diff --git a/DynamicProgramming/SubsetSum.java b/DynamicProgramming/SubsetSum.java new file mode 100644 index 000000000..18a357248 --- /dev/null +++ b/DynamicProgramming/SubsetSum.java @@ -0,0 +1,46 @@ +package DynamicProgramming; + +public class SubsetSum { + + /** + * Driver Code + */ + public static void main(String[] args) { + int[] arr = new int[]{50, 4, 10, 15, 34}; + assert subsetSum(arr, 64); /* 4 + 10 + 15 + 34 = 64 */ + assert subsetSum(arr, 99); /* 50 + 15 + 34 = 99 */ + assert !subsetSum(arr, 5); + assert !subsetSum(arr, 66); + } + + /** + * Test if a set of integers contains a subset that sum to a given integer. + * + * @param arr the array contains integers. + * @param sum target sum of subset. + * @return {@code true} if subset exists, otherwise {@code false}. + */ + private static boolean subsetSum(int[] arr, int sum) { + int n = arr.length; + boolean[][] isSum = new boolean[n + 2][sum + 1]; + + isSum[n + 1][0] = true; + for (int i = 1; i <= sum; i++) { + isSum[n + 1][i] = false; + } + + for (int i = n; i > 0; i--) { + isSum[i][0] = true; + for (int j = 1; j <= arr[i - 1] - 1; j++) { + if (j <= sum) { + isSum[i][j] = isSum[i + 1][j]; + } + } + for (int j = arr[i - 1]; j <= sum; j++) { + isSum[i][j] = (isSum[i + 1][j] || isSum[i + 1][j - arr[i - 1]]); + } + } + + return isSum[1][sum]; + } +} \ No newline at end of file