Simulate one disc-flipping board game move across all eight directions

You are simulating one move of a two-player board game played on an `m x n` grid. Each cell is `0` (empty), `1` (a piece of player 1) or `2` (a piece of player 2). Given the board and one move, in which `player` places a piece on cell `(row, col)`, return the board after the move. When a piece is placed, every straight run of the opponent's pieces that is enclosed between the new piece and another piece of the same player is flipped to the player's color. All eight directions must be checked: up, down, left, right and the four diagonals. If the move is illegal, return the original board unchanged. ### Function Signature ```python def place_piece(board: list[list[int]], row: int, col: int, player: int) -> list[list[int]]: ``` ### Rules - Let `opponent = 3 - player`. In one direction, walk away from `(row, col)` one cell at a time. If the walk passes one or more consecutive `opponent` cells and then reaches a `player` cell, every `opponent` cell passed in that direction is flipped to `player`. - If the first cell in a direction is not an `opponent` cell, or if the walk reaches an empty cell or the edge of the board before reaching a `player` cell, nothing flips in that direction. - All flips are decided from the board as it was before the move. A piece flipped in one direction never causes further flips. - The move is legal only if `(row, col)` is empty and at least one opponent piece flips in at least one direction. A legal move places `player` at `(row, col)` and applies every flip. - If the move is illegal, return the board exactly as given: no piece is placed and nothing flips. - The returned grid has the same dimensions as the input. You may modify `board` in place or build a new grid; only the returned grid is checked. ### Constraints - `1 <= m, n <= 100`, where `m = len(board)` and `n = len(board[i])` for every row `i` - Every cell is `0`, `1` or `2`. - `0 <= row < m` and `0 <= col < n` - `player` is `1` or `2`. - The board may hold any arrangement of pieces; it does not have to be reachable in a real game. ### Examples **Example 1** ```text Input: board = [ [0, 0, 0, 0, 0], [2, 1, 1, 0, 0], [0, 0, 1, 1, 0], [0, 2, 0, 0, 0] ] row = 1, col = 3, player = 2 Output: [ [0, 0, 0, 0, 0], [2, 2, 2, 2, 0], [0, 0, 2, 1, 0], [0, 2, 0, 0, 0] ] ``` To the left, the run `(1, 2)`, `(1, 1)` of player 1 pieces ends at player 2's piece at `(1, 0)`, so both flip. Down and to the left, `(2, 2)` is enclosed by player 2's piece at `(3, 1)` and flips. Straight down, `(2, 3)` is followed by the empty cell `(3, 3)`, so it stays. Every other direction starts with an empty cell. **Example 2** ```text Input: board = [ [0, 0, 0, 0, 0], [2, 1, 1, 0, 0], [0, 0, 1, 1, 0], [0, 2, 0, 0, 0] ] row = 3, col = 0, player = 1 Output: [ [0, 0, 0, 0, 0], [2, 1, 1, 0, 0], [0, 0, 1, 1, 0], [0, 2, 0, 0, 0] ] ``` To the right, player 2's piece at `(3, 1)` is followed by the empty cell `(3, 2)`, so it is not enclosed. Up and up-right start with empty cells, and the other directions leave the board at once. Nothing flips, so the move is illegal and the board is returned unchanged. **Example 3** ```text Input: board = [ [0, 0, 0, 0, 0], [2, 1, 1, 0, 0], [0, 0, 1, 1, 0], [0, 2, 0, 0, 0] ] row = 1, col = 2, player = 2 Output: [ [0, 0, 0, 0, 0], [2, 1, 1, 0, 0], [0, 0, 1, 1, 0], [0, 2, 0, 0, 0] ] ``` Cell `(1, 2)` is already occupied, so the move is illegal, even though `(1, 1)` lies between it and player 2's piece at `(1, 0)`.