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<a href="/2019/08/09/%E3%80%8A%E7%BC%96%E7%A8%8B%E7%8F%A0%E7%8E%91-%E7%AC%AC2%E7%89%88-%E3%80%8B-%E7%AC%AC%E4%B8%80%E7%AB%A0/" class="post-title-link" itemprop="url">《编程珠玑(第2版)》 第一章</a>
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<time title="创建时间：2019-08-09 20:45:54" itemprop="dateCreated datePublished" datetime="2019-08-09T20:45:54+08:00">2019-08-09</time>
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<a href="/categories/%E7%BC%96%E7%A8%8B%E7%8F%A0%E7%8E%91/" itemprop="url" rel="index"><span itemprop="name">编程珠玑</span></a>
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<h2 id="背景"><a href="#背景" class="headerlink" title="背景"></a>背景</h2><p>近日正在阅读《编程珠玑(第2版)》，希望自己能有所收获。《编程珠玑》的内容丰富，每章的后面都有一定量的习题。这篇文章不是为了记录习题的答案而写，仅仅会包含我在学习中觉得对自己有帮助和我觉得有趣的内容。</p>
<h2 id="问题描述"><a href="#问题描述" class="headerlink" title="问题描述"></a>问题描述</h2><p><strong>输入</strong><br>一个最多包含n个正整数的文件，每个数都小于n，其中$n = 10^7$。如果在输入文件中有任何整数重复出现就是致命错误。没有其他数据与该整数相关联。</p>
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<h1 id="200-岛屿的个数"><a href="#200-岛屿的个数" class="headerlink" title="200. 岛屿的个数"></a>200. 岛屿的个数</h1><p>给定一个由 ‘1’（陆地）和 ‘0’（水）组成的的二维网格，计算岛屿的数量。一个岛被水包围，并且它是通过水平方向或垂直方向上相邻的陆地连接而成的。你可以假设网格的四个边均被水包围。</p>
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<p>卡拉兹(Callatz)猜想：</p>
<p>对任何一个正整数 n，如果它是偶数，那么把它砍掉一半；如果它是奇数，那么把 (3n+1) 砍掉一半。这样一直反复砍下去，最后一定在某一步得到 n=1。卡拉兹在 1950 年的世界数学家大会上公布了这个猜想，传说当时耶鲁大学师生齐动员，拼命想证明这个貌似很傻很天真的命题，结果闹得学生们无心学业，一心只证 (3n+1)，以至于有人说这是一个阴谋，卡拉兹是在蓄意延缓美国数学界教学与科研的进展……</p>
<p>我们今天的题目不是证明卡拉兹猜想，而是对给定的任一不超过 1000 的正整数 n，简单地数一下，需要多少步（砍几下）才能得到 n=1？</p>
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