【MEDIUM】Design Tic-Tac-Toe

发布于: 2018-12-20 19:56
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问题

Design a Tic-tac-toe game that is played between two players on a n x n grid.

You may assume the following rules:

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

Once a winning condition is reached, no more moves is allowed. 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(n2) per move() operation?

Hint:

Could you trade extra space such that move() operation can be done in O(1)?

You need two arrays: int rows[n], int cols[n], plus two variables: diagonal, anti_diagonal.

分析过程

  • 输入:下棋的位置
  • 输出:棋盘情况,胜负情况
  • 思路:两个选手,一个下棋时记录为 1,一个记录为 -1,判定胜负的方法为:每一行、每一列、对角线的值累加,为 n 或 -n,即游戏结束,否则游戏继续。

解决方法


class Game {
    
    var board = [[Int]]()
    
    var n: Int {
        return board.count
    }
    
    init(n: Int) {
        for _ in 0..<n {
            board.append([Int].init(repeating: 0, count: n))
        }
    }
    
    // 返回值 true 代表胜利,false 代表比赛继续
    func move(x: Int, y: Int, player: Int) -> Bool {
        board[y][x] = player
        return vaildBoard()
    }
    
    // 检查棋盘,返回 true 代表游戏结束
    internal func vaildBoard() -> Bool {
        // 扫描行
        for line in 0..<n {
            let sum = board[line].reduce(0) { $0 + $1 }
            if sum == n || sum == -n {
                return true
            }
        }
        // 扫描列
        for line in 0..<n {
            var sum = 0
            for field in 0..<n {
                sum += board[field][line]
            }
            if sum == n || sum == -n {
                return true
            }
        }
        // 扫描对角线
        var sum = 0
        for i in 0..<n {
            sum += board[i][i]
            if sum == n || sum == -n {
                return true
            }
        }
        sum = 0
        for i in 0..<n {
            sum += board[n - 1 - i][i]
            if sum == n || sum == -n {
                return true
            }
        }
        
        return false
    }
    
    // 打印棋盘
    func printBoard() {
        print(" -------")
        for line in board {
            let str = line.reduce("") { "\($0) \($1 == 0 ? "-" : $1 ==  1 ? "X" : "O")" }
            print("|\(str) |")
        }
        print(" -------")
    }
}

let game = Game.init(n: 3)
game.printBoard()
/*
 -------
| - - - |
| - - - |
| - - - |
 -------
 */

assert(game.move(x: 0, y: 0, player: 1) == false)
game.printBoard()
/*
 -------
| X - - |
| - - - |
| - - - |
 -------
 */

assert(game.move(x: 2, y: 0, player: -1) == false)
game.printBoard()
/*
 -------
| X - O |
| - - - |
| - - - |
 -------
 */

assert(game.move(x: 2, y: 2, player: 1) == false)
game.printBoard()
/*
 -------
| X - O |
| - - - |
| - - X |
 -------
 */

assert(game.move(x: 1, y: 1, player: -1) == false)
game.printBoard()
/*
 -------
| X - O |
| - O - |
| - - X |
 -------
 */

assert(game.move(x: 0, y: 2, player: 1) == false)
game.printBoard()
/*
 -------
| X - O |
| - O - |
| X - X |
 -------
 */

assert(game.move(x: 0, y: 1, player: -1) == false)
game.printBoard()
/*
 -------
| X - O |
| O O - |
| X - X |
 -------
 */

assert(game.move(x: 1, y: 2, player: 1) == true)
game.printBoard()
/*
 -------
| X - O |
| O O - |
| X X X |
 -------
 */
// 对角线 case
let game = Game.init(n: 3)
game.printBoard()
/*
 -------
| - - - |
| - - - |
| - - - |
 -------
 */

assert(game.move(x: 0, y: 0, player: 1) == false)
game.printBoard()
/*
 -------
| X - - |
| - - - |
| - - - |
 -------
 */

assert(game.move(x: 2, y: 0, player: -1) == false)
game.printBoard()
/*
 -------
| X - O |
| - - - |
| - - - |
 -------
 */

assert(game.move(x: 1, y: 1, player: 1) == false)
game.printBoard()
/*
 -------
| X - O |
| - X - |
| - - - |
 -------
 */

assert(game.move(x: 2, y: 1, player: -1) == false)
game.printBoard()
/*
 -------
| X - O |
| - X O |
| - - - |
 -------
 */

assert(game.move(x: 2, y: 2, player: 1) == true)
game.printBoard()
/*
 -------
| X - O |
| - X O |
| - - X |
 -------
 */

Thanks for reading.

All the best wishes for you! 💕