C++ Program to Solve the 0-1 Knapsack Problem

This is a C++ Program to solve 0-1 knapsack problem. The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a mass and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.

Here is source code of the C++ Program to Solve the 0-1 Knapsack Problem. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

  1. #include<stdio.h>
  2. #include<conio.h>
  3. #include<iostream>
  4.  
  5. using namespace std;
  6.  
  7. // A utility function that returns maximum of two integers
  8. int max(int a, int b)
  9. {
  10.     return (a > b) ? a : b;
  11. }
  12.  
  13. // Returns the maximum value that can be put in a knapsack of capacity W
  14. int knapSack(int W, int wt[], int val[], int n)
  15. {
  16.     // Base Case
  17.     if (n == 0 || W == 0)
  18.         return 0;
  19.  
  20.     // If weight of the nth item is more than Knapsack capacity W, then
  21.     // this item cannot be included in the optimal solution
  22.     if (wt[n - 1] > W)
  23.         return knapSack(W, wt, val, n - 1);
  24.  
  25.     // Return the maximum of two cases: (1) nth item included (2) not included
  26.     else
  27.         return max(val[n - 1] + knapSack(W - wt[n - 1], wt, val, n - 1),
  28.                 knapSack(W, wt, val, n - 1));
  29. }
  30.  
  31. // Driver program to test above function
  32. int main()
  33. {
  34.     cout << "Enter the number of items in a Knapsack:";
  35.     int n, W;
  36.     cin >> n;
  37.     int val[n], wt[n];
  38.     for (int i = 0; i < n; i++)
  39.     {
  40.         cout << "Enter value and weight for item " << i << ":";
  41.         cin >> val[i];
  42.         cin >> wt[i];
  43.     }
  44.  
  45.     //    int val[] = { 60, 100, 120 };
  46.     //    int wt[] = { 10, 20, 30 };
  47.     //    int W = 50;
  48.     cout << "Enter the capacity of knapsack";
  49.     cin >> W;
  50.     cout << knapSack(W, wt, val, n);
  51.  
  52.     return 0;
  53. }

Output:

$ g++ 0-1Knapsack.cpp
$ a.out
 
Enter the number of items in a Knapsack:5
Enter value and weight for item 0:11 111
Enter value and weight for item 1:22 121
Enter value and weight for item 2:33 131
Enter value and weight for item 3:44 141
Enter value and weight for item 4:55 151
Enter the capacity of knapsack 300
99

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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