Design Tic-Tac-Toe

Design

Medium

Design a Tic-tac-toe game that is played between two players on anxngrid.

You may assume the following rules:

1. A move is guaranteed to be valid and is placed on an empty block.

2. Once a winning condition is reached, no more moves is allowed.

3. A player who succeeds in placing n of their marks in a horizontal, vertical, or diagonal row wins the game.

Example:

Given n = 3, assume that player 1 is "X" and player 2 is "O" in the board.

TicTacToe toe = new TicTacToe(3);

toe.move(0, 0, 1); -> Returns 0 (no one wins)
|X| | |
| | | |    // Player 1 makes a move at (0, 0).
| | | |

toe.move(0, 2, 2); -> Returns 0 (no one wins)
|X| |O|
| | | |    // Player 2 makes a move at (0, 2).
| | | |

toe.move(2, 2, 1); -> Returns 0 (no one wins)
|X| |O|
| | | |    // Player 1 makes a move at (2, 2).
| | |X|

toe.move(1, 1, 2); -> Returns 0 (no one wins)
|X| |O|
| |O| |    // Player 2 makes a move at (1, 1).
| | |X|

toe.move(2, 0, 1); -> Returns 0 (no one wins)
|X| |O|
| |O| |    // Player 1 makes a move at (2, 0).
|X| |X|

toe.move(1, 0, 2); -> Returns 0 (no one wins)
|X| |O|
|O|O| |    // Player 2 makes a move at (1, 0).
|X| |X|

toe.move(2, 1, 1); -> Returns 1 (player 1 wins)
|X| |O|
|O|O| |    // Player 1 makes a move at (2, 1).
|X|X|X|

Follow up: Could you do better than O(n^2) permove()operation?

Could you get O(1) per move() operation?

Solution & Analysis

O(n) Time, O(n^2) Space solution

直白解法：board[][]存当前棋盘，每次move()，check横竖和两条对角线是否满足当前选手赢。

class TicTacToe {
    private char[][] board;
    private static char X = 'X';
    private static char O = 'O';
    private int size;

    /** Initialize your data structure here. */
    public TicTacToe(int n) {
        board = new char[n][n];
        size = n;
    }

    /** Player {player} makes a move at ({row}, {col}).
        @param row The row of the board.
        @param col The column of the board.
        @param player The player, can be either 1 or 2.
        @return The current winning condition, can be either:
                0: No one wins.
                1: Player 1 wins.
                2: Player 2 wins. */
    public int move(int row, int col, int player) {
        char c;
        if (player == 1) {
            c = X;
        } else {
            c = O;
        }
        if (board[row][col] != 0) {
            // throw error, occupied
            return 0;
        }
        board[row][col] = c;

        if (hasWon(row, col, size, c)) {
            return player;
        }
        return 0;
    }

    private boolean hasWon(int row, int col, int n, char c) {

        // check horizontal
        boolean rowLine = true;
        for (int i = 0; i < n; i++) {
            rowLine = rowLine && (board[i][col] == c);
        }
        // check vertical
        boolean colLine = true;
        for (int j = 0; j < n; j++) {
            colLine = colLine && (board[row][j] == c);
        }
        // check diagonal
        if (row + col == n - 1 || row == col) {
            boolean diagLine1 = true;
            boolean diagLine2 = true;
            for (int j = 0; j < n; j++) {
                diagLine1 = diagLine1 && (board[j][j] == c);
            }
            for (int j = 0; j < n; j++) {
                diagLine2 = diagLine2 && (board[n - 1 - j][j] == c);
            }
            return rowLine || colLine || diagLine1 || diagLine2;
        } else {
            return rowLine || colLine;
        }
    }
}

/**
 * Your TicTacToe object will be instantiated and called as such:
 * TicTacToe obj = new TicTacToe(n);
 * int param_1 = obj.move(row,col,player);
 */

O(1) Time, O(n) Space solution

存每一行，每一列，每一个对角线的累计值。trick在于player 1用+1, player2用 -1，这样用取累计值的绝对值就可以通过判断是否达到n来判定是否获胜。

Adapted from @bdwalker:

The key observation is that in order to win Tic-Tac-Toe you must have the entire row or column. Thus, we don't need to keep track of an entire n^2 board. We only need to keep a count for each row and column. If at any time a row or column matches the size of the board then that player has won.

To keep track of which player, I add one for Player1 and -1 for Player2. There are two additional variables to keep track of the count of the diagonals. Each time a player places a piece we just need to check the count of that row, column, diagonal and anti-diagonal.

public class TicTacToe {
    private int[] rows;
    private int[] cols;
    private int diagonal;
    private int antiDiagonal;

    /** Initialize your data structure here. */
    public TicTacToe(int n) {
        rows = new int[n];
        cols = new int[n];
    }

    /** Player {player} makes a move at ({row}, {col}).
    @param row The row of the board.
    @param col The column of the board.
    @param player The player, can be either 1 or 2.
    @return The current winning condition, can be either:
            0: No one wins.
            1: Player 1 wins.
            2: Player 2 wins. */
    public int move(int row, int col, int player) {
        int toAdd = player == 1 ? 1 : -1;

        rows[row] += toAdd;
        cols[col] += toAdd;
        if (row == col) {
            diagonal += toAdd;
        }

        if (col + row == cols.length - 1) {
            antiDiagonal += toAdd;
        }

        int size = rows.length;
        if (Math.abs(rows[row]) == size ||
            Math.abs(cols[col]) == size ||
            Math.abs(diagonal) == size  ||
            Math.abs(antiDiagonal) == size) {
            return player;
        }

        return 0;
    }
}

Not using Math.abs(), changing matching target @hot13399:

class TicTacToe {

    int[] rows, cols;
    int d1, d2, n;

    public TicTacToe(int n) {
      rows = new int[n];
      cols = new int[n];
      d1 = 0;
      d2 = 0;
      this.n = n;
    }

    public int move(int row, int col, int player) {
      int val = (player == 1) ? 1 : -1;
      int target = (player == 1) ? n : -n;

      if(row == col) { // diagonal 
        d1 += val;
        if(d1 == target) return player;
      }

      if(row + col + 1 == n) { // diagonal 
        d2 += val;
        if(d2 == target) return player;
      }

      rows[row] += val;
      cols[col] += val;

      if(rows[row] == target || cols[col] == target) return player;

      return 0;
    }
}

Reference

https://leetcode.com/problems/design-tic-tac-toe/discuss/81898/Java-O(1)-solution-easy-to-understand