# 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

• 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);
}
};

• 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)


• 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);
};