Find shared courses between student pairs

### Problem Set (Coding) You are given multiple coding questions from an interview. Implement each function as described. --- ## 1) Course Overlap You are given an array of pairs `(studentId, courseName)` describing which student took which course. **Task:** For every pair of distinct students `(idA, idB)` (where `idA < idB`), compute the list of course names that both students have taken. **Input:** - `String[][] enrollments`, where each element is `{studentId, courseName}`. **Output:** - A list of entries, one per student pair, each containing: - the pair key as a string like `"idA,idB"` - the list of common courses (order does not matter, but should be deterministic if you choose to sort) - Include pairs even if they share no courses (then the list is empty). **Example** Input: ```text [ ["17","Math"], ["17","English"], ["58","Math"], ["61","Physics"] ] ``` Output (one acceptable format): ```text ( "17,58" -> ["Math"], "17,61" -> [], "58,61" -> [] ) ``` --- ## 2) Validate Sudoku-like Grid Given an `n x n` integer grid, validate whether it is a valid **Latin-square style** grid: A grid is valid if: - `n >= 1` - Every value is an integer in `[1, n]` - Each row contains each number `1..n` exactly once - Each column contains each number `1..n` exactly once Return `true` if valid, otherwise `false`. **Examples** ```text grid = [ [1,2,3], [2,3,1], [3,1,2] ] => true ``` ```text grid = [ [0,2,3], [2,3,1], [3,1,2] ] => false (0 is out of range) ``` ```text grid = [ [1,3], [2,1] ] => false (3 is out of range for n=2) ``` --- ## 3) Validate Nonogram A **Nonogram** board is a `R x C` grid of characters where each cell is: - `'B'` = black - `'W'` = white You are also given: - `rowClues`: an array of length `R`, where `rowClues[i]` is a list of run-lengths of consecutive `'B'` groups in row `i` (left to right). - `colClues`: an array of length `C`, where `colClues[j]` is a list of run-lengths of consecutive `'B'` groups in column `j` (top to bottom). **Task:** Return `true` if the board matches *all* row and column clues; otherwise return `false`. Notes: - An empty clue list (e.g., `[]`) means there are **no** black cells in that row/column. **Example** ```text matrix = [ [W,W,W,W], [B,W,W,W], [B,W,B,B], [W,W,B,W], [B,B,W,W] ] rowClues = [ [], [1], [1,2], [1], [2] ] colClues = [ [2,1], [1], [2], [1] ] => true ``` If the clues do not match the derived runs, return `false`.