JavaAlgorithms/DynamicProgramming/MinimumSumPartition.java

package DynamicProgramming;
// Partition a set into two subsets such that the difference of subset sums is minimum

/*
Input:  arr[] = {1, 6, 11, 5}
Output: 1
Explanation:
Subset1 = {1, 5, 6}, sum of Subset1 = 12
Subset2 = {11}, sum of Subset2 = 11

Input:  arr[] = {36, 7, 46, 40}
Output: 23
Explanation:
Subset1 = {7, 46} ;  sum of Subset1 = 53
Subset2 = {36, 40} ; sum of Subset2  = 76
 */

public class MinimumSumPartition {
  public static int subSet(int[] arr) {
    int n = arr.length;
    int sum = getSum(arr);
    boolean[][] dp = new boolean[n + 1][sum + 1];
    for (int i = 0; i <= n; i++) {
      dp[i][0] = true;
    }
    for (int j = 0; j <= sum; j++) {
      dp[0][j] = false;
    }

    // fill dp array
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= sum; j++) {
        if (arr[i - 1] < j) {
          dp[i][j] = dp[i - 1][j - arr[i - 1]] || dp[i - 1][j];
        } else if (arr[i - 1] == j) {
          dp[i][j] = true;
        } else {
          dp[i][j] = dp[i - 1][j];
        }
      }
    }

    // fill the index array
    int[] index = new int[sum];
    int p = 0;
    for (int i = 0; i <= sum / 2; i++) {
      if (dp[n][i]) {
        index[p++] = i;
      }
    }

    return getMin(index, sum);
  }

  /**
   * Calculate sum of array elements
   *
   * @param arr the array
   * @return sum of given array
   */
  public static int getSum(int[] arr) {
    int sum = 0;
    for (int temp : arr) {
      sum += temp;
    }
    return sum;
  }

  public static int getMin(int[] arr, int sum) {
    if (arr.length == 0) {
      return 0;
    }
    int min = Integer.MAX_VALUE;
    for (int temp : arr) {
      min = Math.min(min, sum - 2 * temp);
    }
    return min;
  }

  /** Driver Code */
  public static void main(String[] args) {
    assert subSet(new int[] {1, 6, 11, 5}) == 1;
    assert subSet(new int[] {36, 7, 46, 40}) == 23;
    assert subSet(new int[] {1, 2, 3, 9}) == 3;
  }
}