Program to split a set into equal sum sets where elements in first set are smaller than second in Python

Suppose we have a list of numbers called nums, we have to check whether we can divide the list into two groups A and B such that: The sum of A and the sum of B are same. Here every number in A is strictly smaller than every number in B.

So, if the input is like nums = [3, 4, 5, 12], then the output will be True, as we can have A = [3,4,5] and B = [12] and both have sum 12.

To solve this, we will follow these steps −

• sort the list nums

• total := sum of all elements in nums

• s := 0, i := 0

• while i < size of nums, do

  • n := nums[i]

  • while i < size of nums and nums[i] is same as n, do

    • s := s + nums[i]

    • i := i + 1

  • if s is same as total − s, then

    • return True

• return False

Let us see the following implementation to get better understanding −

Example

 Live Demo

class Solution:
   def solve(self, nums):
      nums.sort()
      total = sum(nums)
      s = 0
      i = 0
      while i < len(nums):
         n = nums[i]
         while i < len(nums) and nums[i] == n:
            s += nums[i]
            i += 1
         if s == total - s:
            return True
      return False
ob = Solution()
nums = [3, 4, 5, 12]
print(ob.solve(nums))

Input

[3, 4, 5, 12]

Output

True