 # C++ Programming Code Examples

## C++ > Mathematics Code Examples

### C++ Program to Solve Knapsack Problem Using Dynamic Programming

``` C++ Program to Solve Knapsack Problem Using Dynamic Programming This is a C++ Program to knapsack problem using dynamic programming. 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. // A Dynamic Programming based solution for 0-1 Knapsack problem #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) { int i, w; int K[n + 1][W + 1]; // Build table K[][] in bottom up manner for (i = 0; i <= n; i++) { for (w = 0; w <= W; w++) { if (i == 0 || w == 0) K[i][w] = 0; else if (wt[i - 1] <= w) K[i][w] = max(val[i - 1] + K[i - 1][w - wt[i - 1]], K[i - 1][w]); else K[i][w] = K[i - 1][w]; } } return K[n][W]; } 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; } ``` 