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
 */

import java.util.*;
import java.lang.*;
import java.io.*;
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);
    }

    public static int getSum(int arr[]){
        if(arr.length <= 0){
            return 0;
        }
        int sum = 0;
        for(int i = 0; i < arr.length; i++){
            sum += arr[i];
        }
        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;
    }

    public static void main(String args[]){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int arr[] = new int[n];
        for(int i = 0 ; i<n; i++){
            arr[i] = in.nextInt();
        }
        System.out.println(subSet(arr));
    }
}