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Partition a set into two subsets such that the difference of subset sums is minimum.

HARD

10 mins

128 upvotes

Dynamic Programming

Arrays

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Problem

Submissions

Partition a set into two subsets such that the difference of subset sums is minimum.

Contributed by

Dhruv Sharma

Hard

0/120

Avg time to solve 10 mins

Success Rate 85 %

128 upvotes

Problem Statement

You are given an array containing N non-negative integers. Your task is to partition this array into two subsets such that the absolute difference between subset sums is minimum.

You just need to find the minimum absolute difference considering any valid division of the array elements.

Note:

1. Each element of the array should belong to exactly one of the subset.

2. Subsets need not be contiguous always. For example, for the array : {1,2,3}, some of the possible divisions are a) {1,2} and {3}  b) {1,3} and {2}.

3. Subset-sum is the sum of all the elements in that subset.

Detailed explanation ( Input/output format, Notes, Constraints, Images )

Input Format:

The first line of input contains the integer T, denoting the number of test cases.

The first line of each test case contains an integer N, denoting the size of the array.

The second and the last line of each test case contains N space-separated integers denoting the array elements.

Output Format:

For each test case, return the minimum possible absolute difference in a separate line.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 10
1 <= N <= 10^3
0 <= ARR[i] <= 10^3
0 <= SUM <= 10^4, 

where SUM denotes the sum of all elements in the array for a given test case.

Time Limit: 1sec

Sample Input 1:

1
4
1 2 3 4

Sample Output 1:

Explanation for sample input 1:

We can partition the given array into {2,3} and {1,4}, as this will give us the minimum possible absolute difference i.e (5-5=0) in this case.

Sample Input 2:

1
3
8 6 5

Sample Output 2:

Explanation for sample input 2:

We can partition the given array into {8} and {6,5}, as this will give us the minimum possible absolute difference i.e (11-8=3) in this case

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