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class="container" id="main-content" tabindex="-1"><div class="post"><article class="post-block h-entry"><div class="post-meta p-author h-card visually-hidden"><img class="author-avatar u-photo" src="../favicon.png" alt="Cytrogen"><span class="p-name">Cytrogen</span><a class="u-url" href="https://cytrogen.icu">https://cytrogen.icu</a></div><a class="post-permalink u-url u-uid visually-hidden" href="https://cytrogen.icu/posts/9408.html">永久链接</a><div class="p-summary visually-hidden"><p>想必大家都有玩过「扫雷」这款游戏，尤其是经历过 Windows 早年版本时代的人们，在计算机的开始菜单里找了半天，好不容易找到「游戏」文件夹，里面赫然躺着一个应用程序。双击打开，看到一个黄黄的微笑，心想这游戏肯定很简单吧！然后便被炸弹炸死。</p></div><div class="visually-hidden"><a class="p-category" href="../categories/%E6%B8%B8%E6%88%8F%E8%AF%B4%E6%98%8E/">游戏说明</a><a class="p-category" href="../tags/%E6%89%AB%E9%9B%B7/">扫雷</a></div><a class="u-syndication visually-hidden" target="_blank" rel="noopener" href="https://m.otter.homes/@Cytrogen/116076986398086371">https://m.otter.homes/@Cytrogen/116076986398086371</a><h1 class="post-title p-name">用笑脸玩扫雷</h1><div class="post-info"><time class="post-date dt-published" datetime="2026-02-14T05:00:00.000Z">2/14/2026</time><time class="dt-updated visually-hidden" datetime="2026-02-19T07:42:07.357Z"></time></div><div class="post-content e-content"><html><head></head><body><p>想必大家都有玩过「扫雷」这款游戏，尤其是经历过 Windows 早年版本时代的人们，在计算机的开始菜单里找了半天，好不容易找到「游戏」文件夹，里面赫然躺着一个应用程序。双击打开，看到一个黄黄的微笑，心想这游戏肯定很简单吧！然后便被炸弹炸死。</p>
<span id="more"></span>
<p><img src="/posts/9408/start.png" alt=""></p>
<p>好吧，这游戏到底该怎么玩呢？首先，你可以点开一个网格，看看下面有没有雷，就像是现实生活中挖雷一般。你可以右键给一个网格插上旗子，标记该网格，假设它底下有雷。</p>
<p>那就点开一个网格看看吧！</p>
<p><img src="/posts/9408/first_click.png" alt=""></p>
<p>看来我们挖出了一个大区域。其中没有数字的网格，代表它的周围（即相邻的八个格子）没有雷；有数字的网格，上面的数字代表周围存在多少个雷，例如 1 就是相邻的格子里有 1 个雷、2 就是相邻的格子里有 2 个雷……</p>
<p>知道了这一条规则后，我们可以快速锁定这些 1 们：因为它们的周围只有 1 个格子，也只有 1 个雷，那么雷到底在哪里，很显而易见了吧~</p>
<p><img src="/posts/9408/eight_ones.png" alt=""></p>
<p>给这些定有雷的格子插上旗后，我们可以进一步推测出，旁边的 1 的雷已经被找到了，那么它们的周围就不可能再有其他雷 —— 全部挖开！</p>
<p>持续做下去后，很快你便会发现，已经没有可以用这种推理方法挖开或者插旗的格子了。当然，这不意味着扫雷无法再继续进行下去，只是我们还没有明白该游戏的本质。</p>
<p>扫雷的核心逻辑在于「公共区域的控制权」。什么是公共区域？当两个数字相邻时，它们周围的一圈格子在中间部分一定是重叠的。除了这片公共区域，它们又各自拥有属于自己的一小块独占区域。</p>
<p>假设我们决定观察这两个相邻的数字：M 和 N。M 周围有 M 个雷，N 周围也有 N 个雷，它们中间夹着的几个格子是它们共同拥有的。无论这些公共格子通过什么方式排列雷，它们对 M 和 N 的贡献是一样的。如果 M 是 1，N 也是 1，意味着 M 需要在它的视野里找到 1 颗雷，N 也需要找到 1 颗雷 —— 因为 M 通过公共区域得到了满足，那么 N 作为邻居，自然也得到了满足。如果此时 N 还有额外的独占区域格子，那么格子必然不能有雷，否则 N 周围的雷数就会超标。</p>
<p>明白了这些后，恭喜你，你理解了扫雷游戏里的「1-1」定式！</p>
<p>接着我们用这个逻辑去理解「1-2」定式。想象这么一个场景，M 是 1，N 是 2。这意味着公共区域内最多只能有 1 颗雷，绝对不能再多。既然最多只能有 1 颗雷，那么 N 的最后那颗雷哪里来？答案是在 N 的独占区域内。也就是说，我们可以通过减法公式 N - M = 1，来得出答案 1 颗雷必然存在于大数字的独占区域内。</p>
<p>再来看「1-2-1」定式。我们这里使用 M = 1、N = 2、O = 1 来代表这个场景。假设我们把雷放在 N 的正下方，这颗雷会同时被 M、N、O 看到，且同时满足 M 和 O 的条件。可是，中间的 N 还差 1 颗雷。但这颗雷没有地方放了，因为如果再在任何地方放雷，左右两边的 1 就会变成 2，也就违背了已知条件。所以，结论只有一个：中间那个公共格子绝对不能有雷。既然中间不能有雷，为了满足中间的 2，雷只能被迫分布在两个 1 的下方。也就是说，「1-2-1」是一个硬性定式，只要看到了就可以断定两个 1 下面有雷，而 2 的下面没有。</p>
<p><img src="/posts/9408/one-two-one.png" alt=""></p>
<p>如果将两个「1-2」叠加起来，我们能得到「1-2-2-1」定式。左边的「1-2」结构意味着，为了补足 2 的雷数，最左边的雷必须在 2 的独占区域。同理，右边的「2-1」结构意味着最右边的雷也必须在 2 的独占区域。这样一来，两个 2 外侧的雷都确定了。现在只需要找到公共区域的雷。由于它们原本都是 2，现在各减去确定的 1 颗，剩下的需求便变成了「1-1」的局面。</p>
<p>根据前面提到的「1-1」逻辑，中间往往是安全的，或者雷的分布是对称的。结果便是，两头的 1 下面有雷，中间的两个 2 下面往往可以挖开。不过该定式需要取决于雷的具体排列，不过逻辑核心依然是先确定外侧的必然雷。</p>
<p>其实，这些定式本质上都是数个「1-1」或者「1-2」组成的，只要理解底层逻辑，都可以通过这些减法公式来判断雷的位置。但是呢，在实际的中盘博弈中，数字周围通常已经插上了旗帜。如果不扣除这些已知的雷，直接套用减法公式，新手容易将实质上的「1-2」误判为「2-2」或者「3-3」等对称局面，从而得出完全相反的安全结论并导致踩雷。</p>
<p>过去我为作业写过 <a target="_blank" rel="noopener" href="https://github.com/Cytrogen/CS50AI_2023/blob/main/minesweeper/minesweeper.py">一个简单的扫雷 AI</a>。因为对该游戏的不熟悉，代码里并没有赋予 AI 处理任何需要综合判断的局面的能力。这对我们而言也是同样的，如果只是随便将定式套在数字上，而没有考虑到更为综合的情况的话，得到的可能就是一个爆炸的雷，和一个死掉的小黄脸了。</p>
<p>该文章仅讲述扫雷游戏的入门玩法，参考 <a target="_blank" rel="noopener" href="https://zhuanlan.zhihu.com/p/27550382">该文章</a>，想要更多了解的也请阅读该文章。</p>
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