Available Captures for Rook

Problem Description

You are given an 8 x 8 matrix representing a chessboard. There is exactly one white rook represented by 'R', some number of white bishops 'B', and some number of black pawns 'p'. Empty squares are represented by '.'. A rook can move any number of squares horizontally or vertically until it reaches another piece or the edge of the board. A rook is attacking a pawn if it can move to the pawn's square in one move. A rook cannot move through other pieces. Return the number of pawns the white rook is attacking.

Key Insights

• The rook can move vertically and horizontally.
• The rook's path to a pawn can be blocked by bishops or other pawns.
• We need to check all four directions (up, down, left, right) from the rook's position to count the reachable pawns.

Space and Time Complexity

Time Complexity: O(1) - The board size is fixed at 8x8, so the number of operations is constant. Space Complexity: O(1) - We are using a constant amount of extra space.

Solution

To solve this problem, we will:

1. Identify the position of the rook on the board.
2. Check in all four directions (up, down, left, right) until we either find a pawn or a blocking piece (bishop or edge of the board).
3. Count how many pawns the rook can attack based on the results from the four directions.

We will use a simple traversal approach, checking each direction one by one until we reach a blocking piece or the edge of the board.

Code Solutions