├── README
└── one-liners.sh


/README:
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1 | A repo with assorted one-liners I come up with to do simple math stuff
2 | using regexps.
3 | 
4 | These are not golf exercises (they all can be shortened indeed), the
5 | motivation is to explore the technique Abigail uses in his famous
6 | primality test.
7 | 


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/one-liners.sh:
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 1 | # Prints "coprime" if the arguments are relatively prime.
 2 | perl -le 'print "coprime" if "@{[1 x pop]} @{[1 x pop]}" !~ /^(11+)\1* \1+$/' 3 4
 3 | coprime
 4 | 
 5 | # Number of divisors. This solution shows off how to embed a loop in the
 6 | # regexp by forcing backtracking. In this case using the Perl (??{ ... })
 7 | # construct, but the techinique is generic.
 8 | perl -le '(1 x pop) =~ /^(1+)\1*$(??{++$t})/; print $t' 8
 9 | 4
10 | 
11 | # Prime factorization.
12 | perl -le '$_ = 1 x pop; print $+[1] and s/$1/1/g while /^(11+?)\1*$/' 60
13 | 2
14 | 2
15 | 3
16 | 5
17 | 
18 | # n mod m.
19 | perl -le "(1 x shift) =~ /(1{@{[shift]}})*/; print length $'" 17 8
20 | 1
21 | 
22 | # Fraction reduction to lowest terms.
23 | perl -le '$_ = "@{[1 x shift]} @{[1 x shift]}"; s/$1/1/g while /^(11+?)\1* \1+$/; print length $& while /1+/g' 60 24
24 | 5
25 | 2
26 | 
27 | # Euler's phi function: number of positive integers less than or equal to n relatively prime to n.
28 | perl -le '$n = pop; print~~grep {"@{[1 x $_]} @{[1 x $n]}" !~ /^(11+)\1* \1+$/} 1..$n' 60
29 | 16
30 | 
31 | # Greatest common divisor (gcd).
32 | perl -le '"@{[1 x pop]} @{[1 x pop]}" =~ /(1+)\1* \1+$/ && print $+[1]' 27 36
33 | 9
34 | 
35 | # Square-free test: an integer is square-free if it is divisible by no perfect square (except 1).
36 | perl -le '$_ = 1 x pop; s/$1/1/g && /^($&)+$/ && exit while /(11+?)\1*$/; print "square-free"' 15
37 | square-free
38 | 
39 | # Perfect square test: an integer is a perfect square if it is equal to n^2 for some n.
40 | perl -le '$_ = 1 x (pop||1); 1 while /^(11+?)\1*$/ && /^(($1){$+[1]})+$/ && s/$1/1/g; print "perfect square" if /^1$/' 64
41 | perfect square
42 | 
43 | # Alternative perfect square test.
44 | perl -le '$_ = 1 x pop; $n = 1; $n += 2 while s/1{$n}//; $_ || print "perfect square"' 64
45 | perfect square
46 | 
47 | # Integer square root.
48 | perl -le '$_ = 1 x pop; $n = 1; $n += 2 while s/1{$n}/0/; print tr/0//d' 2012
49 | 44
50 | 
51 | # Triangular number test.
52 | perl -le '$_ = 1 x pop; 1 while s/($1 1)//x; $_ || print "triangular"' 21
53 | triangular
54 | 
55 | # Continued fraction.
56 | perl -le '($_, $q) = map {1 x $_} @ARGV; $q = $& while print s/$q//g||0 and s/1+/$q/' 93 415
57 | 0
58 | 4
59 | 2
60 | 6
61 | 7
62 | 
63 | # Sieve of Eratosthenes.
64 | perl -le '$_ = join " ", map {1 x $_} 2..pop; print $+[1] and s/\b($1)+\b *//g while s/(1+) ?//' 10
65 | 2
66 | 3
67 | 5
68 | 7
69 | 
70 | # Perfect number test: Perfect numbers are positive integers that are equal to
71 | # the sum of their proper positive divisors.
72 | perl -le '$n = 1 x pop; $n =~ /^(1+)\1+$(??{$s.=$^N})/; print "perfect number" if $s eq $n' 496
73 | perfect number
74 | 
75 | # Fibonacci numbers.
76 | perl -le '$f = "1 1"; $f =~ s/(1+) (1+)/$1$2 $1/ for 3..pop; $f =~ /1+/; print $+[0]' 16
77 | 987
78 | 


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