794. Valid Tic-Tac-Toe State

Description

Given a Tic-Tac-Toe board as a string array board, return true if and only if it is possible to reach this board position during the course of a valid tic-tac-toe game.

The board is a 3 x 3 array that consists of characters ' ', 'X', and 'O'. The ' ' character represents an empty square.

Here are the rules of Tic-Tac-Toe:

• Players take turns placing characters into empty squares ' '.
• The first player always places 'X' characters, while the second player always places 'O' characters.
• 'X' and 'O' characters are always placed into empty squares, never filled ones.
• The game ends when there are three of the same (non-empty) character filling any row, column, or diagonal.
• The game also ends if all squares are non-empty.
• No more moves can be played if the game is over.

 

Example 1:

Input: board = ["O  ","   ","   "]
Output: false
Explanation: The first player always plays "X".

Example 2:

Input: board = ["XOX"," X ","   "]
Output: false
Explanation: Players take turns making moves.

Example 3:

Input: board = ["XOX","O O","XOX"]
Output: true

 

Constraints:

• board.length == 3
• board[i].length == 3
• board[i][j] is either 'X', 'O', or ' '.

Solutions

Solution 1

Python3JavaC++GoJavaScript

class Solution:
    def validTicTacToe(self, board: List[str]) -> bool:
        def win(x):
            for i in range(3):
                if all(board[i][j] == x for j in range(3)):
                    return True
                if all(board[j][i] == x for j in range(3)):
                    return True
            if all(board[i][i] == x for i in range(3)):
                return True
            return all(board[i][2 - i] == x for i in range(3))

        x = sum(board[i][j] == 'X' for i in range(3) for j in range(3))
        o = sum(board[i][j] == 'O' for i in range(3) for j in range(3))
        if x != o and x - 1 != o:
            return False
        if win('X') and x - 1 != o:
            return False
        return not (win('O') and x != o)

class Solution {
    private String[] board;

    public boolean validTicTacToe(String[] board) {
        this.board = board;
        int x = count('X'), o = count('O');
        if (x != o && x - 1 != o) {
            return false;
        }
        if (win('X') && x - 1 != o) {
            return false;
        }
        return !(win('O') && x != o);
    }

    private boolean win(char x) {
        for (int i = 0; i < 3; ++i) {
            if (board[i].charAt(0) == x && board[i].charAt(1) == x && board[i].charAt(2) == x) {
                return true;
            }
            if (board[0].charAt(i) == x && board[1].charAt(i) == x && board[2].charAt(i) == x) {
                return true;
            }
        }
        if (board[0].charAt(0) == x && board[1].charAt(1) == x && board[2].charAt(2) == x) {
            return true;
        }
        return board[0].charAt(2) == x && board[1].charAt(1) == x && board[2].charAt(0) == x;
    }

    private int count(char x) {
        int cnt = 0;
        for (var row : board) {
            for (var c : row.toCharArray()) {
                if (c == x) {
                    ++cnt;
                }
            }
        }
        return cnt;
    }
}

class Solution {
public:
    bool validTicTacToe(vector<string>& board) {
        auto count = [&](char x) {
            int ans = 0;
            for (auto& row : board)
                for (auto& c : row) ans += c == x;
            return ans;
        };
        auto win = [&](char x) {
            for (int i = 0; i < 3; ++i) {
                if (board[i][0] == x && board[i][1] == x && board[i][2] == x) return true;
                if (board[0][i] == x && board[1][i] == x && board[2][i] == x) return true;
            }
            if (board[0][0] == x && board[1][1] == x && board[2][2] == x) return true;
            return board[0][2] == x && board[1][1] == x && board[2][0] == x;
        };
        int x = count('X'), o = count('O');
        if (x != o && x - 1 != o) return false;
        if (win('X') && x - 1 != o) return false;
        return !(win('O') && x != o);
    }
};

func validTicTacToe(board []string) bool {
    var x, o int
    for _, row := range board {
        for _, c := range row {
            if c == 'X' {
                x++
            } else if c == 'O' {
                o++
            }
        }
    }
    win := func(x byte) bool {
        for i := 0; i < 3; i++ {
            if board[i][0] == x && board[i][1] == x && board[i][2] == x {
                return true
            }
            if board[0][i] == x && board[1][i] == x && board[2][i] == x {
                return true
            }
        }
        if board[0][0] == x && board[1][1] == x && board[2][2] == x {
            return true
        }
        return board[0][2] == x && board[1][1] == x && board[2][0] == x
    }
    if x != o && x-1 != o {
        return false
    }
    if win('X') && x-1 != o {
        return false
    }
    return !(win('O') && x != o)
}

/**
 * @param {string[]} board
 * @return {boolean}
 */
var validTicTacToe = function (board) {
    function count(x) {
        let cnt = 0;
        for (const row of board) {
            for (const c of row) {
                cnt += c == x;
            }
        }
        return cnt;
    }
    function win(x) {
        for (let i = 0; i < 3; ++i) {
            if (board[i][0] == x && board[i][1] == x && board[i][2] == x) {
                return true;
            }
            if (board[0][i] == x && board[1][i] == x && board[2][i] == x) {
                return true;
            }
        }
        if (board[0][0] == x && board[1][1] == x && board[2][2] == x) {
            return true;
        }
        return board[0][2] == x && board[1][1] == x && board[2][0] == x;
    }
    const [x, o] = [count('X'), count('O')];
    if (x != o && x - 1 != o) {
        return false;
    }
    if (win('X') && x - 1 != o) {
        return false;
    }
    return !(win('O') && x != o);
};

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