LeetCode 1877. Minimize Maximum Pair Sum in Array

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Intuition

  • Pairing the biggest number with the smallest number leads to the minimum pair sum for the biggest number.
  • Remove them from the array, find the next biggest and smallest number, and pair them.
  • Find the maximum pair sum while pairing and return it after the array is empty.

Approach

  1. Sort nums in ascending order.
  2. Initialise ans with 0, which represents that the maximum pair sum in nums is 0.
  3. Iterate over nums from 0 to nums.size() / 2 - 1.
  4. On each iteration:
    1. Pair nums[i] with nums[nums.size()-1-i].
    2. Calculate their pair sum and update ans.
  5. Return ans.

Pseudocode of this problem:

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minPairSum(nums):
	Input nums array of positive integers of size n
	Output the minimized maximum pair sum
	
	sort nums in ascending order
	ans = 0
	for all i from 0 to n / 2:
		// Pair nums[i] (the minimum number) with nums[n-1-i] (the maximum number)
		ans = max(ans, nums[i] + nums[n-1-i])
	end for
	return ans

Complexity

Time complexity: $O(nlogn)$.

  • Sorting nums in ascending order is $O(nlogn)$.

  • $n / 2$ iterations to pair elements and find the maximum pair sum.

  • In each iteration:

    • Calculate the pair sum and update the maximum pair sum is $O(1)$.

  • Overall complexity is $O(nlogn)$.

Space complexity: $O(1)$.

Code

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class Solution {
public:
  int minPairSum(vector<int>& nums) {
    sort(nums.begin(), nums.end());
    int ans = 0;
    for (int i = 0; i < nums.size() / 2; i++) {
      ans = max(ans, nums[i] + nums[nums.size()-1-i]);
    }
    return ans;
  }
};