 | MCCCCXCIII 753 | XXXIII 754 | MMMDCLXIII 755 | MMMMDCL 756 | DCCCXXXXIIII 757 | MMDLVII 758 | DXXXVII 759 | MCCCCXXIIII 760 | MCVII 761 | MMMMDCCXL 762 | MMMMCXXXXIIII 763 | MCCCCXXIV 764 | MMCLXVIII 765 | MMXCIII 766 | MDCCLXXX 767 | MCCCLIIII 768 | MMDCLXXI 769 | MXI 770 | MCMLIV 771 | MMMCCIIII 772 | DCCLXXXVIIII 773 | MDCLIV 774 | MMMDCXIX 775 | CMLXXXI 776 | DCCLXXXVII 777 | XXV 778 | MMMXXXVI 779 | MDVIIII 780 | CLXIII 781 | MMMCDLVIIII 782 | MMCCCCVII 783 | MMMLXX 784 | MXXXXII 785 | MMMMCCCLXVIII 786 | MMDCCCXXVIII 787 | MMMMDCXXXXI 788 | MMMMDCCCXXXXV 789 | MMMXV 790 | MMMMCCXVIIII 791 | MMDCCXIIII 792 | MMMXXVII 793 | MDCCLVIIII 794 | MMCXXIIII 795 | MCCCLXXIV 796 | DCLVIII 797 | MMMLVII 798 | MMMCXLV 799 | MMXCVII 800 | MMMCCCLXXXVII 801 | MMMMCCXXII 802 | DXII 803 | MMMDLV 804 | MCCCLXXVIII 805 | MMMCLIIII 806 | MMMMCLXXXX 807 | MMMCLXXXIIII 808 | MDCXXIII 809 | MMMMCCXVI 810 | MMMMDLXXXIII 811 | MMMDXXXXIII 812 | MMMMCCCCLV 813 | MMMDLXXXI 814 | MMMCCLXXVI 815 | MMMMXX 816 | MMMMDLVI 817 | MCCCCLXXX 818 | MMMXXII 819 | MMXXII 820 | MMDCCCCXXXI 821 | MMMDXXV 822 | MMMDCLXXXVIIII 823 | MMMDLXXXXVII 824 | MDLXIIII 825 | CMXC 826 | MMMXXXVIII 827 | MDLXXXVIII 828 | MCCCLXXVI 829 | MMCDLIX 830 | MMDCCCXVIII 831 | MDCCCXXXXVI 832 | MMMMCMIV 833 | MMMMDCIIII 834 | MMCCXXXV 835 | XXXXVI 836 | MMMMCCXVII 837 | MMCCXXIV 838 | MCMLVIIII 839 | MLXXXIX 840 | MMMMLXXXIX 841 | CLXXXXIX 842 | MMMDCCCCLVIII 843 | MMMMCCLXXIII 844 | MCCCC 845 | DCCCLIX 846 | MMMCCCLXXXII 847 | MMMCCLXVIIII 848 | MCLXXXV 849 | CDLXXXVII 850 | DCVI 851 | MMX 852 | MMCCXIII 853 | MMMMDCXX 854 | MMMMXXVIII 855 | DCCCLXII 856 | MMMMCCCXLIII 857 | MMMMCLXV 858 | DXCI 859 | MMMMCLXXX 860 | MMMDCCXXXXI 861 | MMMMXXXXVI 862 | DCLX 863 | MMMCCCXI 864 | MCCLXXX 865 | MMCDLXXII 866 | DCCLXXI 867 | MMMCCCXXXVI 868 | MCCCCLXXXVIIII 869 | CDLVIII 870 | DCCLVI 871 | MMMMDCXXXVIII 872 | MMCCCLXXXIII 873 | MMMMDCCLXXV 874 | MMMXXXVI 875 | CCCLXXXXIX 876 | CV 877 | CCCCXIII 878 | CCCCXVI 879 | MDCCCLXXXIIII 880 | MMDCCLXXXII 881 | MMMMCCCCLXXXI 882 | MXXV 883 | MMCCCLXXVIIII 884 | MMMCCXII 885 | MMMMCCXXXIII 886 | MMCCCLXXXVI 887 | MMMDCCCLVIIII 888 | MCCXXXVII 889 | MDCLXXV 890 | XXXV 891 | MMDLI 892 | MMMCCXXX 893 | MMMMCXXXXV 894 | CCCCLIX 895 | MMMMDCCCLXXIII 896 | MMCCCXVII 897 | DCCCXVI 898 | MMMCCCXXXXV 899 | MDCCCCXCV 900 | CLXXXI 901 | MMMMDCCLXX 902 | MMMDCCCIII 903 | MMCLXXVII 904 | MMMDCCXXIX 905 | MMDCCCXCIIII 906 | MMMCDXXIIII 907 | MMMMXXVIII 908 | MMMMDCCCCLXVIII 909 | MDCCCXX 910 | MMMMCDXXI 911 | MMMMDLXXXIX 912 | CCXVI 913 | MDVIII 914 | MMCCLXXI 915 | MMMDCCCLXXI 916 | MMMCCCLXXVI 917 | MMCCLXI 918 | MMMMDCCCXXXIV 919 | DLXXXVI 920 | MMMMDXXXII 921 | MMMXXIIII 922 | MMMMCDIV 923 | MMMMCCCXLVIII 924 | MMMMCXXXVIII 925 | MMMCCCLXVI 926 | MDCCXVIII 927 | MMCXX 928 | CCCLIX 929 | MMMMDCCLXXII 930 | MDCCCLXXV 931 | MMMMDCCCXXIV 932 | DCCCXXXXVIII 933 | MMMDCCCCXXXVIIII 934 | MMMMCCXXXV 935 | MDCLXXXIII 936 | MMCCLXXXIV 937 | MCLXXXXIIII 938 | DXXXXIII 939 | MCCCXXXXVIII 940 | MMCLXXIX 941 | MMMMCCLXIV 942 | MXXII 943 | MMMCXIX 944 | MDCXXXVII 945 | MMDCCVI 946 | MCLXXXXVIII 947 | MMMCXVI 948 | MCCCLX 949 | MMMCDX 950 | CCLXVIIII 951 | MMMCCLX 952 | MCXXVIII 953 | LXXXII 954 | MCCCCLXXXI 955 | MMMI 956 | MMMCCCLXIV 957 | MMMCCCXXVIIII 958 | CXXXVIII 959 | MMCCCXX 960 | MMMCCXXVIIII 961 | MCCLXVI 962 | MMMCCCCXXXXVI 963 | MMDCCXCIX 964 | MCMLXXI 965 | MMCCLXVIII 966 | CDLXXXXIII 967 | MMMMDCCXXII 968 | MMMMDCCLXXXVII 969 | MMMDCCLIV 970 | MMCCLXIII 971 | MDXXXVII 972 | DCCXXXIIII 973 | MCII 974 | MMMDCCCLXXI 975 | MMMLXXIII 976 | MDCCCLIII 977 | MMXXXVIII 978 | MDCCXVIIII 979 | MDCCCCXXXVII 980 | MMCCCXVI 981 | MCMXXII 982 | MMMCCCLVIII 983 | MMMMDCCCXX 984 | MCXXIII 985 | MMMDLXI 986 | MMMMDXXII 987 | MDCCCX 988 | MMDXCVIIII 989 | MMMDCCCCVIII 990 | MMMMDCCCCXXXXVI 991 | MMDCCCXXXV 992 | MMCXCIV 993 | MCMLXXXXIII 994 | MMMCCCLXXVI 995 | MMMMDCLXXXV 996 | CMLXIX 997 | DCXCII 998 | MMXXVIII 999 | MMMMCCCXXX 1000 | XXXXVIIII -------------------------------------------------------------------------------- /data/ep99.txt: -------------------------------------------------------------------------------- 1 | 519432,525806 2 | 632382,518061 3 | 78864,613712 4 | 466580,530130 5 | 780495,510032 6 | 525895,525320 7 | 15991,714883 8 | 960290,502358 9 | 760018,511029 10 | 166800,575487 11 | 210884,564478 12 | 555151,523163 13 | 681146,515199 14 | 563395,522587 15 | 738250,512126 16 | 923525,503780 17 | 595148,520429 18 | 177108,572629 19 | 750923,511482 20 | 440902,532446 21 | 881418,505504 22 | 422489,534197 23 | 979858,501616 24 | 685893,514935 25 | 747477,511661 26 | 167214,575367 27 | 234140,559696 28 | 940238,503122 29 | 728969,512609 30 | 232083,560102 31 | 900971,504694 32 | 688801,514772 33 | 189664,569402 34 | 891022,505104 35 | 445689,531996 36 | 119570,591871 37 | 821453,508118 38 | 371084,539600 39 | 911745,504251 40 | 623655,518600 41 | 144361,582486 42 | 352442,541775 43 | 420726,534367 44 | 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672276,515708 998 | 325361,545187 999 | 172115,573985 1000 | 13846,725685 -------------------------------------------------------------------------------- /data/ep81.txt: -------------------------------------------------------------------------------- 1 | 4445,2697,5115,718,2209,2212,654,4348,3079,6821,7668,3276,8874,4190,3785,2752,9473,7817,9137,496,7338,3434,7152,4355,4552,7917,7827,2460,2350,691,3514,5880,3145,7633,7199,3783,5066,7487,3285,1084,8985,760,872,8609,8051,1134,9536,5750,9716,9371,7619,5617,275,9721,2997,2698,1887,8825,6372,3014,2113,7122,7050,6775,5948,2758,1219,3539,348,7989,2735,9862,1263,8089,6401,9462,3168,2758,3748,5870 2 | 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510,3556,5377,1406,5721,4946,2635,7847,4251,8293,8281,6351,4912,287,2870,3380,3948,5322,3840,4738,9563,1906,6298,3234,8959,1562,6297,8835,7861,239,6618,1322,2553,2213,5053,5446,4402,6500,5182,8585,6900,5756,9661,903,5186,7687,5998,7997,8081,8955,4835,6069,2621,1581,732,9564,1082,1853,5442,1342,520,1737,3703,5321,4793,2776,1508,1647,9101,2499,6891,4336,7012,3329,3212,1442,9993,3988,4930,7706 9 | 9444,3401,5891,9716,1228,7107,109,3563,2700,6161,5039,4992,2242,8541,7372,2067,1294,3058,1306,320,8881,5756,9326,411,8650,8824,5495,8282,8397,2000,1228,7817,2099,6473,3571,5994,4447,1299,5991,543,7874,2297,1651,101,2093,3463,9189,6872,6118,872,1008,1779,2805,9084,4048,2123,5877,55,3075,1737,9459,4535,6453,3644,108,5982,4437,5213,1340,6967,9943,5815,669,8074,1838,6979,9132,9315,715,5048 10 | 3327,4030,7177,6336,9933,5296,2621,4785,2755,4832,2512,2118,2244,4407,2170,499,7532,9742,5051,7687,970,6924,3527,4694,5145,1306,2165,5940,2425,8910,3513,1909,6983,346,6377,4304,9330,7203,6605,3709,3346,970,369,9737,5811,4427,9939,3693,8436,5566,1977,3728,2399,3985,8303,2492,5366,9802,9193,7296,1033,5060,9144,2766,1151,7629,5169,5995,58,7619,7565,4208,1713,6279,3209,4908,9224,7409,1325,8540 11 | 6882,1265,1775,3648,4690,959,5837,4520,5394,1378,9485,1360,4018,578,9174,2932,9890,3696,116,1723,1178,9355,7063,1594,1918,8574,7594,7942,1547,6166,7888,354,6932,4651,1010,7759,6905,661,7689,6092,9292,3845,9605,8443,443,8275,5163,7720,7265,6356,7779,1798,1754,5225,6661,1180,8024,5666,88,9153,1840,3508,1193,4445,2648,3538,6243,6375,8107,5902,5423,2520,1122,5015,6113,8859,9370,966,8673,2442 12 | 7338,3423,4723,6533,848,8041,7921,8277,4094,5368,7252,8852,9166,2250,2801,6125,8093,5738,4038,9808,7359,9494,601,9116,4946,2702,5573,2921,9862,1462,1269,2410,4171,2709,7508,6241,7522,615,2407,8200,4189,5492,5649,7353,2590,5203,4274,710,7329,9063,956,8371,3722,4253,4785,1194,4828,4717,4548,940,983,2575,4511,2938,1827,2027,2700,1236,841,5760,1680,6260,2373,3851,1841,4968,1172,5179,7175,3509 13 | 4420,1327,3560,2376,6260,2988,9537,4064,4829,8872,9598,3228,1792,7118,9962,9336,4368,9189,6857,1829,9863,6287,7303,7769,2707,8257,2391,2009,3975,4993,3068,9835,3427,341,8412,2134,4034,8511,6421,3041,9012,2983,7289,100,1355,7904,9186,6920,5856,2008,6545,8331,3655,5011,839,8041,9255,6524,3862,8788,62,7455,3513,5003,8413,3918,2076,7960,6108,3638,6999,3436,1441,4858,4181,1866,8731,7745,3744,1000 14 | 356,8296,8325,1058,1277,4743,3850,2388,6079,6462,2815,5620,8495,5378,75,4324,3441,9870,1113,165,1544,1179,2834,562,6176,2313,6836,8839,2986,9454,5199,6888,1927,5866,8760,320,1792,8296,7898,6121,7241,5886,5814,2815,8336,1576,4314,3109,2572,6011,2086,9061,9403,3947,5487,9731,7281,3159,1819,1334,3181,5844,5114,9898,4634,2531,4412,6430,4262,8482,4546,4555,6804,2607,9421,686,8649,8860,7794,6672 15 | 9870,152,1558,4963,8750,4754,6521,6256,8818,5208,5691,9659,8377,9725,5050,5343,2539,6101,1844,9700,7750,8114,5357,3001,8830,4438,199,9545,8496,43,2078,327,9397,106,6090,8181,8646,6414,7499,5450,4850,6273,5014,4131,7639,3913,6571,8534,9703,4391,7618,445,1320,5,1894,6771,7383,9191,4708,9706,6939,7937,8726,9382,5216,3685,2247,9029,8154,1738,9984,2626,9438,4167,6351,5060,29,1218,1239,4785 16 | 192,5213,8297,8974,4032,6966,5717,1179,6523,4679,9513,1481,3041,5355,9303,9154,1389,8702,6589,7818,6336,3539,5538,3094,6646,6702,6266,2759,4608,4452,617,9406,8064,6379,444,5602,4950,1810,8391,1536,316,8714,1178,5182,5863,5110,5372,4954,1978,2971,5680,4863,2255,4630,5723,2168,538,1692,1319,7540,440,6430,6266,7712,7385,5702,620,641,3136,7350,1478,3155,2820,9109,6261,1122,4470,14,8493,2095 17 | 1046,4301,6082,474,4974,7822,2102,5161,5172,6946,8074,9716,6586,9962,9749,5015,2217,995,5388,4402,7652,6399,6539,1349,8101,3677,1328,9612,7922,2879,231,5887,2655,508,4357,4964,3554,5930,6236,7384,4614,280,3093,9600,2110,7863,2631,6626,6620,68,1311,7198,7561,1768,5139,1431,221,230,2940,968,5283,6517,2146,1646,869,9402,7068,8645,7058,1765,9690,4152,2926,9504,2939,7504,6074,2944,6470,7859 18 | 4659,736,4951,9344,1927,6271,8837,8711,3241,6579,7660,5499,5616,3743,5801,4682,9748,8796,779,1833,4549,8138,4026,775,4170,2432,4174,3741,7540,8017,2833,4027,396,811,2871,1150,9809,2719,9199,8504,1224,540,2051,3519,7982,7367,2761,308,3358,6505,2050,4836,5090,7864,805,2566,2409,6876,3361,8622,5572,5895,3280,441,7893,8105,1634,2929,274,3926,7786,6123,8233,9921,2674,5340,1445,203,4585,3837 19 | 5759,338,7444,7968,7742,3755,1591,4839,1705,650,7061,2461,9230,9391,9373,2413,1213,431,7801,4994,2380,2703,6161,6878,8331,2538,6093,1275,5065,5062,2839,582,1014,8109,3525,1544,1569,8622,7944,2905,6120,1564,1839,5570,7579,1318,2677,5257,4418,5601,7935,7656,5192,1864,5886,6083,5580,6202,8869,1636,7907,4759,9082,5854,3185,7631,6854,5872,5632,5280,1431,2077,9717,7431,4256,8261,9680,4487,4752,4286 20 | 1571,1428,8599,1230,7772,4221,8523,9049,4042,8726,7567,6736,9033,2104,4879,4967,6334,6716,3994,1269,8995,6539,3610,7667,6560,6065,874,848,4597,1711,7161,4811,6734,5723,6356,6026,9183,2586,5636,1092,7779,7923,8747,6887,7505,9909,1792,3233,4526,3176,1508,8043,720,5212,6046,4988,709,5277,8256,3642,1391,5803,1468,2145,3970,6301,7767,2359,8487,9771,8785,7520,856,1605,8972,2402,2386,991,1383,5963 21 | 1822,4824,5957,6511,9868,4113,301,9353,6228,2881,2966,6956,9124,9574,9233,1601,7340,973,9396,540,4747,8590,9535,3650,7333,7583,4806,3593,2738,8157,5215,8472,2284,9473,3906,6982,5505,6053,7936,6074,7179,6688,1564,1103,6860,5839,2022,8490,910,7551,7805,881,7024,1855,9448,4790,1274,3672,2810,774,7623,4223,4850,6071,9975,4935,1915,9771,6690,3846,517,463,7624,4511,614,6394,3661,7409,1395,8127 22 | 8738,3850,9555,3695,4383,2378,87,6256,6740,7682,9546,4255,6105,2000,1851,4073,8957,9022,6547,5189,2487,303,9602,7833,1628,4163,6678,3144,8589,7096,8913,5823,4890,7679,1212,9294,5884,2972,3012,3359,7794,7428,1579,4350,7246,4301,7779,7790,3294,9547,4367,3549,1958,8237,6758,3497,3250,3456,6318,1663,708,7714,6143,6890,3428,6853,9334,7992,591,6449,9786,1412,8500,722,5468,1371,108,3939,4199,2535 23 | 7047,4323,1934,5163,4166,461,3544,2767,6554,203,6098,2265,9078,2075,4644,6641,8412,9183,487,101,7566,5622,1975,5726,2920,5374,7779,5631,3753,3725,2672,3621,4280,1162,5812,345,8173,9785,1525,955,5603,2215,2580,5261,2765,2990,5979,389,3907,2484,1232,5933,5871,3304,1138,1616,5114,9199,5072,7442,7245,6472,4760,6359,9053,7876,2564,9404,3043,9026,2261,3374,4460,7306,2326,966,828,3274,1712,3446 24 | 3975,4565,8131,5800,4570,2306,8838,4392,9147,11,3911,7118,9645,4994,2028,6062,5431,2279,8752,2658,7836,994,7316,5336,7185,3289,1898,9689,2331,5737,3403,1124,2679,3241,7748,16,2724,5441,6640,9368,9081,5618,858,4969,17,2103,6035,8043,7475,2181,939,415,1617,8500,8253,2155,7843,7974,7859,1746,6336,3193,2617,8736,4079,6324,6645,8891,9396,5522,6103,1857,8979,3835,2475,1310,7422,610,8345,7615 25 | 9248,5397,5686,2988,3446,4359,6634,9141,497,9176,6773,7448,1907,8454,916,1596,2241,1626,1384,2741,3649,5362,8791,7170,2903,2475,5325,6451,924,3328,522,90,4813,9737,9557,691,2388,1383,4021,1609,9206,4707,5200,7107,8104,4333,9860,5013,1224,6959,8527,1877,4545,7772,6268,621,4915,9349,5970,706,9583,3071,4127,780,8231,3017,9114,3836,7503,2383,1977,4870,8035,2379,9704,1037,3992,3642,1016,4303 26 | 5093,138,4639,6609,1146,5565,95,7521,9077,2272,974,4388,2465,2650,722,4998,3567,3047,921,2736,7855,173,2065,4238,1048,5,6847,9548,8632,9194,5942,4777,7910,8971,6279,7253,2516,1555,1833,3184,9453,9053,6897,7808,8629,4877,1871,8055,4881,7639,1537,7701,2508,7564,5845,5023,2304,5396,3193,2955,1088,3801,6203,1748,3737,1276,13,4120,7715,8552,3047,2921,106,7508,304,1280,7140,2567,9135,5266 27 | 6237,4607,7527,9047,522,7371,4883,2540,5867,6366,5301,1570,421,276,3361,527,6637,4861,2401,7522,5808,9371,5298,2045,5096,5447,7755,5115,7060,8529,4078,1943,1697,1764,5453,7085,960,2405,739,2100,5800,728,9737,5704,5693,1431,8979,6428,673,7540,6,7773,5857,6823,150,5869,8486,684,5816,9626,7451,5579,8260,3397,5322,6920,1879,2127,2884,5478,4977,9016,6165,6292,3062,5671,5968,78,4619,4763 28 | 9905,7127,9390,5185,6923,3721,9164,9705,4341,1031,1046,5127,7376,6528,3248,4941,1178,7889,3364,4486,5358,9402,9158,8600,1025,874,1839,1783,309,9030,1843,845,8398,1433,7118,70,8071,2877,3904,8866,6722,4299,10,1929,5897,4188,600,1889,3325,2485,6473,4474,7444,6992,4846,6166,4441,2283,2629,4352,7775,1101,2214,9985,215,8270,9750,2740,8361,7103,5930,8664,9690,8302,9267,344,2077,1372,1880,9550 29 | 5825,8517,7769,2405,8204,1060,3603,7025,478,8334,1997,3692,7433,9101,7294,7498,9415,5452,3850,3508,6857,9213,6807,4412,7310,854,5384,686,4978,892,8651,3241,2743,3801,3813,8588,6701,4416,6990,6490,3197,6838,6503,114,8343,5844,8646,8694,65,791,5979,2687,2621,2019,8097,1423,3644,9764,4921,3266,3662,5561,2476,8271,8138,6147,1168,3340,1998,9874,6572,9873,6659,5609,2711,3931,9567,4143,7833,8887 30 | 6223,2099,2700,589,4716,8333,1362,5007,2753,2848,4441,8397,7192,8191,4916,9955,6076,3370,6396,6971,3156,248,3911,2488,4930,2458,7183,5455,170,6809,6417,3390,1956,7188,577,7526,2203,968,8164,479,8699,7915,507,6393,4632,1597,7534,3604,618,3280,6061,9793,9238,8347,568,9645,2070,5198,6482,5000,9212,6655,5961,7513,1323,3872,6170,3812,4146,2736,67,3151,5548,2781,9679,7564,5043,8587,1893,4531 31 | 5826,3690,6724,2121,9308,6986,8106,6659,2142,1642,7170,2877,5757,6494,8026,6571,8387,9961,6043,9758,9607,6450,8631,8334,7359,5256,8523,2225,7487,1977,9555,8048,5763,2414,4948,4265,2427,8978,8088,8841,9208,9601,5810,9398,8866,9138,4176,5875,7212,3272,6759,5678,7649,4922,5422,1343,8197,3154,3600,687,1028,4579,2084,9467,4492,7262,7296,6538,7657,7134,2077,1505,7332,6890,8964,4879,7603,7400,5973,739 32 | 1861,1613,4879,1884,7334,966,2000,7489,2123,4287,1472,3263,4726,9203,1040,4103,6075,6049,330,9253,4062,4268,1635,9960,577,1320,3195,9628,1030,4092,4979,6474,6393,2799,6967,8687,7724,7392,9927,2085,3200,6466,8702,265,7646,8665,7986,7266,4574,6587,612,2724,704,3191,8323,9523,3002,704,5064,3960,8209,2027,2758,8393,4875,4641,9584,6401,7883,7014,768,443,5490,7506,1852,2005,8850,5776,4487,4269 33 | 4052,6687,4705,7260,6645,6715,3706,5504,8672,2853,1136,8187,8203,4016,871,1809,1366,4952,9294,5339,6872,2645,6083,7874,3056,5218,7485,8796,7401,3348,2103,426,8572,4163,9171,3176,948,7654,9344,3217,1650,5580,7971,2622,76,2874,880,2034,9929,1546,2659,5811,3754,7096,7436,9694,9960,7415,2164,953,2360,4194,2397,1047,2196,6827,575,784,2675,8821,6802,7972,5996,6699,2134,7577,2887,1412,4349,4380 34 | 4629,2234,6240,8132,7592,3181,6389,1214,266,1910,2451,8784,2790,1127,6932,1447,8986,2492,5476,397,889,3027,7641,5083,5776,4022,185,3364,5701,2442,2840,4160,9525,4828,6602,2614,7447,3711,4505,7745,8034,6514,4907,2605,7753,6958,7270,6936,3006,8968,439,2326,4652,3085,3425,9863,5049,5361,8688,297,7580,8777,7916,6687,8683,7141,306,9569,2384,1500,3346,4601,7329,9040,6097,2727,6314,4501,4974,2829 35 | 8316,4072,2025,6884,3027,1808,5714,7624,7880,8528,4205,8686,7587,3230,1139,7273,6163,6986,3914,9309,1464,9359,4474,7095,2212,7302,2583,9462,7532,6567,1606,4436,8981,5612,6796,4385,5076,2007,6072,3678,8331,1338,3299,8845,4783,8613,4071,1232,6028,2176,3990,2148,3748,103,9453,538,6745,9110,926,3125,473,5970,8728,7072,9062,1404,1317,5139,9862,6496,6062,3338,464,1600,2532,1088,8232,7739,8274,3873 36 | 2341,523,7096,8397,8301,6541,9844,244,4993,2280,7689,4025,4196,5522,7904,6048,2623,9258,2149,9461,6448,8087,7245,1917,8340,7127,8466,5725,6996,3421,5313,512,9164,9837,9794,8369,4185,1488,7210,1524,1016,4620,9435,2478,7765,8035,697,6677,3724,6988,5853,7662,3895,9593,1185,4727,6025,5734,7665,3070,138,8469,6748,6459,561,7935,8646,2378,462,7755,3115,9690,8877,3946,2728,8793,244,6323,8666,4271 37 | 6430,2406,8994,56,1267,3826,9443,7079,7579,5232,6691,3435,6718,5698,4144,7028,592,2627,217,734,6194,8156,9118,58,2640,8069,4127,3285,694,3197,3377,4143,4802,3324,8134,6953,7625,3598,3584,4289,7065,3434,2106,7132,5802,7920,9060,7531,3321,1725,1067,3751,444,5503,6785,7937,6365,4803,198,6266,8177,1470,6390,1606,2904,7555,9834,8667,2033,1723,5167,1666,8546,8152,473,4475,6451,7947,3062,3281 38 | 2810,3042,7759,1741,2275,2609,7676,8640,4117,1958,7500,8048,1757,3954,9270,1971,4796,2912,660,5511,3553,1012,5757,4525,6084,7198,8352,5775,7726,8591,7710,9589,3122,4392,6856,5016,749,2285,3356,7482,9956,7348,2599,8944,495,3462,3578,551,4543,7207,7169,7796,1247,4278,6916,8176,3742,8385,2310,1345,8692,2667,4568,1770,8319,3585,4920,3890,4928,7343,5385,9772,7947,8786,2056,9266,3454,2807,877,2660 39 | 6206,8252,5928,5837,4177,4333,207,7934,5581,9526,8906,1498,8411,2984,5198,5134,2464,8435,8514,8674,3876,599,5327,826,2152,4084,2433,9327,9697,4800,2728,3608,3849,3861,3498,9943,1407,3991,7191,9110,5666,8434,4704,6545,5944,2357,1163,4995,9619,6754,4200,9682,6654,4862,4744,5953,6632,1054,293,9439,8286,2255,696,8709,1533,1844,6441,430,1999,6063,9431,7018,8057,2920,6266,6799,356,3597,4024,6665 40 | 3847,6356,8541,7225,2325,2946,5199,469,5450,7508,2197,9915,8284,7983,6341,3276,3321,16,1321,7608,5015,3362,8491,6968,6818,797,156,2575,706,9516,5344,5457,9210,5051,8099,1617,9951,7663,8253,9683,2670,1261,4710,1068,8753,4799,1228,2621,3275,6188,4699,1791,9518,8701,5932,4275,6011,9877,2933,4182,6059,2930,6687,6682,9771,654,9437,3169,8596,1827,5471,8909,2352,123,4394,3208,8756,5513,6917,2056 41 | 5458,8173,3138,3290,4570,4892,3317,4251,9699,7973,1163,1935,5477,6648,9614,5655,9592,975,9118,2194,7322,8248,8413,3462,8560,1907,7810,6650,7355,2939,4973,6894,3933,3784,3200,2419,9234,4747,2208,2207,1945,2899,1407,6145,8023,3484,5688,7686,2737,3828,3704,9004,5190,9740,8643,8650,5358,4426,1522,1707,3613,9887,6956,2447,2762,833,1449,9489,2573,1080,4167,3456,6809,2466,227,7125,2759,6250,6472,8089 42 | 3266,7025,9756,3914,1265,9116,7723,9788,6805,5493,2092,8688,6592,9173,4431,4028,6007,7131,4446,4815,3648,6701,759,3312,8355,4485,4187,5188,8746,7759,3528,2177,5243,8379,3838,7233,4607,9187,7216,2190,6967,2920,6082,7910,5354,3609,8958,6949,7731,494,8753,8707,1523,4426,3543,7085,647,6771,9847,646,5049,824,8417,5260,2730,5702,2513,9275,4279,2767,8684,1165,9903,4518,55,9682,8963,6005,2102,6523 43 | 1998,8731,936,1479,5259,7064,4085,91,7745,7136,3773,3810,730,8255,2705,2653,9790,6807,2342,355,9344,2668,3690,2028,9679,8102,574,4318,6481,9175,5423,8062,2867,9657,7553,3442,3920,7430,3945,7639,3714,3392,2525,4995,4850,2867,7951,9667,486,9506,9888,781,8866,1702,3795,90,356,1483,4200,2131,6969,5931,486,6880,4404,1084,5169,4910,6567,8335,4686,5043,2614,3352,2667,4513,6472,7471,5720,1616 44 | 8878,1613,1716,868,1906,2681,564,665,5995,2474,7496,3432,9491,9087,8850,8287,669,823,347,6194,2264,2592,7871,7616,8508,4827,760,2676,4660,4881,7572,3811,9032,939,4384,929,7525,8419,5556,9063,662,8887,7026,8534,3111,1454,2082,7598,5726,6687,9647,7608,73,3014,5063,670,5461,5631,3367,9796,8475,7908,5073,1565,5008,5295,4457,1274,4788,1728,338,600,8415,8535,9351,7750,6887,5845,1741,125 45 | 3637,6489,9634,9464,9055,2413,7824,9517,7532,3577,7050,6186,6980,9365,9782,191,870,2497,8498,2218,2757,5420,6468,586,3320,9230,1034,1393,9886,5072,9391,1178,8464,8042,6869,2075,8275,3601,7715,9470,8786,6475,8373,2159,9237,2066,3264,5000,679,355,3069,4073,494,2308,5512,4334,9438,8786,8637,9774,1169,1949,6594,6072,4270,9158,7916,5752,6794,9391,6301,5842,3285,2141,3898,8027,4310,8821,7079,1307 46 | 8497,6681,4732,7151,7060,5204,9030,7157,833,5014,8723,3207,9796,9286,4913,119,5118,7650,9335,809,3675,2597,5144,3945,5090,8384,187,4102,1260,2445,2792,4422,8389,9290,50,1765,1521,6921,8586,4368,1565,5727,7855,2003,4834,9897,5911,8630,5070,1330,7692,7557,7980,6028,5805,9090,8265,3019,3802,698,9149,5748,1965,9658,4417,5994,5584,8226,2937,272,5743,1278,5698,8736,2595,6475,5342,6596,1149,6920 47 | 8188,8009,9546,6310,8772,2500,9846,6592,6872,3857,1307,8125,7042,1544,6159,2330,643,4604,7899,6848,371,8067,2062,3200,7295,1857,9505,6936,384,2193,2190,301,8535,5503,1462,7380,5114,4824,8833,1763,4974,8711,9262,6698,3999,2645,6937,7747,1128,2933,3556,7943,2885,3122,9105,5447,418,2899,5148,3699,9021,9501,597,4084,175,1621,1,1079,6067,5812,4326,9914,6633,5394,4233,6728,9084,1864,5863,1225 48 | 9935,8793,9117,1825,9542,8246,8437,3331,9128,9675,6086,7075,319,1334,7932,3583,7167,4178,1726,7720,695,8277,7887,6359,5912,1719,2780,8529,1359,2013,4498,8072,1129,9998,1147,8804,9405,6255,1619,2165,7491,1,8882,7378,3337,503,5758,4109,3577,985,3200,7615,8058,5032,1080,6410,6873,5496,1466,2412,9885,5904,4406,3605,8770,4361,6205,9193,1537,9959,214,7260,9566,1685,100,4920,7138,9819,5637,976 49 | 3466,9854,985,1078,7222,8888,5466,5379,3578,4540,6853,8690,3728,6351,7147,3134,6921,9692,857,3307,4998,2172,5783,3931,9417,2541,6299,13,787,2099,9131,9494,896,8600,1643,8419,7248,2660,2609,8579,91,6663,5506,7675,1947,6165,4286,1972,9645,3805,1663,1456,8853,5705,9889,7489,1107,383,4044,2969,3343,152,7805,4980,9929,5033,1737,9953,7197,9158,4071,1324,473,9676,3984,9680,3606,8160,7384,5432 50 | 1005,4512,5186,3953,2164,3372,4097,3247,8697,3022,9896,4101,3871,6791,3219,2742,4630,6967,7829,5991,6134,1197,1414,8923,8787,1394,8852,5019,7768,5147,8004,8825,5062,9625,7988,1110,3992,7984,9966,6516,6251,8270,421,3723,1432,4830,6935,8095,9059,2214,6483,6846,3120,1587,6201,6691,9096,9627,6671,4002,3495,9939,7708,7465,5879,6959,6634,3241,3401,2355,9061,2611,7830,3941,2177,2146,5089,7079,519,6351 51 | 7280,8586,4261,2831,7217,3141,9994,9940,5462,2189,4005,6942,9848,5350,8060,6665,7519,4324,7684,657,9453,9296,2944,6843,7499,7847,1728,9681,3906,6353,5529,2822,3355,3897,7724,4257,7489,8672,4356,3983,1948,6892,7415,4153,5893,4190,621,1736,4045,9532,7701,3671,1211,1622,3176,4524,9317,7800,5638,6644,6943,5463,3531,2821,1347,5958,3436,1438,2999,994,850,4131,2616,1549,3465,5946,690,9273,6954,7991 52 | 9517,399,3249,2596,7736,2142,1322,968,7350,1614,468,3346,3265,7222,6086,1661,5317,2582,7959,4685,2807,2917,1037,5698,1529,3972,8716,2634,3301,3412,8621,743,8001,4734,888,7744,8092,3671,8941,1487,5658,7099,2781,99,1932,4443,4756,4652,9328,1581,7855,4312,5976,7255,6480,3996,2748,1973,9731,4530,2790,9417,7186,5303,3557,351,7182,9428,1342,9020,7599,1392,8304,2070,9138,7215,2008,9937,1106,7110 53 | 7444,769,9688,632,1571,6820,8743,4338,337,3366,3073,1946,8219,104,4210,6986,249,5061,8693,7960,6546,1004,8857,5997,9352,4338,6105,5008,2556,6518,6694,4345,3727,7956,20,3954,8652,4424,9387,2035,8358,5962,5304,5194,8650,8282,1256,1103,2138,6679,1985,3653,2770,2433,4278,615,2863,1715,242,3790,2636,6998,3088,1671,2239,957,5411,4595,6282,2881,9974,2401,875,7574,2987,4587,3147,6766,9885,2965 54 | 3287,3016,3619,6818,9073,6120,5423,557,2900,2015,8111,3873,1314,4189,1846,4399,7041,7583,2427,2864,3525,5002,2069,748,1948,6015,2684,438,770,8367,1663,7887,7759,1885,157,7770,4520,4878,3857,1137,3525,3050,6276,5569,7649,904,4533,7843,2199,5648,7628,9075,9441,3600,7231,2388,5640,9096,958,3058,584,5899,8150,1181,9616,1098,8162,6819,8171,1519,1140,7665,8801,2632,1299,9192,707,9955,2710,7314 55 | 1772,2963,7578,3541,3095,1488,7026,2634,6015,4633,4370,2762,1650,2174,909,8158,2922,8467,4198,4280,9092,8856,8835,5457,2790,8574,9742,5054,9547,4156,7940,8126,9824,7340,8840,6574,3547,1477,3014,6798,7134,435,9484,9859,3031,4,1502,4133,1738,1807,4825,463,6343,9701,8506,9822,9555,8688,8168,3467,3234,6318,1787,5591,419,6593,7974,8486,9861,6381,6758,194,3061,4315,2863,4665,3789,2201,1492,4416 56 | 126,8927,6608,5682,8986,6867,1715,6076,3159,788,3140,4744,830,9253,5812,5021,7616,8534,1546,9590,1101,9012,9821,8132,7857,4086,1069,7491,2988,1579,2442,4321,2149,7642,6108,250,6086,3167,24,9528,7663,2685,1220,9196,1397,5776,1577,1730,5481,977,6115,199,6326,2183,3767,5928,5586,7561,663,8649,9688,949,5913,9160,1870,5764,9887,4477,6703,1413,4995,5494,7131,2192,8969,7138,3997,8697,646,1028 57 | 8074,1731,8245,624,4601,8706,155,8891,309,2552,8208,8452,2954,3124,3469,4246,3352,1105,4509,8677,9901,4416,8191,9283,5625,7120,2952,8881,7693,830,4580,8228,9459,8611,4499,1179,4988,1394,550,2336,6089,6872,269,7213,1848,917,6672,4890,656,1478,6536,3165,4743,4990,1176,6211,7207,5284,9730,4738,1549,4986,4942,8645,3698,9429,1439,2175,6549,3058,6513,1574,6988,8333,3406,5245,5431,7140,7085,6407 58 | 7845,4694,2530,8249,290,5948,5509,1588,5940,4495,5866,5021,4626,3979,3296,7589,4854,1998,5627,3926,8346,6512,9608,1918,7070,4747,4182,2858,2766,4606,6269,4107,8982,8568,9053,4244,5604,102,2756,727,5887,2566,7922,44,5986,621,1202,374,6988,4130,3627,6744,9443,4568,1398,8679,397,3928,9159,367,2917,6127,5788,3304,8129,911,2669,1463,9749,264,4478,8940,1109,7309,2462,117,4692,7724,225,2312 59 | 4164,3637,2000,941,8903,39,3443,7172,1031,3687,4901,8082,4945,4515,7204,9310,9349,9535,9940,218,1788,9245,2237,1541,5670,6538,6047,5553,9807,8101,1925,8714,445,8332,7309,6830,5786,5736,7306,2710,3034,1838,7969,6318,7912,2584,2080,7437,6705,2254,7428,820,782,9861,7596,3842,3631,8063,5240,6666,394,4565,7865,4895,9890,6028,6117,4724,9156,4473,4552,602,470,6191,4927,5387,884,3146,1978,3000 60 | 4258,6880,1696,3582,5793,4923,2119,1155,9056,9698,6603,3768,5514,9927,9609,6166,6566,4536,4985,4934,8076,9062,6741,6163,7399,4562,2337,5600,2919,9012,8459,1308,6072,1225,9306,8818,5886,7243,7365,8792,6007,9256,6699,7171,4230,7002,8720,7839,4533,1671,478,7774,1607,2317,5437,4705,7886,4760,6760,7271,3081,2997,3088,7675,6208,3101,6821,6840,122,9633,4900,2067,8546,4549,2091,7188,5605,8599,6758,5229 61 | 7854,5243,9155,3556,8812,7047,2202,1541,5993,4600,4760,713,434,7911,7426,7414,8729,322,803,7960,7563,4908,6285,6291,736,3389,9339,4132,8701,7534,5287,3646,592,3065,7582,2592,8755,6068,8597,1982,5782,1894,2900,6236,4039,6569,3037,5837,7698,700,7815,2491,7272,5878,3083,6778,6639,3589,5010,8313,2581,6617,5869,8402,6808,2951,2321,5195,497,2190,6187,1342,1316,4453,7740,4154,2959,1781,1482,8256 62 | 7178,2046,4419,744,8312,5356,6855,8839,319,2962,5662,47,6307,8662,68,4813,567,2712,9931,1678,3101,8227,6533,4933,6656,92,5846,4780,6256,6361,4323,9985,1231,2175,7178,3034,9744,6155,9165,7787,5836,9318,7860,9644,8941,6480,9443,8188,5928,161,6979,2352,5628,6991,1198,8067,5867,6620,3778,8426,2994,3122,3124,6335,3918,8897,2655,9670,634,1088,1576,8935,7255,474,8166,7417,9547,2886,5560,3842 63 | 6957,3111,26,7530,7143,1295,1744,6057,3009,1854,8098,5405,2234,4874,9447,2620,9303,27,7410,969,40,2966,5648,7596,8637,4238,3143,3679,7187,690,9980,7085,7714,9373,5632,7526,6707,3951,9734,4216,2146,3602,5371,6029,3039,4433,4855,4151,1449,3376,8009,7240,7027,4602,2947,9081,4045,8424,9352,8742,923,2705,4266,3232,2264,6761,363,2651,3383,7770,6730,7856,7340,9679,2158,610,4471,4608,910,6241 64 | 4417,6756,1013,8797,658,8809,5032,8703,7541,846,3357,2920,9817,1745,9980,7593,4667,3087,779,3218,6233,5568,4296,2289,2654,7898,5021,9461,5593,8214,9173,4203,2271,7980,2983,5952,9992,8399,3468,1776,3188,9314,1720,6523,2933,621,8685,5483,8986,6163,3444,9539,4320,155,3992,2828,2150,6071,524,2895,5468,8063,1210,3348,9071,4862,483,9017,4097,6186,9815,3610,5048,1644,1003,9865,9332,2145,1944,2213 65 | 9284,3803,4920,1927,6706,4344,7383,4786,9890,2010,5228,1224,3158,6967,8580,8990,8883,5213,76,8306,2031,4980,5639,9519,7184,5645,7769,3259,8077,9130,1317,3096,9624,3818,1770,695,2454,947,6029,3474,9938,3527,5696,4760,7724,7738,2848,6442,5767,6845,8323,4131,2859,7595,2500,4815,3660,9130,8580,7016,8231,4391,8369,3444,4069,4021,556,6154,627,2778,1496,4206,6356,8434,8491,3816,8231,3190,5575,1015 66 | 3787,7572,1788,6803,5641,6844,1961,4811,8535,9914,9999,1450,8857,738,4662,8569,6679,2225,7839,8618,286,2648,5342,2294,3205,4546,176,8705,3741,6134,8324,8021,7004,5205,7032,6637,9442,5539,5584,4819,5874,5807,8589,6871,9016,983,1758,3786,1519,6241,185,8398,495,3370,9133,3051,4549,9674,7311,9738,3316,9383,2658,2776,9481,7558,619,3943,3324,6491,4933,153,9738,4623,912,3595,7771,7939,1219,4405 67 | 2650,3883,4154,5809,315,7756,4430,1788,4451,1631,6461,7230,6017,5751,138,588,5282,2442,9110,9035,6349,2515,1570,6122,4192,4174,3530,1933,4186,4420,4609,5739,4135,2963,6308,1161,8809,8619,2796,3819,6971,8228,4188,1492,909,8048,2328,6772,8467,7671,9068,2226,7579,6422,7056,8042,3296,2272,3006,2196,7320,3238,3490,3102,37,1293,3212,4767,5041,8773,5794,4456,6174,7279,7054,2835,7053,9088,790,6640 68 | 3101,1057,7057,3826,6077,1025,2955,1224,1114,6729,5902,4698,6239,7203,9423,1804,4417,6686,1426,6941,8071,1029,4985,9010,6122,6597,1622,1574,3513,1684,7086,5505,3244,411,9638,4150,907,9135,829,981,1707,5359,8781,9751,5,9131,3973,7159,1340,6955,7514,7993,6964,8198,1933,2797,877,3993,4453,8020,9349,8646,2779,8679,2961,3547,3374,3510,1129,3568,2241,2625,9138,5974,8206,7669,7678,1833,8700,4480 69 | 4865,9912,8038,8238,782,3095,8199,1127,4501,7280,2112,2487,3626,2790,9432,1475,6312,8277,4827,2218,5806,7132,8752,1468,7471,6386,739,8762,8323,8120,5169,9078,9058,3370,9560,7987,8585,8531,5347,9312,1058,4271,1159,5286,5404,6925,8606,9204,7361,2415,560,586,4002,2644,1927,2824,768,4409,2942,3345,1002,808,4941,6267,7979,5140,8643,7553,9438,7320,4938,2666,4609,2778,8158,6730,3748,3867,1866,7181 70 | 171,3771,7134,8927,4778,2913,3326,2004,3089,7853,1378,1729,4777,2706,9578,1360,5693,3036,1851,7248,2403,2273,8536,6501,9216,613,9671,7131,7719,6425,773,717,8803,160,1114,7554,7197,753,4513,4322,8499,4533,2609,4226,8710,6627,644,9666,6260,4870,5744,7385,6542,6203,7703,6130,8944,5589,2262,6803,6381,7414,6888,5123,7320,9392,9061,6780,322,8975,7050,5089,1061,2260,3199,1150,1865,5386,9699,6501 71 | 3744,8454,6885,8277,919,1923,4001,6864,7854,5519,2491,6057,8794,9645,1776,5714,9786,9281,7538,6916,3215,395,2501,9618,4835,8846,9708,2813,3303,1794,8309,7176,2206,1602,1838,236,4593,2245,8993,4017,10,8215,6921,5206,4023,5932,6997,7801,262,7640,3107,8275,4938,7822,2425,3223,3886,2105,8700,9526,2088,8662,8034,7004,5710,2124,7164,3574,6630,9980,4242,2901,9471,1491,2117,4562,1130,9086,4117,6698 72 | 2810,2280,2331,1170,4554,4071,8387,1215,2274,9848,6738,1604,7281,8805,439,1298,8318,7834,9426,8603,6092,7944,1309,8828,303,3157,4638,4439,9175,1921,4695,7716,1494,1015,1772,5913,1127,1952,1950,8905,4064,9890,385,9357,7945,5035,7082,5369,4093,6546,5187,5637,2041,8946,1758,7111,6566,1027,1049,5148,7224,7248,296,6169,375,1656,7993,2816,3717,4279,4675,1609,3317,42,6201,3100,3144,163,9530,4531 73 | 7096,6070,1009,4988,3538,5801,7149,3063,2324,2912,7911,7002,4338,7880,2481,7368,3516,2016,7556,2193,1388,3865,8125,4637,4096,8114,750,3144,1938,7002,9343,4095,1392,4220,3455,6969,9647,1321,9048,1996,1640,6626,1788,314,9578,6630,2813,6626,4981,9908,7024,4355,3201,3521,3864,3303,464,1923,595,9801,3391,8366,8084,9374,1041,8807,9085,1892,9431,8317,9016,9221,8574,9981,9240,5395,2009,6310,2854,9255 74 | 8830,3145,2960,9615,8220,6061,3452,2918,6481,9278,2297,3385,6565,7066,7316,5682,107,7646,4466,68,1952,9603,8615,54,7191,791,6833,2560,693,9733,4168,570,9127,9537,1925,8287,5508,4297,8452,8795,6213,7994,2420,4208,524,5915,8602,8330,2651,8547,6156,1812,6271,7991,9407,9804,1553,6866,1128,2119,4691,9711,8315,5879,9935,6900,482,682,4126,1041,428,6247,3720,5882,7526,2582,4327,7725,3503,2631 75 | 2738,9323,721,7434,1453,6294,2957,3786,5722,6019,8685,4386,3066,9057,6860,499,5315,3045,5194,7111,3137,9104,941,586,3066,755,4177,8819,7040,5309,3583,3897,4428,7788,4721,7249,6559,7324,825,7311,3760,6064,6070,9672,4882,584,1365,9739,9331,5783,2624,7889,1604,1303,1555,7125,8312,425,8936,3233,7724,1480,403,7440,1784,1754,4721,1569,652,3893,4574,5692,9730,4813,9844,8291,9199,7101,3391,8914 76 | 6044,2928,9332,3328,8588,447,3830,1176,3523,2705,8365,6136,5442,9049,5526,8575,8869,9031,7280,706,2794,8814,5767,4241,7696,78,6570,556,5083,1426,4502,3336,9518,2292,1885,3740,3153,9348,9331,8051,2759,5407,9028,7840,9255,831,515,2612,9747,7435,8964,4971,2048,4900,5967,8271,1719,9670,2810,6777,1594,6367,6259,8316,3815,1689,6840,9437,4361,822,9619,3065,83,6344,7486,8657,8228,9635,6932,4864 77 | 8478,4777,6334,4678,7476,4963,6735,3096,5860,1405,5127,7269,7793,4738,227,9168,2996,8928,765,733,1276,7677,6258,1528,9558,3329,302,8901,1422,8277,6340,645,9125,8869,5952,141,8141,1816,9635,4025,4184,3093,83,2344,2747,9352,7966,1206,1126,1826,218,7939,2957,2729,810,8752,5247,4174,4038,8884,7899,9567,301,5265,5752,7524,4381,1669,3106,8270,6228,6373,754,2547,4240,2313,5514,3022,1040,9738 78 | 2265,8192,1763,1369,8469,8789,4836,52,1212,6690,5257,8918,6723,6319,378,4039,2421,8555,8184,9577,1432,7139,8078,5452,9628,7579,4161,7490,5159,8559,1011,81,478,5840,1964,1334,6875,8670,9900,739,1514,8692,522,9316,6955,1345,8132,2277,3193,9773,3923,4177,2183,1236,6747,6575,4874,6003,6409,8187,745,8776,9440,7543,9825,2582,7381,8147,7236,5185,7564,6125,218,7991,6394,391,7659,7456,5128,5294 79 | 2132,8992,8160,5782,4420,3371,3798,5054,552,5631,7546,4716,1332,6486,7892,7441,4370,6231,4579,2121,8615,1145,9391,1524,1385,2400,9437,2454,7896,7467,2928,8400,3299,4025,7458,4703,7206,6358,792,6200,725,4275,4136,7390,5984,4502,7929,5085,8176,4600,119,3568,76,9363,6943,2248,9077,9731,6213,5817,6729,4190,3092,6910,759,2682,8380,1254,9604,3011,9291,5329,9453,9746,2739,6522,3765,5634,1113,5789 80 | 5304,5499,564,2801,679,2653,1783,3608,7359,7797,3284,796,3222,437,7185,6135,8571,2778,7488,5746,678,6140,861,7750,803,9859,9918,2425,3734,2698,9005,4864,9818,6743,2475,132,9486,3825,5472,919,292,4411,7213,7699,6435,9019,6769,1388,802,2124,1345,8493,9487,8558,7061,8777,8833,2427,2238,5409,4957,8503,3171,7622,5779,6145,2417,5873,5563,5693,9574,9491,1937,7384,4563,6842,5432,2751,3406,7981 81 | --------------------------------------------------------------------------------