Have you landed a coding internship or a job interview in your dream company?
If yes, you must not leave any chance to grab this opportunity and this is why practising common coding questions is important to clear your interview with ease.
Therefore, we have come up with a very common question that you can be asked in your coding interview, ie, how to find the minimum subset sum difference?
Here, we have explained to you what the problem is along with all methods that you can use to resolve the problem in the most efficient way.
Problem Statement
You will be provided with a set S consisting of all integer values. You will have to divide the set into two sets Set1 and Set2 in a way that there is a minimum subset sum difference.
It simply means that if you are given a set S and the subset S1 has n elements then there will be (m-n) elements present in subset S2 in such a way that the abs( sum(s1) - sum(s2)) is minimum.
To understand the problem in a better way, let’s consider the following example:
You are given an array Ar= { 1, 6, 5, 11}
The output of the program will be 1.
Explanation:
S1= { 1, 6, 5}
S2= {11}
The difference between the sum of these subsets is 1.
Methods to Find Minimum Subset Sum Difference
To find the minimum subset sum difference, you can use the following three methods:
Recursive Solution
Dynamic programming
Dynamic programming with less space complexity
Here, let’s discuss all these methods in detail below.
Recursive Approach
The recursive approach is one of the common and basic approaches that you can use to find the minimum subset sum difference. In this method, you will have to generate all the possible sums of the given set of integers and check if the current solution is optimal or not.
Complexity Analysis
Time Complexity: The time complexity of this method is calculated as O(2 ^n).
Space Complexity: The space complexity of this method is calculated as O(n).
Dynamic Programming
The brute force or recursion process is quite a space and time-consuming. This is why dynamic programming is preferred to find the minimum subset sum difference of the given set of integers. In this method, you will have to divide the sets into two equal parts and then the problem is solved through subproblems.
To find the minimum subset sum difference through dynamic programming, here are the steps that you need to follow:
To begin with, you will have to divide the given set into two sets.
Now, while you are partitioning it, you will have to keep the following factors in your mind:
Let dynamic[n+1][sum+1]= {1 in case any subset from 1st to nth term has a sum equal to elements in j, otherwise, return 0}
You will now have to run i from 1 to n and j from 1 to the sum of elements
Therefore dynamic[n+1][sum+1] will return 1 in case
A Sum of j can be achieved including ith item
A Sum of j can be achieved excluding the ith item.
Consider the sum of the elements as S.
Now, in order to find the minimum sum difference, you will have to find the value of j such that min{sum j*2: dynamic[n][j]==1}. Here, the value of j ranges from 0 to sum/2.
Complexity Analysis
Time Complexity: The time complexity of this algorithm is calculated as O(n*sum). Here, n denotes the number of elements and sum is the total of all the elements.
Space Complexity: The space complexity of this algorithm is calculated as O(n*sum).
Dynamic Programming With Less Space Complexity
The dynamic programming method to find the minimum subset sum difference is quite efficient but also space-consuming. Therefore, a more optimized version of dynamic programming can be used to find the subset sum difference...
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