0794. Valid Tic Tac Toe State

794. Valid Tic-Tac-Toe State #

题目 #

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:

https://assets.leetcode.com/uploads/2021/05/15/tictactoe1-grid.jpg

Input: board = ["O  ","   ","   "]
Output: false
Explanation: The first player always plays "X".

Example 2:

https://assets.leetcode.com/uploads/2021/05/15/tictactoe2-grid.jpg

Input: board = ["XOX"," X ","   "]
Output: false
Explanation: Players take turns making moves.

Example 3:

https://assets.leetcode.com/uploads/2021/05/15/tictactoe3-grid.jpg

Input: board = ["XXX","   ","OOO"]
Output: false

Example 4:

https://assets.leetcode.com/uploads/2021/05/15/tictactoe4-grid.jpg

Input: board = ["XOX","O O","XOX"]
Output: true

Constraints:

  • board.length == 3
  • board[i].length == 3
  • board[i][j] is either ‘X’, ‘O’, or ' ‘.

题目大意 #

给你一个字符串数组 board 表示井字游戏的棋盘。当且仅当在井字游戏过程中,棋盘有可能达到 board 所显示的状态时,才返回 true 。

井字游戏的棋盘是一个 3 x 3 数组,由字符 ' ‘,‘X’ 和 ‘O’ 组成。字符 ' ' 代表一个空位。

以下是井字游戏的规则:

  • 玩家轮流将字符放入空位(’ ‘)中。
  • 玩家 1 总是放字符 ‘X’ ,而玩家 2 总是放字符 ‘O’ 。
  • ‘X’ 和 ‘O’ 只允许放置在空位中,不允许对已放有字符的位置进行填充。
  • 当有 3 个相同(且非空)的字符填充任何行、列或对角线时,游戏结束。
  • 当所有位置非空时,也算为游戏结束。
  • 如果游戏结束,玩家不允许再放置字符。

解题思路 #

分类模拟:

  • 根据题意棋盘在任意时候,要么 X 的数量比 O 的数量多 1,要么两者相等
  • X 的数量等于 O 的数量时,任何行、列或对角线都不会出现 3 个相同的 X
  • X 的数量比 O 的数量多 1 时,任何行、列或对角线都不会出现 3 个相同的 O

代码 #

package leetcode

func validTicTacToe(board []string) bool {
	cntX, cntO := 0, 0
	for i := range board {
		for j := range board[i] {
			if board[i][j] == 'X' {
				cntX++
			} else if board[i][j] == 'O' {
				cntO++
			}
		}
	}
	if cntX < cntO || cntX > cntO+1 {
		return false
	}
	if cntX == cntO {
		return process(board, 'X')
	}
	return process(board, 'O')
}

func process(board []string, c byte) bool {
	//某一行是"ccc"
	if board[0] == string([]byte{c, c, c}) || board[1] == string([]byte{c, c, c}) || board[2] == string([]byte{c, c, c}) {
		return false
	}
	//某一列是"ccc"
	if (board[0][0] == c && board[1][0] == c && board[2][0] == c) ||
		(board[0][1] == c && board[1][1] == c && board[2][1] == c) ||
		(board[0][2] == c && board[1][2] == c && board[2][2] == c) {
		return false
	}
	//某一对角线是"ccc"
	if (board[0][0] == c && board[1][1] == c && board[2][2] == c) ||
		(board[0][2] == c && board[1][1] == c && board[2][0] == c) {
		return false
	}
	return true
}

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