Solve common array/graph interview problems

You are given several independent coding tasks. Implement each function according to the specification below. ## 1) Rotate a square matrix in-place **Input:** An integer matrix `M` of size `n x n`. **Task:** Rotate the matrix **90 degrees clockwise** **in-place** (modify `M` directly). **Constraints:** - `1 <= n <= 500` - Aim for `O(n^2)` time and `O(1)` extra space. **Example:** - Input: ``` [[1,2,3], [4,5,6], [7,8,9]] ``` - Output: ``` [[7,4,1], [8,5,2], [9,6,3]] ``` --- ## 2) Shortest word transformation steps **Input:** - `begin`: a lowercase word - `end`: a lowercase word - `words`: a list of lowercase words (dictionary) **Task:** Return the length of the shortest sequence of transformations from `begin` to `end`, where: - Each step changes **exactly one character**. - Every intermediate word must exist in `words`. - If no sequence exists, return `0`. **Constraints:** - All words have the same length `L`. - `1 <= |words| <= 50_000`, `1 <= L <= 10`. **Example:** - `begin = "hit"`, `end = "cog"`, `words = ["hot","dot","dog","lot","log","cog"]` - Output: `5` (e.g., `hit -> hot -> dot -> dog -> cog`) --- ## 3) Compute the H-index A researcher’s H-index is defined as the maximum integer `h` such that the researcher has **at least `h` papers** with **at least `h` citations each**. **Input:** An array `citations` where `citations[i]` is the number of citations for paper `i`. **Task:** Return the researcher’s H-index. **Constraints:** - `0 <= n <= 200_000` - `0 <= citations[i] <= 1_000_000_000` - Prefer `O(n)` or `O(n log n)` time. **Example:** - Input: `[3,0,6,1,5]` - Output: `3` (three papers have at least 3 citations)