Zigzag diagonal walk through a matrix from a chosen left-column start

Walk through a matrix along its diagonals in a zigzag. The walk only ever moves in two directions, up-right and down-left; when the next step would leave the matrix, it bounces onto the neighboring diagonal and reverses direction. The walk may start at the top-left cell or at any other cell of the leftmost column. Return the values in the order the walk visits them. The report gives only the movement rule and the possible starting cells; this version fixes the remaining details in the Rules below. ### Function Signature ```python def diagonal_bounce(matrix: list[list[int]], start_row: int) -> list[int]: ``` ### Rules - Rows are numbered from `0` at the top to `m - 1`, and columns from `0` on the left to `n - 1`. The walk starts at cell `(start_row, 0)`, moving up-right. - Moving up-right from `(r, c)`: if `(r - 1, c + 1)` is inside the matrix, step there. Otherwise bounce: if `c == n - 1`, step down to `(r + 1, c)`; else step right to `(r, c + 1)`. After a bounce the direction is down-left. - Moving down-left from `(r, c)`: if `(r + 1, c - 1)` is inside the matrix, step there. Otherwise bounce: if `r == m - 1`, step right to `(r, c + 1)`; else step down to `(r + 1, c)`. After a bounce the direction is up-right. - The walk ends at the bottom-right cell `(m - 1, n - 1)`, which it always reaches. Report every visited cell once, in visit order, including the start and the end. - When `start_row > 0`, the cells `(r, c)` with `r + c < start_row` are never visited. ### Constraints - `m = len(matrix)`, `n = len(matrix[0])`, every row has length `n`, and `1 <= m * n <= 10^5` - `0 <= start_row < m` - `-10^9 <= matrix[r][c] <= 10^9` ### Examples **Example 1** ```text Input: matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], start_row = 0 Output: [1, 2, 4, 7, 5, 3, 6, 8, 9] ``` From 1, the up-right step would leave the top edge, so the walk bounces right to 2 and turns down-left to 4. At the left edge it bounces down to 7 and goes up-right through 5 to 3. At the right edge it bounces down to 6, goes down-left to 8, and at the bottom edge bounces right to 9, the bottom-right cell. **Example 2** ```text Input: matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], start_row = 1 Output: [4, 2, 3, 5, 7, 8, 6, 9] ``` From 4 the walk goes up-right to 2, bounces right to 3 at the top edge, goes down-left through 5 to 7, bounces right to 8 at the bottom edge, goes up-right to 6, and bounces down to 9 at the right edge. The cell holding 1 is never visited. **Example 3** ```text Input: matrix = [[1, 2, 3, 4], [5, 6, 7, 8]], start_row = 1 Output: [5, 2, 3, 6, 7, 4, 8] ``` 5 up-right to 2; bounce right to 3; down-left to 6; bounce right to 7 at the bottom edge; up-right to 4; bounce down to 8 at the right edge.