Remove Chosen Values from an Array Prefix

### Problem Given the integer array `nums` and integer `val`, remove every occurrence of `val` in place. Return the number `k` of elements whose values differ from `val`. The first `k` positions of the modified array must contain exactly the retained occurrences, including repeated values that are not equal to `val`. Their order may change. The remaining positions and the array's eventual size are unimportant to this task. Preserve the original interface: ```cpp int removeElement(vector<int>& nums, int val); ``` The returned value is only the integer count. The required prefix is an observable mutation of `nums`, not an additional returned array or tuple. ### Examples ```text Input: nums = [4,1,4,2,1], val = 4 Returned k: 3 One valid first k values: [2,1,1] ``` The prefix `[1,2,1]` is also valid. Both retain the two occurrences of `1` and the one occurrence of `2`. ```text Input: nums = [], val = 6 Returned k: 0 Required first k values: [] ``` ### Constraints & Assumptions - `0 <= nums.length <= 100`. - Every input entry is between 0 and 50, inclusive. - `0 <= val <= 100`. - Modify the supplied array in place and return the retained count. - Retained occurrences may appear in any order; they need not be sorted or keep their original relative order. Values after the retained prefix are ignored. ### Clarifying Questions to Ask - Are repeated retained values deduplicated? No; keep each occurrence not equal to `val`. - Is returning the correct count enough? No; the first `k` positions must also have the correct retained values. - Must the original relative order remain? No; any order of the retained occurrences is allowed. ```hint Identify the observable part The judge needs the count and the retained prefix. Values beyond that prefix do not have to be assigned a special marker. ``` ### What a Strong Answer Covers - In-place mutation of the retained prefix alongside the integer return value. - Exactly the required multiplicities, with every occurrence of `val` excluded. - Empty input, all-removed input, and a removal value absent from the array. - A correctness argument that does not depend on one particular retained order. ### Follow-up Questions - What implementation choices become possible because the retained order may change? - How can a judge compare the retained occurrences without imposing an output order?