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简单
数组
矩阵
模拟

999. 可以被一步捕获的棋子数

English Version

题目描述

给定一个 8 x 8 的棋盘，只有一个 白色的车，用字符 'R' 表示。棋盘上还可能存在白色的象 'B' 以及黑色的卒 'p'。空方块用字符 '.' 表示。

车可以按水平或竖直方向（上，下，左，右）移动任意个方格直到它遇到另一个棋子或棋盘的边界。如果它能够在一次移动中移动到棋子的方格，则能够 吃掉 棋子。

注意：车不能穿过其它棋子，比如象和卒。这意味着如果有其它棋子挡住了路径，车就不能够吃掉棋子。

返回白车将能 吃掉 的 卒的数量。

 

示例 1：

输入：[[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".","R",".",".",".","p"],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."]]
输出：3
解释：
在本例中，车能够吃掉所有的卒。

示例 2：

输入：[[".",".",".",".",".",".",".","."],[".","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",".","."],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."]]
输出：0
解释：
象阻止了车吃掉任何卒。

示例 3：

输入：[[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".","p",".",".",".","."],["p","p",".","R",".","p","B","."],[".",".",".",".",".",".",".","."],[".",".",".","B",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".",".",".",".",".","."]]
输出：3
解释： 
车可以吃掉位置 b5，d6 和 f5 的卒。

 

提示：

  1. board.length == 8
  2. board[i].length == 8
  3. board[i][j] 可以是 'R'，'.'，'B' 或 'p'
  4. 只有一个格子上存在 board[i][j] == 'R'

解法

方法一：模拟

我们先遍历棋盘，找到车的位置 $(x, y)$，然后从 $(x, y)$ 出发，向上下左右四个方向遍历：

  • 如果遇到象或者边界，那么该方向停止遍历；
  • 如果遇到卒，那么答案加一，然后该方向停止遍历；
  • 否则，继续遍历。

遍历完四个方向后，即可得到答案。

时间复杂度 $O(m \times n)$，其中 $m$ 和 $n$ 分别是棋盘的行数和列数，本题中 $m = n = 8$。空间复杂度 $O(1)$。

Python3

class Solution:
    def numRookCaptures(self, board: List[List[str]]) -> int:
        ans = 0
        dirs = (-1, 0, 1, 0, -1)
        for i in range(8):
            for j in range(8):
                if board[i][j] == "R":
                    for a, b in pairwise(dirs):
                        x, y = i, j
                        while 0 <= x + a < 8 and 0 <= y + b < 8:
                            x, y = x + a, y + b
                            if board[x][y] == "p":
                                ans += 1
                                break
                            if board[x][y] == "B":
                                break
        return ans

Java

class Solution {
    public int numRookCaptures(char[][] board) {
        int ans = 0;
        int[] dirs = {-1, 0, 1, 0, -1};
        for (int i = 0; i < 8; ++i) {
            for (int j = 0; j < 8; ++j) {
                if (board[i][j] == 'R') {
                    for (int k = 0; k < 4; ++k) {
                        int x = i, y = j;
                        int a = dirs[k], b = dirs[k + 1];
                        while (x + a >= 0 && x + a < 8 && y + b >= 0 && y + b < 8
                            && board[x + a][y + b] != 'B') {
                            x += a;
                            y += b;
                            if (board[x][y] == 'p') {
                                ++ans;
                                break;
                            }
                        }
                    }
                }
            }
        }
        return ans;
    }
}

C++

class Solution {
public:
    int numRookCaptures(vector<vector<char>>& board) {
        int ans = 0;
        int dirs[5] = {-1, 0, 1, 0, -1};
        for (int i = 0; i < 8; ++i) {
            for (int j = 0; j < 8; ++j) {
                if (board[i][j] == 'R') {
                    for (int k = 0; k < 4; ++k) {
                        int x = i, y = j;
                        int a = dirs[k], b = dirs[k + 1];
                        while (x + a >= 0 && x + a < 8 && y + b >= 0 && y + b < 8 && board[x + a][y + b] != 'B') {
                            x += a;
                            y += b;
                            if (board[x][y] == 'p') {
                                ++ans;
                                break;
                            }
                        }
                    }
                }
            }
        }
        return ans;
    }
};

Go

func numRookCaptures(board [][]byte) (ans int) {
	dirs := [5]int{-1, 0, 1, 0, -1}
	for i := 0; i < 8; i++ {
		for j := 0; j < 8; j++ {
			if board[i][j] == 'R' {
				for k := 0; k < 4; k++ {
					x, y := i, j
					a, b := dirs[k], dirs[k+1]
					for x+a >= 0 && x+a < 8 && y+b >= 0 && y+b < 8 && board[x+a][y+b] != 'B' {
						x, y = x+a, y+b
						if board[x][y] == 'p' {
							ans++
							break
						}
					}
				}
			}
		}
	}
	return
}