# Minimum Subset Sum Difference | Dynamic Problem.

Hello guys, Today we will solve an existing problem which is

**Minimum Subset Sum Difference.**This is a DP based problem.

In this question, we have given an array which contains some elements and we have to find the minimum difference of subsets.

## Example:

**arr[ ]={1,2,7};**

The minimum difference of this question is 4. How?

### Explanation:

In this question, we have to find 2 subsets which sum is equal to the sum of the whole array and the difference of 2 subsets is minimum.

The subsets of the given array are {1,2},{7} because the sum of these 2 subsets is 10 and it is equal to the sum of a given array which is also 10 and the difference of these 2 arrays is minimum.

### Solution:

I take a fixed array element or value of the n. You can take input in runtime.

**int n=3;
int a[]={1,2,7,8};
int sum=0;
for(int i=0;i<a.length;i++)
{
sum+=a[i];
}
boolean[][] t=new boolean[n+1][sum+1];
ArrayList<Integer> ar=new ArrayList<Integer>();
//int[][] t=new int[n+1][sum+1];
for(int i=0;i<n+1;i++)
{
for(int j=0;j<sum+1;j++)
{
if(i==0&&j==0)
{
t[i][j]=true;
}
else if(i==0)
{
t[i][j]=false;
}
else if(j==0)
{
t[i][j]=true;
}
else
{
if(a[i-1]<=j)
{
t[i][j]=Boolean.logicalOr((t[i-1][j-a[i-1]]),t[i-1][j]);
// t[i][j]=Integer.sum((t[i-1][j-a[i-1]]),t[i-1][j]);
}
else
{
t[i][j]=t[i-1][j];
}
}
}
}
for(int l=0;l<(sum+1)/2;l++)
{
if(t[n][l]==true)
{
ar.add(l);
}
}
int min=Integer.MAX_VALUE;
for(int m=0;m<ar.size();m++)
{
min=Integer.min(min,sum-2*(ar.get(m)));
}
System.out.println(min);
**

**Solution: 4;**

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