 # C++ Programming Code Examples

## C++ > Mathematics Code Examples

### Program to Solve the 0-1 Knapsack Problem

``` 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. #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; } ``` 