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1958. 检查操作是否合法

题目描述

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' 。

解法

方法一：枚举

思考

合法落子需在某一方向上形成「本色—对方若干—本色」的好线段。棋盘 \(8\times 8\)，八个方向各走一遍即可。

自落点沿方向前进，统计步数；途中遇到空格或提前遇到本色则该方向失败，步数大于 \(1\) 且碰到本色则成功。

无需真的翻转棋子。

我们枚举所有可能的方向，对于每个方向 \((a, b)\)，我们从 \((\textit{rMove}, \textit{cMove})\) 出发，用一个变量 \(\textit{cnt}\) 记录我们走过的格子数，如果我们在走的过程中遇到了颜色为 \(\textit{color}\) 的格子，且 \(\textit{cnt} > 1\)，那么我们就找到了一个好线段，返回 \(\textit{true}\)。

枚举结束后，如果我们没有找到任何好线段，那么返回 \(\textit{false}\)。

时间复杂度 \(O(m + n)\)，其中 \(m\) 为 \(\textit{board}\) 的行数，而 \(n\) 为 \(\textit{board}\) 的列数，本题中 \(m = n = 8\)。空间复杂度 \(O(1)\)。

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class Solution:
    def checkMove(
        self, board: List[List[str]], rMove: int, cMove: int, color: str
    ) -> bool:
        for a in range(-1, 2):
            for b in range(-1, 2):
                if a == 0 and b == 0:
                    continue
                i, j = rMove, cMove
                cnt = 0
                while 0 <= i + a < 8 and 0 <= j + b < 8:
                    cnt += 1
                    i, j = i + a, j + b
                    if cnt > 1 and board[i][j] == color:
                        return True
                    if board[i][j] in (color, "."):
                        break
        return False

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class Solution {
    public boolean checkMove(char[][] board, int rMove, int cMove, char color) {
        for (int a = -1; a <= 1; ++a) {
            for (int b = -1; b <= 1; ++b) {
                if (a == 0 && b == 0) {
                    continue;
                }
                int i = rMove, j = cMove;
                int cnt = 0;
                while (0 <= i + a && i + a < 8 && 0 <= j + b && j + b < 8) {
                    i += a;
                    j += b;
                    if (++cnt > 1 && board[i][j] == color) {
                        return true;
                    }
                    if (board[i][j] == color || board[i][j] == '.') {
                        break;
                    }
                }
            }
        }
        return false;
    }
}

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class Solution {
public:
    bool checkMove(vector<vector<char>>& board, int rMove, int cMove, char color) {
        for (int a = -1; a <= 1; ++a) {
            for (int b = -1; b <= 1; ++b) {
                if (a == 0 && b == 0) {
                    continue;
                }
                int i = rMove, j = cMove;
                int cnt = 0;
                while (0 <= i + a && i + a < 8 && 0 <= j + b && j + b < 8) {
                    i += a;
                    j += b;
                    if (++cnt > 1 && board[i][j] == color) {
                        return true;
                    }
                    if (board[i][j] == color || board[i][j] == '.') {
                        break;
                    }
                }
            }
        }
        return false;
    }
};

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func checkMove(board [][]byte, rMove int, cMove int, color byte) bool {
    for a := -1; a <= 1; a++ {
        for b := -1; b <= 1; b++ {
            if a == 0 && b == 0 {
                continue
            }
            i, j := rMove, cMove
            cnt := 0
            for 0 <= i+a && i+a < 8 && 0 <= j+b && j+b < 8 {
                i += a
                j += b
                cnt++
                if cnt > 1 && board[i][j] == color {
                    return true
                }
                if board[i][j] == color || board[i][j] == '.' {
                    break
                }
            }
        }
    }
    return false
}

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function checkMove(board: string[][], rMove: number, cMove: number, color: string): boolean {
    for (let a = -1; a <= 1; ++a) {
        for (let b = -1; b <= 1; ++b) {
            if (a === 0 && b === 0) {
                continue;
            }
            let [i, j] = [rMove, cMove];
            let cnt = 0;
            while (0 <= i + a && i + a < 8 && 0 <= j + b && j + b < 8) {
                i += a;
                j += b;
                if (++cnt > 1 && board[i][j] === color) {
                    return true;
                }
                if (board[i][j] === color || board[i][j] === '.') {
                    break;
                }
            }
        }
    }
    return false;
}

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