Swap Row and Column Indices of a Rectangular Matrix

### Problem Return the transpose of `matrix`: the value at input row r, column c must appear at output row c, column r. An m-by-n input therefore produces an n-by-m matrix. ```cpp class Solution { public: vector<vector<int>> transpose(vector<vector<int>>& matrix); }; ``` ### Examples **Example 1:** ```text Input: matrix = [[2,-1,4],[7,0,5]] Output: [[2,7],[-1,0],[4,5]] Explanation: Each input column becomes one output row. ``` **Example 2:** ```text Input: matrix = [[9],[3],[6]] Output: [[9,3,6]] Explanation: A three-row column becomes a one-row matrix. ``` ### Constraints - `m == matrix.length`, `n == matrix[i].length`. - `1 <= m,n <= 1000` and `1 <= m*n <= 10^5`. - `-10^9 <= matrix[i][j] <= 10^9`. ### Contract considerations The input is rectangular, and transposition changes positions rather than element values. ```hint Read the boundary condition Write the output dimensions before choosing loop bounds. ``` ### Boundary reminders The input is rectangular, and transposition changes positions rather than element values.