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MinimumSumPartition.java

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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 void main (String[] args)

{

Scanner sc = new Scanner(System.in);

int t = sc.nextInt();

while(t-->0)

{

int n = sc.nextInt();

int arr[] = new int[n];

int sum = 0;

for(int i = 0;i < n;i++)

{

arr[i] = sc.nextInt();

sum += arr[i];

}

int ans[] = new int[sum];

ans = subset(arr,sum);

int min = Integer.MAX_VALUE;

for (int i = 0; i < ans.length; i++)

min = Math.min(min,(sum-2*ans[i]));

System.out.println(min);

}

static int[] subset(int arr[],int sum)

{

int n = arr.length;

boolean dp[][] = new boolean[n+1][sum+1];

for(int i = 0; i <= n; i++)

dp[i][0] = true;

for(int i = 1; i <= sum; i++)

dp[0][i] = false;

// subset sum concept

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

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

}

//storing last dp column whose value is true till sum/2

int index[] = new int[sum];

int p = 0;

for(int i = 0 ; i <= sum / 2; i++)

{

if(dp[n][i] == true)

index[p++] = i;

}

return index;

}