第6-3课：博弈树与井字棋（Tic-Tac-Toe）
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第6-3课：博弈树与井字棋（Tic-Tac-Toe）
上一课简单介绍了博弈树，从编程实现算法的角度看，博弈树是三种树中最简单的一种，无论是原理还是实现都不复杂。这一课，我们就以简单的井字棋（Tic-Tac-Toe）游戏为例，介绍一下如何用博弈树实现一个简单的井字棋 AI，最后的结果并不复杂，我希望大家把关注点放在如何设计数据模型、如何确定落子，以及将博弈树的理论应用到具体的问题等这样的过程上，而不是最后的结果。
Tic-Tac-Toe——规则简单的博弈
小时候，我不知道这游戏的真名是 Tic-Tac-Toe，只知道无聊的时候，和小伙伴们找块沙地，用小树枝画个井字就可以玩半天。井字棋总体来说没什么难度，只要稍微动动脑，两个人玩基本上都是平局，现在想想也没啥意思，但正因为井字棋规则非常简单，所以适合用来做博弈树算法讲解的例子。
这一课的重点依然是实现过程，也就是说如何将博弈树的理论应用到一个简单的游戏实现中，将上一课介绍的算法伪代码翻译成具体的算法实现。
棋盘与棋子的数学模型
井字棋游戏的棋盘类似一个 3 × 3 的九宫格形状，直观上很容易想到用一个 3 × 3 的二维数组表示棋盘，二维数组每个元素的值代表棋盘上对应位置的状态，有三种，分别是空、O 型棋子或 X 型棋子。使用二维数组的好处是数据访问比较直观，二维数组的两个下标可以直接表示棋子的位置，但缺点也很明显，首先是遍历棋盘需要用两重循环处理两个下标，其次是行、列以及斜线方向上都要做是否满足三点连线的判断，根据行、列和斜线的下标变化特点，需要用几套不同的方法处理。
我之前多次说过，很多高效的棋类游戏都用一维数组建模，这一课用井字棋游戏
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