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999. Available Captures for Rook

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 (up, down, left, right) 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.

Note: A rook cannot move through other pieces, such as bishops or pawns. This means a rook cannot attack a pawn if there is another piece blocking the path.

Return the number of pawns the white rook is attacking.

 

Example 1:

Input: board = [[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".","R",".",".",".","p"],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."]]

Output: 3

Explanation:

In this example, the rook is attacking all the pawns.

Example 2:

Input: board = [[".",".",".",".",".",".","."],[".","p","p","p","p","p",".","."],[".","p","p","B","p","p",".","."],[".","p","B","R","B","p",".","."],[".","p","p","B","p","p",".","."],[".","p","p","p","p","p",".","."],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."]]

Output: 0

Explanation:

The bishops are blocking the rook from attacking any of the pawns.

Example 3:

Input: board = [[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".","p",".",".",".","."],["p","p",".","R",".","p","B","."],[".",".",".",".",".",".",".","."],[".",".",".","B",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".",".",".",".",".","."]]

Output: 3

Explanation:

The rook is attacking the pawns at positions b5, d6, and f5.

 

Constraints:

  • board.length == 8
  • board[i].length == 8
  • board[i][j] is either 'R', '.', 'B', or 'p'
  • There is exactly one cell with board[i][j] == 'R'

Solutions

Solution 1: Simulation

We first traverse the board to find the position of the rook $(i, j)$. Then, starting from $(i, j)$, we traverse in four directions: up, down, left, and right.

  • If it is not the boundary and not a bishop, continue moving forward.
  • If it is a pawn, increment the answer by one and stop traversing in that direction.

After traversing in all four directions, we get the answer.

The time complexity is $O(m \times n)$, where $m$ and $n$ are the number of rows and columns of the board, respectively. In this problem, $m = n = 8$. The space complexity is $O(1)$.

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class Solution:
    def numRookCaptures(self, board: List[List[str]]) -> int:
        dirs = (-1, 0, 1, 0, -1)
        n = len(board)
        for i in range(n):
            for j in range(n):
                if board[i][j] == "R":
                    ans = 0
                    for a, b in pairwise(dirs):
                        x, y = i + a, j + b
                        while 0 <= x < n and 0 <= y < n and board[x][y] != "B":
                            if board[x][y] == "p":
                                ans += 1
                                break
                            x, y = x + a, y + b
                    return ans

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class Solution {
    public int numRookCaptures(char[][] board) {
        final int[] dirs = {-1, 0, 1, 0, -1};
        int n = board.length;
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                if (board[i][j] == 'R') {
                    int ans = 0;
                    for (int k = 0; k < 4; ++k) {
                        int x = i + dirs[k], y = j + dirs[k + 1];
                        while (x >= 0 && x < n && y >= 0 && y < n && board[x][y] != 'B') {
                            if (board[x][y] == 'p') {
                                ++ans;
                                break;
                            }
                            x += dirs[k];
                            y += dirs[k + 1];
                        }
                    }
                    return ans;
                }
            }
        }
        return 0;
    }
}

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class Solution {
public:
    int numRookCaptures(vector<vector