1958.检查操作是否合法

【LetMeFly】1958.检查操作是否合法：8个方向分别遍历

力扣题目链接：https://leetcode.cn/problems/check-if-move-is-legal/

给你一个下标从 0 开始的 8 x 8 网格 board ，其中 board[r][c] 表示游戏棋盘上的格子 (r, c) 。棋盘上空格用 '.' 表示，白色格子用 'W' 表示，黑色格子用 'B' 表示。

游戏中每次操作步骤为：选择一个空格子，将它变成你正在执行的颜色（要么白色，要么黑色）。但是，合法 操作必须满足：涂色后这个格子是 好线段的一个端点 （好线段可以是水平的，竖直的或者是对角线）。

好线段 指的是一个包含 三个或者更多格子（包含端点格子）的线段，线段两个端点格子为 同一种颜色 ，且中间剩余格子的颜色都为 另一种颜色 （线段上不能有任何空格子）。你可以在下图找到好线段的例子：

给你两个整数 rMove 和 cMove 以及一个字符 color ，表示你正在执行操作的颜色（白或者黑），如果将格子 (rMove, cMove) 变成颜色 color 后，是一个 合法 操作，那么返回 true ，如果不是合法操作返回 false 。

 

示例 1：

输入：board = [[".",".",".","B",".",".",".","."],[".",".",".","W",".",".",".","."],[".",".",".","W",".",".",".","."],[".",".",".","W",".",".",".","."],["W","B","B",".","W","W","W","B"],[".",".",".","B",".",".",".","."],[".",".",".","B",".",".",".","."],[".",".",".","W",".",".",".","."]], rMove = 4, cMove = 3, color = "B"
输出：true
解释：'.'，'W' 和 'B' 分别用颜色蓝色，白色和黑色表示。格子 (rMove, cMove) 用 'X' 标记。
以选中格子为端点的两个好线段在上图中用红色矩形标注出来了。

示例 2：

输入：board = [[".",".",".",".",".",".",".","."],[".","B",".",".","W",".",".","."],[".",".","W",".",".",".",".","."],[".",".",".","W","B",".",".","."],[".",".",".",".",".",".",".","."],[".",".",".",".","B","W",".","."],[".",".",".",".",".",".","W","."],[".",".",".",".",".",".",".","B"]], rMove = 4, cMove = 4, color = "W"
输出：false
解释：虽然选中格子涂色后，棋盘上产生了好线段，但选中格子是作为中间格子，没有产生以选中格子为端点的好线段。

 

提示：

• board.length == board[r].length == 8
• 0 <= rMove, cMove < 8
• board[rMove][cMove] == '.'
• color 要么是 'B' 要么是 'W' 。

解题方法：8个方向分别模拟

本题编号1958。

思路

从修改位置开始向8个方向分别模拟，一旦某个方向符合“好线段”则返回true，全部模拟完未返回则返回false。

对于某个方向，要确保：

1. 下一个格子是反色
2. 之后的格子中，在遇到空格之前，遇到同色

具体细节

1. 颜色的反色：color ^ 'W' ^ 'B'（这是因为两个相同值异或结果为0，0异或一个数结果为这个数）；
2. 其实可以不用真的修改rMove, cMove这个格子的颜色。

时空复杂度

• 时间复杂度$O(CD)$。其中格子大小是$C\times C$，$C=8$；方向个数是$D$，$D=8$。
• 空间复杂度$O(1)$

AC代码

C++

const int directions[8][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};
class Solution {
private:
    inline bool inBorad(int x, int y) {
        return x >= 0 && x < 8 && y >= 0 && y < 8;
    }
public:
    bool checkMove(vector<vector<char>>& board, int rMove, int cMove, char color) {
        board[rMove][cMove] = color;
        for (int d = 0; d < 8; d++) {
            int x = rMove, y = cMove;
            int dx = directions[d][0], dy = directions[d][1];
            x += dx, y += dy;
            if (!inBorad(x, y)) {
                continue;
            }
            if (board[x][y] != (color ^ 'B' ^ 'W')) {
                continue;
            }
            while (inBorad(x + dx, y + dy)) {
                x = x + dx, y = y + dy;
                if (board[x][y] == color) {
                    return true;
                }
                if (board[x][y] == '.') {
                    break;
                }
            }
        }
        return false;
    }
};

/*
..W.BWWB
BW.W.WBB
.WBWW.WW
WW.W..BB
BWBBWWB.
W.W..BWW
B.BB..BB
.W.W.W.W

5 4 W
*/

Go

package main

func inBoard(x int, y int) bool {
    return 0 <= x && x < 8 && 0 <= y && y < 8
}

func checkMove(board [][]byte, rMove int, cMove int, color byte) bool {
    directions := []struct{x, y int}{{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1}}
    for _, thisDirection := range directions {
        dx, dy := thisDirection.x, thisDirection.y
        x, y := rMove + dx, cMove + dy
        if !inBoard(x, y) || board[x][y] == '.' || board[x][y] == color {
            continue
        }
        for inBoard(x + dx, y + dy) {
            x, y = x + dx, y + dy
            if board[x][y] == color {
                return true
            }
            if board[x][y] == '.' {
                break
            }
        }
    }
    return false
}

Java

class Solution {
    private static final int[][] directions = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};

    private boolean inBoard(int x, int y) {
        return x >= 0 && x < 8 && y >= 0 && y < 8;
    }

    public boolean checkMove(char[][] board, int rMove, int cMove, char color) {
        for (int d = 0; d < 8; d++) {
            int dx = directions[d][0], dy = directions[d][1];
            int x = rMove + dx, y = cMove + dy;
            if (!inBoard(x, y) || board[x][y] == '.' || board[x][y] == color) {
                continue;
            }
            while (inBoard(x + dx, y + dy)) {
                x = x + dx;
                y = y + dy;
                if (board[x][y] == color) {
                    return true;
                }
                if (board[x][y] == '.') {
                    break;
                }
            }
        }
        return false;
    }
}

Python

from typing import List

DIRECTIONS = [[0, 1], [0, -1], [1, 0], [-1, 0], [1, 1], [1, -1], [-1, 1], [-1, -1]]

class Solution:
    def inBoard(self, x: int, y: int) -> bool:
        return 0 <= x < 8 and 0 <= y < 8
    
    def checkMove(self, board: List[List[str]], rMove: int, cMove: int, color: str) -> bool:
        board[rMove][cMove] = color  # 其实不真的修改也没问题
        for tx, ty in DIRECTIONS:
            x, y = rMove + tx, cMove + ty
            if not self.inBoard(x, y):
                continue
            if board[x][y] == color or board[x][y] == '.':
                continue
            while self.inBoard(x + tx, y + ty):
                x, y = x + tx, y + ty
                if board[x][y] == color:
                    return True
                if board[x][y] == '.':
                    break
        return False

同步发文于CSDN和我的个人博客，原创不易，转载经作者同意后请附上原文链接哦~

Tisfy：https://letmefly.blog.csdn.net/article/details/140249215