18. Max Number of K-Sum Pairs.cpp

/*
Max Number of K-Sum Pairs
=========================

You are given an integer array nums and an integer k.

In one operation, you can pick two numbers from the array whose sum equals k and remove them from the array.

Return the maximum number of operations you can perform on the array.

Example 1:
Input: nums = [1,2,3,4], k = 5
Output: 2
Explanation: Starting with nums = [1,2,3,4]:
- Remove numbers 1 and 4, then nums = [2,3]
- Remove numbers 2 and 3, then nums = []
There are no more pairs that sum up to 5, hence a total of 2 operations.

Example 2:
Input: nums = [3,1,3,4,3], k = 6
Output: 1
Explanation: Starting with nums = [3,1,3,4,3]:
- Remove the first two 3's, then nums = [1,4,3]
There are no more pairs that sum up to 6, hence a total of 1 operation.

Constraints:
1 <= nums.length <= 105
1 <= nums[i] <= 109
1 <= k <= 109

Hint #1  
The abstract problem asks to count the number of disjoint pairs with a given sum k.

Hint #2  
For each possible value x, it can be paired up with k - x.

Hint #3  
The number of such pairs equals to min(count(x), count(k-x)), unless that x = k / 2, where the number of such pairs will be floor(count(x) / 2).
*/

class Solution
{
public:
  int maxOperations(vector<int> &nums, int k)
  {
    sort(nums.begin(), nums.end());
    int i = 0, j = nums.size() - 1, ans = 0;
    while (i < j)
    {
      if (nums[i] + nums[j] == k)
      {
        ans++;
        i++;
        j--;
      }
      else if (nums[i] + nums[j] > k)
        j--;
      else
        i++;
    }
    return ans;
  }
};