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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

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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)

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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