PAT/source/html/b1001.html

害死人不偿命的(3n+1)猜想
<div class="ques-view"><p>卡拉兹(Callatz)猜想：</p>
<p>对任何一个正整数 <span class="katex"><span class="katex-mathml"><math><mrow><mi>n</mi></mrow>n</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span></span></span></span>，如果它是偶数，那么把它砍掉一半；如果它是奇数，那么把 <span class="katex"><span class="katex-mathml"><math><mrow><mo>(</mo><mn>3</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow>(3n+1)</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mopen">(</span><span class="mord mathrm">3</span><span class="mord mathit">n</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mclose">)</span></span></span></span> 砍掉一半。这样一直反复砍下去，最后一定在某一步得到 <span class="katex"><span class="katex-mathml"><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow>n=1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span><span class="mrel">=</span><span class="mord mathrm">1</span></span></span></span>。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 <span class="katex"><span class="katex-mathml"><math><mrow><mo>(</mo><mn>3</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow>(3n+1)</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mopen">(</span><span class="mord mathrm">3</span><span class="mord mathit">n</span><span class="mbin">+</span><span class="mord mathrm">1</span><span class="mclose">)</span></span></span></span>，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 <span class="katex"><span class="katex-mathml"><math><mrow><mi>n</mi></mrow>n</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span></span></span></span>，简单地数一下，需要多少步（砍几下）才能得到 <span class="katex"><span class="katex-mathml"><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow>n=1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span><span class="mrel">=</span><span class="mord mathrm">1</span></span></span></span>？</p>
<h3 id="-">输入格式：</h3>
<p>每个测试输入包含 1 个测试用例，即给出正整数 <span class="katex"><span class="katex-mathml"><math><mrow><mi>n</mi></mrow>n</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span></span></span></span> 的值。</p>
<h3 id="-">输出格式：</h3>
<p>输出从 <span class="katex"><span class="katex-mathml"><math><mrow><mi>n</mi></mrow>n</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span></span></span></span> 计算到 1 需要的步数。</p>
<h3 id="-">输入样例：</h3>
<pre><code class="lang-in">3
</code></pre>
<h3 id="-">输出样例：</h3>
<pre><code class="lang-out">5
</code></pre>
</div>