794. Valid Tic-Tac-Toe State

A Tic-Tac-Toe board is given 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, and 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 3 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 = ["XXX", "   ", "OOO"]
Output: false
 
Example 4:
Input: board = ["XOX", "O O", "XOX"]
Output: true

Note:

• board is a length-3 array of strings, where each string board[i] has length 3.
• Each board[i][j] is a character in the set {" ", "X", "O"}.

Approach  #1: Simulate. [Java]

class Solution {
    public boolean validTicTacToe(String[] board) {
        int numX = 0;
        int numO = 0;
        for (String str : board) {
            for (int i = 0; i < str.length(); ++i) {
                if (str.charAt(i) == 'X') numX++;
                else if (str.charAt(i) == 'O') numO++;
            }
        }
        if (numO > numX) return false;   // ["O  ", "   ", "   "]
        if (numX > numO+1) return false; // ["XOX", " X ", "   "]
        if (gameOver(board, 'X') && numX == numO) return false; // ["XXX", "   ", "OOO"]
        if (gameOver(board, 'O') && numX > numO) return false;  // ["OXX","XOX","OXO"]
 
        return true;
    }
 
    private boolean gameOver(String[] board, char c) {
        char[][] charArr = new char[3][3];
        for (int i = 0; i < 3; ++i) {
            for (int j = 0; j < 3; ++j) {
                charArr[i][j] = board[i].charAt(j);
            }
        }
        // top
        if (charArr[0][1] == c && charArr[0][0] == c && charArr[0][2] == c)
            return true;
 
        // bottom
        if (charArr[1][1] == c && charArr[1][0] == c && charArr[1][2] == c)
            return true;
 
        // left
        if (charArr[1][0] == c && charArr[0][0] == c && charArr[2][0] == c)
            return true;
 
        // right
        if (charArr[1][2] == c && charArr[0][2] == c && charArr[2][2] == c)
            return true;
 
        // center
        if (charArr[1][1] == c && charArr[0][1] == c && charArr[2][1] == c)
            return true;
        if (charArr[1][1] == c && charArr[1][0] == c && charArr[1][2] == c)
            return true;
        if (charArr[1][1] == c && charArr[0][2] == c && charArr[2][0] == c)
            return true;
        if (charArr[1][1] == c && charArr[0][0] == c && charArr[2][2] == c)
            return true;
 
        return false;
    }
}