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.**

Here’s the list of Best Reference Books in C++ Programming, Data Structures and Algorithms.