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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];

}