C Program for Subset Sum Problem using Dynamic Programming
We can solve the problem in Pseudo-polynomial time we can use the Dynamic programming approach.
So we will create a 2D array of size (n + 1) * (sum + 1) of type boolean. The state dp[i][j] will be true if there exists a subset of elements from set[0 . . . i] with sum value = ‘j’.
The dynamic programming relation is as follows:
if (A[i-1] > j)
dp[i][j] = dp[i-1][j]
else
dp[i][j] = dp[i-1][j] OR dp[i-1][j-set[i-1]]
Below is the implementation of the above approach:
C
// A Dynamic Programming solution// for subset sum problem#include <stdio.h>#include <stdbool.h>// Returns true if there is a subset of set[]// with sum equal to given sumbool isSubsetSum(int set[], int n, int sum){ // The value of subset[i][j] will be true if // there is a subset of set[0..j-1] with sum // equal to i bool subset[n + 1][sum + 1]; // If sum is 0, then answer is true for (int i = 0; i <= n; i++) subset[i][0] = true; // If sum is not 0 and set is empty, // then answer is false for (int i = 1; i <= sum; i++) subset[0][i] = false; // Fill the subset table in bottom up manner for (int i = 1; i <= n; i++) { for (int j = 1; j <= sum; j++) { if (j < set[i - 1]) subset[i][j] = subset[i - 1][j]; if (j >= set[i - 1]) subset[i][j] = subset[i - 1][j] || subset[i - 1][j - set[i - 1]]; } } return subset[n][sum];}// Driver codeint main(){ int set[] = { 3, 34, 4, 12, 5, 2 }; int sum = 9; int n = sizeof(set) / sizeof(set[0]); if (isSubsetSum(set, n, sum) == true) printf("Found a subset with given sum"); else printf("No subset with given sum"); return 0;}// This code is contributed by Arjun Tyagi. |
Found a subset with given sum
Time Complexity: O(sum * n), where n is the size of the array.
Auxiliary Space: O(sum*n), as the size of the 2-D array is sum*n.
C Program for Subset Sum Problem | DP-25
Write a C program for a given set of non-negative integers and a value sum, the task is to check if there is a subset of the given set whose sum is equal to the given sum.
Examples:
Input: set[] = {3, 34, 4, 12, 5, 2}, sum = 9
Output: True
Explanation: There is a subset (4, 5) with sum 9.Input: set[] = {3, 34, 4, 12, 5, 2}, sum = 30
Output: False
Explanation: There is no subset that adds up to 30.