Check an Array Against the Good-Array Definition

# Check an Array Against the Good-Array Definition You are given an integer array `nums`. For a positive integer `k`, define `base[k] = [1, 2, ..., k - 1, k, k]`. This array has length `k + 1`: each integer from `1` through `k - 1` occurs once, and `k` occurs twice. For example, `base[1] = [1,1]` and `base[3] = [1,2,3,3]`. An array is good if it is a permutation of `base[k]` for some `k`. A permutation is an arrangement of the same values with the same multiplicities. Return `true` if `nums` is good, or `false` otherwise. ### Examples **Example 1** ```text Input: nums = [4,2,1,4,3] Output: true ``` These values can be arranged as `[1,2,3,4,4]`, which is `base[4]`. **Example 2** ```text Input: nums = [1,2,2,4,4] Output: false ``` The array has five elements, but it cannot be arranged as `[1,2,3,4,4]`: it has a second `2` and no `3`. ### Constraints - `1 <= nums.length <= 100`. - `1 <= nums[i] <= 200`. ### Clarifying Questions - Does the order of the input values matter? No; any arrangement with the required multiplicities qualifies. - Can values be inserted or removed? No; the full input must be a permutation of the required array. - Which value may occur twice? Only the largest value in the corresponding `base[k]`; every smaller positive value must occur exactly once. - Is a one-element input good? No; even `base[1]` has two elements. ### C++ Interface ```cpp class Solution { public: bool isGood(vector<int>& nums) { } }; ``` ### Reasoning Checkpoints - Check the complete multiplicity requirement rather than just the largest value. - Account for input values outside the candidate pattern. - Preserve the input's elements when checking whether a rearrangement exists. ```hint Candidate pattern How does the length of base[k] constrain which value of k could match a given input length? ```