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.
#include<stdio.h>
#include<conio.h>
#include<iostream>
using namespace std;
// A utility function that returns maximum of two integers
int max(int a, int b)
{
return (a > b) ? a : b;
}
// Returns the maximum value that can be put in a knapsack of capacity W
int knapSack(int W, int wt[], int val[], int n)
{
// Base Case
if (n == 0 || W == 0)
return 0;
// If weight of the nth item is more than Knapsack capacity W, then
// this item cannot be included in the optimal solution
if (wt[n - 1] > W)
return knapSack(W, wt, val, n - 1);
// Return the maximum of two cases: (1) nth item included (2) not included
else
return max(val[n - 1] + knapSack(W - wt[n - 1], wt, val, n - 1),
knapSack(W, wt, val, n - 1));
}
// Driver program to test above function
int main()
{
cout << "Enter the number of items in a Knapsack:";
int n, W;
cin >> n;
int val[n], wt[n];
for (int i = 0; i < n; i++)
{
cout << "Enter value and weight for item " << i << ":";
cin >> val[i];
cin >> wt[i];
}
// int val[] = { 60, 100, 120 };
// int wt[] = { 10, 20, 30 };
// int W = 50;
cout << "Enter the capacity of knapsack";
cin >> W;
cout << knapSack(W, wt, val, n);
return 0;
}
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
Sanfoundry Global Education & Learning Series – 1000 C++ Programs.
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