└── 0-1 Knapsack.py


/0-1 Knapsack.py:
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  1 | 
  2 | n = 4
  3 | W = 16
  4 | p = [40, 30, 50, 10]
  5 | w = [2, 5, 10, 5]
  6 | p_per_weight = [20, 6, 5, 2]
  7 | 
  8 | 
  9 | class Priority_Queue:
 10 |     def __init__(self):
 11 |         self.pqueue = []
 12 |         self.length = 0
 13 |     
 14 |     def insert(self, node):
 15 |         for i in self.pqueue:
 16 |             get_bound(i)
 17 |         i = 0
 18 |         while i < len(self.pqueue):
 19 |             if self.pqueue[i].bound > node.bound:
 20 |                 break
 21 |             i+=1
 22 |         self.pqueue.insert(i,node)
 23 |         self.length += 1
 24 | 
 25 |     def print_pqueue(self):
 26 |         for i in list(range(len(self.pqueue))):
 27 |             print ("pqueue",i, "=", self.pqueue[i].bound)
 28 |                     
 29 |     def remove(self):
 30 |         try:
 31 |             result = self.pqueue.pop()
 32 |             self.length -= 1
 33 |         except: 
 34 |             print("Priority queue is empty, cannot pop from empty list.")
 35 |         else:
 36 |             return result
 37 |         
 38 | class Node:
 39 |     def __init__(self, level, profit, weight):
 40 |         self.level = level
 41 |         self.profit = profit
 42 |         self.weight = weight
 43 |         self.items = []
 44 |         
 45 |             
 46 | def get_bound(node):
 47 |     if node.weight >= W:
 48 |         return 0
 49 |     else:
 50 |         result = node.profit
 51 |         j = node.level + 1
 52 |         totweight = node.weight
 53 |         while j <= n-1 and totweight + w[j] <= W:
 54 |             totweight = totweight + w[j]
 55 |             result = result + p[j]
 56 |             j+=1
 57 |         k = j
 58 |         if k<=n-1:
 59 |             result = result + (W - totweight) * p_per_weight[k]
 60 |         return result
 61 | 
 62 | 
 63 | nodes_generated = 0
 64 | pq = Priority_Queue()
 65 | 
 66 | v = Node(-1, 0, 0) 
 67 | nodes_generated+=1
 68 | maxprofit = 0 
 69 | v.bound = get_bound(v)
 70 | 
 71 | 
 72 | 
 73 | pq.insert(v)
 74 | 
 75 | while pq.length != 0:
 76 |     
 77 |     v = pq.remove() 
 78 | 
 79 | 
 80 |     if v.bound > maxprofit: #check if node is still promising
 81 |         #set u to the child that includes the next item
 82 |         u = Node(0, 0, 0)
 83 |         nodes_generated+=1
 84 |         u.level = v.level + 1
 85 |         u.profit = v.profit + p[u.level]
 86 |         u.weight = v.weight + w[u.level]
 87 |         #take v's list and add u's list
 88 |         u.items = v.items.copy()
 89 |         u.items.append(u.level) # adds next item
 90 | #        print("child that includes the next item: ")
 91 | #        print("Child 1:")
 92 | #        print("u.level = ", u.level, "u.profit = ", u.profit, "u.weight = ", u.weight)
 93 | #        print("u.items = ", u.items)
 94 |         if u.weight <= W and u.profit > maxprofit: 
 95 |             #update maxprofit
 96 |             maxprofit = u.profit
 97 | #            print("\nmaxprofit updated = ", maxprofit)
 98 |             bestitems = u.items
 99 | #            print("bestitems = ", bestitems)
100 |         u.bound = get_bound(u)
101 | #        print("u.bound = ", u.bound)
102 |         if u.bound > maxprofit:
103 |             pq.insert(u)
104 | #            print("Node u1 inserted into pq.")
105 | #            print("Priority Queue : ") 
106 | #            pq.print_pqueue()
107 |         #set u to the child that does not include the next item
108 |         u2 = Node(u.level, v.profit, v.weight)
109 |         nodes_generated+=1
110 |         u2.bound = get_bound(u2)
111 |         u2.items = v.items.copy()
112 | #        print("child that doesn't include the next item: ")
113 | #        print("Child 2:")
114 | #        print("u2.level = ", u2.level, "u2.profit = ", u2.profit, "u2.weight = ", u2.weight, "u2.bound = ", u2.bound)
115 | #        print("u2.items = ", u2.items)
116 |         if u2.bound > maxprofit:
117 |             pq.insert(u2)
118 | 
119 | print("\nEND maxprofit = ", maxprofit, "nodes generated = ", nodes_generated)
120 | print("bestitems = ", bestitems)
121 | 
122 |         
123 | 
124 | 
125 | 
126 |         
127 | 


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