Remove as Many Target-Sum Pairs as Possible

### Problem One operation removes two distinct occurrences from `nums` whose values sum to `k`. Each occurrence can be removed only once. Return the maximum number of operations. ```cpp class Solution { public: int maxOperations(vector<int>& nums, int k); }; ``` ### Examples **Example 1:** ```text nums = [2,4,2,4,4], k = 6 Output: 2 Explanation: Match each of the two 2s with one 4. ``` **Example 2:** ```text nums = [5,5,5,1], k = 10 Output: 1 Explanation: Two of the three 5 occurrences form one pair. ``` ### Constraints - `1 <= nums.length <= 10^5`. - `1 <= nums[i] <= 10^9`. - `1 <= k <= 10^9`. ### Clarifying Questions Pairs need not be adjacent. Equal-valued occurrences may pair when their doubled value equals k, but one occurrence cannot pair with itself. ```hint Inspect the structure Can two equal values represent different removable occurrences, and when would an occurrence be reused illegally? ``` ### Reasoning checkpoints - Use two distinct occurrences per operation and never reuse an occurrence. - Prove the maximum count, including the case when both required pair values are equal. ### Optional extensions How would sorting and two pointers achieve the same count without hashing?