0-1 Knapsack Problem - Dynamic Programming in C

This is an implementation of the 0-1 knapsack problem in C using dynamic programming. The problem consists of a set of items, each with a weight and a value, and a knapsack with a maximum weight capacity. The goal is to determine the subset of items that maximizes the total value of the knapsack without exceeding its weight capacity.

How to use

To use this implementation, include the knapsack.c file in your project and call the knapSack() function with the following parameters:

• W: the maximum weight capacity of the knapsack
• wt[]: an array of weights for each item
• val[]: an array of values for each item
• n: the number of items

The function will return the maximum value that can be put in the knapsack without exceeding its weight capacity.

#include "0-1knapsack.c"

int main() {
    int W = 50;
    int wt[] = {10, 20, 30};
    int val[] = {60, 100, 120};
    int n = sizeof(wt)/sizeof(wt[0]);
    printf("%d", knapSack(W, wt, val, n));

    return 0;
}

Note

This implementation uses dynamic memory allocation to create a 2D array with variable size, so please remember to free the allocated memory after using the function.

Time and Space Complexity

The time complexity of this implementation is O(nW) where n is the number of items, W is the knapsack capacity. The space complexity is also O(nW) for the 2D array.

I hope this implementation helps you solve the 0-1 knapsack problem in your project. If you have any questions or suggestions, feel free to reach out.

Copyright (c) 2022, Max Base