How to divide a set into two subsets such that difference between the sum of numbers in two sets is minimal?

Question

Given a set of numbers, divide the numbers into two subsets such that difference between the sum of numbers in two subsets is minimal.

T

Answer 1

I'll convert this problem to subset sum problem
let's  take array int[] A = { 10,20,15,5,25,33 };
it should be divided into {25 20 10} and { 33 20 } and answer is 55-53=2

Notations : SUM == sum of whole array
            sum1 == sum of subset1
            sum2 == sum of subset1

step 1: get sum of whole array  SUM=108
step 2:  whichever way we divide our array into two part one thing will remain true
          sum1+ sum2= SUM
step 3: if our intention is to get minimum sum difference then sum1 and sum2 should be near SUM/2 (example sum1=54 and sum2=54 then diff=0 )

steon 4: let's try combinations


        sum1 = 54 AND sum2 = 54   (not possible to divide like this) 
        sum1 = 55 AND sum2 = 53   (possible and our solution, should break here)
        sum1 = 56 AND sum2 = 52  
        sum1 = 57 AND sum2 = 51 .......so on
        pseudo code
        SUM=Array.sum();
        sum1 = SUM/2;
        sum2 = SUM-sum1;
        while(true){
          if(subSetSuMProblem(A,sum1) && subSetSuMProblem(A,sum2){
           print "possible"
           break;
          }
         else{
          sum1++;
          sum2--;
         }
         }

Java code for the same

import java.util.ArrayList;
import java.util.List;

public class MinimumSumSubsetPrint {


public static void main(String[] args) {
    int[] A = {10, 20, 15, 5, 25, 32};
    int sum = 0;
    for (int i = 0; i < A.length; i++) {
        sum += A[i];
    }
    subsetSumDynamic(A, sum);

}

private static boolean subsetSumDynamic(int[] A, int sum) {
    int n = A.length;
    boolean[][] T = new boolean[n + 1][sum + 1];


    // sum2[0][0]=true;

    for (int i = 0; i <= n; i++) {
        T[i][0] = true;
    }

    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= sum; j++) {
            if (A[i - 1] > j) {
                T[i][j] = T[i - 1][j];
            } else {
                T[i][j] = T[i - 1][j] || T[i - 1][j - A[i - 1]];
            }
        }
    }

    int sum1 = sum / 2;
    int sum2 = sum - sum1;
    while (true) {
        if (T[n][sum1] && T[n][sum2]) {
            printSubsets(T, sum1, n, A);
            printSubsets(T, sum2, n, A);
            break;
        } else {
            sum1 = sum1 - 1;
            sum2 = sum - sum1;
            System.out.println(sum1 + ":" + sum2);
        }
    }


    return T[n][sum];
}

private static void printSubsets(boolean[][] T, int sum, int n, int[] A) {
    List sumvals = new ArrayList();
    int i = n;
    int j = sum;
    while (i > 0 && j > 0) {
        if (T[i][j] == T[i - 1][j]) {
            i--;
        } else {
            sumvals.add(A[i - 1]);

            j = j - A[i - 1];
            i--;

        }
    }


    System.out.println();
    for (int p : sumvals) {
        System.out.print(p + " ");
    }
    System.out.println();
}


}