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C++ Program to Solve the 0-1 Knapsack Problem
In 0-1 knapsack problem, a set of items are given, each with a weight and a value. We need to determine the number of each item to include in a collection so that the total weight is less than or equal to the given limit and the total value is large as possible.
Input
Value = [10, 20, 30, 40, 60, 70] Weight=[1, 2, 3, 6, 7, 4] int w=7
Output
knapsack value is: 100
Algorithm
Begin Input: set of items each with a weight and a value Set knapsack capacity Number of items=sizeof(values) / sizeof(values[0]) Knapsack(Values (stored in array v), Weights (stored in array w), Number of distinct items (n), Knapsack capacity W) If (w < 0) Return If no items left or capacity becomes 0 Return 0 Include current item n in knapSack (v[n]) and recurs for remaining items (n - 1) with decreased capacity (W - w[n]) Exclude current item n from knapSack and recurs for remaining items (n - 1) Return maximum value we get by including or excluding current item End
Example Code
#include <iostream> #include <climits> using namespace std; int knapSack(int v[], int w[], int n, int W) { if (W < 0) return INT_MIN; if (n < 0 || W == 0) return 0; int in = v[n] + knapSack(v, w, n - 1, W - w[n]); int ex = knapSack(v, w, n - 1, W); return max (in, ex); } int main() { int v[] = { 10, 20, 30, 40, 60, 70 }; int w[] = { 1, 2, 3, 6, 7, 4 }; int W = 7; int n = sizeof(v) / sizeof(v[0]); cout << "Knapsack value is " << knapSack(v, w, n - 1, W); return 0; }
Output
Knapsack value is 100
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