<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Python on kenji.blog</title><link>http://kenji.blog/en/tags/python/</link><description>Recent content in Python on kenji.blog</description><generator>Hugo -- gohugo.io</generator><language>en</language><copyright>kenjinote</copyright><lastBuildDate>Fri, 18 Apr 2025 00:58:11 +0900</lastBuildDate><atom:link href="http://kenji.blog/en/tags/python/index.xml" rel="self" type="application/rss+xml"/><item><title>FizzBuzz</title><link>http://kenji.blog/en/p/fizzbuzz/</link><pubDate>Fri, 18 Apr 2025 00:58:11 +0900</pubDate><guid>http://kenji.blog/en/p/fizzbuzz/</guid><description>&lt;img src="http://kenji.blog/p/fizzbuzz/img.png" alt="Featured image of post FizzBuzz" />&lt;h2 id="what-exactly-is-fizzbuzz-anyway">What exactly is FizzBuzz, anyway?
&lt;/h2>&lt;p>Hello!&lt;/p>
&lt;p>Today, I&amp;rsquo;d like to write about &amp;ldquo;FizzBuzz&amp;rdquo;.&lt;/p>
&lt;p>Whether you&amp;rsquo;re thinking, &amp;ldquo;Ah, I know that one!&amp;rdquo; or &amp;ldquo;I&amp;rsquo;ve heard of it, but don&amp;rsquo;t really get it,&amp;rdquo; please stick with me for a bit. It takes just a few minutes to read, and you might just have an &amp;ldquo;aha&amp;rdquo; moment.&lt;/p>
&lt;hr>
&lt;h3 id="is-it-true-that-youre-disqualified-as-a-programmer-if-you-cant-write-fizzbuzz">Is it true that &amp;ldquo;you&amp;rsquo;re disqualified as a programmer if you can&amp;rsquo;t write FizzBuzz&amp;rdquo;?
&lt;/h3>&lt;p>Roughly speaking, FizzBuzz looks like this.&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
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&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;span class="lnt">8
&lt;/span>&lt;span class="lnt">9
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-python" data-lang="python">&lt;span class="line">&lt;span class="cl">&lt;span class="k">for&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="ow">in&lt;/span> &lt;span class="nb">range&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">101&lt;/span>&lt;span class="p">):&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">%&lt;/span> &lt;span class="mi">15&lt;/span> &lt;span class="o">==&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s2">&amp;#34;FizzBuzz&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">elif&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">%&lt;/span> &lt;span class="mi">3&lt;/span> &lt;span class="o">==&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s2">&amp;#34;Fizz&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">elif&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">%&lt;/span> &lt;span class="mi">5&lt;/span> &lt;span class="o">==&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s2">&amp;#34;Buzz&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">else&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>Yes, this is the famous &amp;ldquo;FizzBuzz problem.&amp;rdquo;&lt;/p>
&lt;p>You go through the numbers from 1 to 100 in order,&lt;br>
if it&amp;rsquo;s a multiple of 3, print &amp;ldquo;Fizz&amp;rdquo;, if it&amp;rsquo;s a multiple of 5, print &amp;ldquo;Buzz&amp;rdquo;,&lt;br>
and if it&amp;rsquo;s a multiple of both, print &amp;ldquo;FizzBuzz.&amp;rdquo; It&amp;rsquo;s extremely simple.&lt;/p>
&lt;p>And yet, for some reason, it&amp;rsquo;s often treated like a &amp;ldquo;minimum test for programmers.&amp;rdquo; It comes up in interviews, and on social media you&amp;rsquo;ll occasionally see people flexing with comments like, &amp;ldquo;If you can&amp;rsquo;t even write FizzBuzz&amp;hellip;&amp;rdquo;&lt;/p>
&lt;p>But wait a minute.&lt;/p>
&lt;p>Can we really definitively say, &amp;ldquo;Couldn&amp;rsquo;t write FizzBuzz = can&amp;rsquo;t program&amp;rdquo;?&lt;/p>
&lt;hr>
&lt;h3 id="its-not-about-whether-you-can-do-it-but-whether-youre-in-a-state-to-do-it">It&amp;rsquo;s not about whether you can do it, but whether you&amp;rsquo;re in a &amp;ldquo;state&amp;rdquo; to do it
&lt;/h3>&lt;p>It&amp;rsquo;s true that FizzBuzz requires an understanding of syntax and basic logical thinking. So it makes sense that it&amp;rsquo;s used to &amp;ldquo;check the basics.&amp;rdquo;&lt;/p>
&lt;p>But, hear me out.&lt;/p>
&lt;p>If the environment is different, the results will be different.&lt;/p>
&lt;p>For example,&lt;/p>
&lt;ul>
&lt;li>When you&amp;rsquo;re nervous in front of an interviewer you&amp;rsquo;ve just met&lt;/li>
&lt;li>When you&amp;rsquo;re suddenly handed a whiteboard and don&amp;rsquo;t have an editor at hand&lt;/li>
&lt;li>When you suddenly draw a blank and think, &amp;ldquo;Wait, what&amp;rsquo;s modulo again?&amp;rdquo;&lt;/li>
&lt;/ul>
&lt;p>&amp;hellip;Doesn&amp;rsquo;t that happen? We&amp;rsquo;re human, after all. I think it does.&lt;/p>
&lt;p>Therefore, rather than &amp;ldquo;whether you can write FizzBuzz,&amp;rdquo; I think what&amp;rsquo;s actually more important is &amp;ldquo;whether you can get yourself into a state where you can write FizzBuzz.&amp;rdquo;&lt;/p>
&lt;hr>
&lt;h3 id="the-pitfall-of-the-common-advice-to-just-train-and-youll-be-fine">The pitfall of the common advice to &amp;ldquo;just train and you&amp;rsquo;ll be fine&amp;rdquo;
&lt;/h3>&lt;p>When this topic comes up, the advice &amp;ldquo;so practice every day!&amp;rdquo; tends to appear.&lt;/p>
&lt;p>It&amp;rsquo;s true that repeated practice will enable you to write it smoothly, and that in itself is a good thing. But if you stand on the premise that &amp;ldquo;you&amp;rsquo;re disqualified if you can&amp;rsquo;t write FizzBuzz,&amp;rdquo; it can turn into pure fear.&lt;/p>
&lt;p>In other words, it tends to create a structure where you feel, &amp;ldquo;I made a mistake = I&amp;rsquo;m useless.&amp;rdquo;&lt;/p>
&lt;p>For example, on days when you oversleep, don&amp;rsquo;t you tend to think, &amp;ldquo;I&amp;rsquo;m lazy&amp;hellip;&amp;rdquo;? But it might just be that your body was accidentally tired.&lt;/p>
&lt;p>The same goes for FizzBuzz.&lt;/p>
&lt;hr>
&lt;h3 id="that-being-said-fizzbuzz-is-still-a-good-question">That being said, FizzBuzz is still a good question
&lt;/h3>&lt;p>That being said, there&amp;rsquo;s nothing wrong with FizzBuzz.&lt;/p>
&lt;p>Rather, I think it&amp;rsquo;s a very well-made question. The rules are simple, and it&amp;rsquo;s easy to expand. For example, if you change it like this, it deepens your thinking even more.&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-python" data-lang="python">&lt;span class="line">&lt;span class="cl">&lt;span class="k">for&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="ow">in&lt;/span> &lt;span class="nb">range&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">101&lt;/span>&lt;span class="p">):&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">output&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="s2">&amp;#34;&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">%&lt;/span> &lt;span class="mi">3&lt;/span> &lt;span class="o">==&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">output&lt;/span> &lt;span class="o">+=&lt;/span> &lt;span class="s2">&amp;#34;Fizz&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">%&lt;/span> &lt;span class="mi">5&lt;/span> &lt;span class="o">==&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">output&lt;/span> &lt;span class="o">+=&lt;/span> &lt;span class="s2">&amp;#34;Buzz&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">output&lt;/span> &lt;span class="ow">or&lt;/span> &lt;span class="n">i&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>This is an example showing that &amp;ldquo;you don&amp;rsquo;t have to use if-elif-else to write it.&amp;rdquo; It&amp;rsquo;s a bit smart, isn&amp;rsquo;t it?&lt;/p>
&lt;p>In other words, FizzBuzz doesn&amp;rsquo;t just show &amp;ldquo;whether you could do it,&amp;rdquo; but also serves as an entry point to see &amp;ldquo;how you write it&amp;rdquo; and &amp;ldquo;how deeply you understand it.&amp;rdquo;&lt;/p>
&lt;hr>
&lt;h3 id="in-conclusion">In conclusion
&lt;/h3>&lt;p>I don&amp;rsquo;t think you need to attach excessive meaning to whether you can do FizzBuzz or not.&lt;/p>
&lt;p>Even if you couldn&amp;rsquo;t write it, it might simply mean &amp;ldquo;you were just a little off your game,&amp;rdquo; and often you can do it if you think about it carefully later.&lt;/p>
&lt;p>Let&amp;rsquo;s not rush and proceed slowly.&lt;/p>
&lt;p>Code is written by humans. Because we&amp;rsquo;re human, there are times when we forget things or get nervous. I think it&amp;rsquo;s enough if we can accept that and move forward little by little.&lt;/p>
&lt;p>Well then, let&amp;rsquo;s take it easy and write some code today too.&lt;/p></description></item><item><title>Tower of Hanoi</title><link>http://kenji.blog/en/p/%E3%83%8F%E3%83%8E%E3%82%A4%E3%81%AE%E5%A1%94/</link><pubDate>Thu, 17 Apr 2025 22:23:14 +0900</pubDate><guid>http://kenji.blog/en/p/%E3%83%8F%E3%83%8E%E3%82%A4%E3%81%AE%E5%A1%94/</guid><description>&lt;img src="http://kenji.blog/p/%E3%83%8F%E3%83%8E%E3%82%A4%E3%81%AE%E5%A1%94/img.png" alt="Featured image of post Tower of Hanoi" />&lt;h1 id="tower-of-hanoi">Tower of Hanoi
&lt;/h1>&lt;p>Hello!&lt;/p>
&lt;p>Today, I would like to explain the &amp;ldquo;Tower of Hanoi&amp;rdquo; along with a Python sample program.&lt;/p>
&lt;hr>
&lt;h2 id="what-is-the-tower-of-hanoi">What is the Tower of Hanoi?
&lt;/h2>&lt;p>The Tower of Hanoi is a puzzle using three rods and multiple disks. The disks vary in size and are initially stacked on one rod in decreasing order of size. The rules are as follows:&lt;/p>
&lt;ol>
&lt;li>Only one disk can be moved at a time.&lt;/li>
&lt;li>A larger disk cannot be placed on top of a smaller disk.&lt;/li>
&lt;/ol>
&lt;p>This puzzle is considered an excellent teaching material for learning recursive thinking. Recursion is a method of solving a problem by breaking it down into smaller problems of the same type. In the Tower of Hanoi, to move n disks, the operation of moving n-1 disks is repeated.&lt;/p>
&lt;hr>
&lt;h2 id="lets-solve-the-tower-of-hanoi-in-python">Let&amp;rsquo;s Solve the Tower of Hanoi in Python
&lt;/h2>&lt;p>Below is a sample code to solve the Tower of Hanoi in Python.&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt"> 1
&lt;/span>&lt;span class="lnt"> 2
&lt;/span>&lt;span class="lnt"> 3
&lt;/span>&lt;span class="lnt"> 4
&lt;/span>&lt;span class="lnt"> 5
&lt;/span>&lt;span class="lnt"> 6
&lt;/span>&lt;span class="lnt"> 7
&lt;/span>&lt;span class="lnt"> 8
&lt;/span>&lt;span class="lnt"> 9
&lt;/span>&lt;span class="lnt">10
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-python" data-lang="python">&lt;span class="line">&lt;span class="cl">&lt;span class="k">def&lt;/span> &lt;span class="nf">hanoi&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">n&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">source&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">target&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">auxiliary&lt;/span>&lt;span class="p">):&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="n">n&lt;/span> &lt;span class="o">==&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">f&lt;/span>&lt;span class="s2">&amp;#34;Move disk 1 from &lt;/span>&lt;span class="si">{&lt;/span>&lt;span class="n">source&lt;/span>&lt;span class="si">}&lt;/span>&lt;span class="s2"> to &lt;/span>&lt;span class="si">{&lt;/span>&lt;span class="n">target&lt;/span>&lt;span class="si">}&lt;/span>&lt;span class="s2">&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">hanoi&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">n&lt;/span> &lt;span class="o">-&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">source&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">auxiliary&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">target&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">f&lt;/span>&lt;span class="s2">&amp;#34;Move disk &lt;/span>&lt;span class="si">{&lt;/span>&lt;span class="n">n&lt;/span>&lt;span class="si">}&lt;/span>&lt;span class="s2"> from &lt;/span>&lt;span class="si">{&lt;/span>&lt;span class="n">source&lt;/span>&lt;span class="si">}&lt;/span>&lt;span class="s2"> to &lt;/span>&lt;span class="si">{&lt;/span>&lt;span class="n">target&lt;/span>&lt;span class="si">}&lt;/span>&lt;span class="s2">&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">hanoi&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">n&lt;/span> &lt;span class="o">-&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">auxiliary&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">target&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">source&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1"># Example: Move 3 disks from A to C&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">hanoi&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="mi">3&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="s1">&amp;#39;A&amp;#39;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="s1">&amp;#39;C&amp;#39;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="s1">&amp;#39;B&amp;#39;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>In this code, the &lt;code>hanoi&lt;/code> function is called recursively, and the steps to move the disks are printed. For example, in the case of 3 disks, you will get the following output:&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">Move disk 1 from A to C
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">Move disk 2 from A to B
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">Move disk 1 from C to B
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">Move disk 3 from A to C
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">Move disk 1 from B to A
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">Move disk 2 from B to C
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">Move disk 1 from A to C
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>In this way, by using a recursive approach, even complex problems can be solved simply.&lt;/p>
&lt;hr>
&lt;h2 id="how-long-does-it-take-to-move-64-disks">How Long Does It Take to Move 64 Disks?
&lt;/h2>&lt;p>The minimum number of moves for the Tower of Hanoi is 2^n - 1. This means that to move 64 disks, it requires 2^64 - 1 moves, or approximately 1.84 × 10^19 moves. Even if you could make one move per second, it would take about 584.9 billion years. This is roughly 42 times the age of the universe (about 13.7 billion years).&lt;/p>
&lt;p>Thus, as the number of disks increases, the required number of moves increases exponentially. Therefore, it is not realistic to actually move 64 disks.&lt;/p>
&lt;hr>
&lt;h2 id="conclusion">Conclusion
&lt;/h2>&lt;p>The Tower of Hanoi is a perfect puzzle for learning recursive thinking. Using Python, you can easily implement its solution. However, care must be taken as the required number of moves increases sharply as the number of disks increases.&lt;/p>
&lt;p>By understanding the recursive approach and actually writing the code, you can improve your programming skills. By all means, give the Tower of Hanoi a try.&lt;/p>
&lt;hr></description></item><item><title>Python Code Snippets</title><link>http://kenji.blog/en/p/python%E3%82%B3%E3%83%BC%E3%83%89%E7%89%87/</link><pubDate>Mon, 24 Feb 2025 18:21:14 +0900</pubDate><guid>http://kenji.blog/en/p/python%E3%82%B3%E3%83%BC%E3%83%89%E7%89%87/</guid><description>&lt;img src="http://kenji.blog/p/python%E3%82%B3%E3%83%BC%E3%83%89%E7%89%87/img.png" alt="Featured image of post Python Code Snippets" />&lt;p>Introduction of sample code using standard libraries.&lt;/p>
&lt;h1 id="download-and-display-an-image">Download and display an image
&lt;/h1>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt"> 1
&lt;/span>&lt;span class="lnt"> 2
&lt;/span>&lt;span class="lnt"> 3
&lt;/span>&lt;span class="lnt"> 4
&lt;/span>&lt;span class="lnt"> 5
&lt;/span>&lt;span class="lnt"> 6
&lt;/span>&lt;span class="lnt"> 7
&lt;/span>&lt;span class="lnt"> 8
&lt;/span>&lt;span class="lnt"> 9
&lt;/span>&lt;span class="lnt">10
&lt;/span>&lt;span class="lnt">11
&lt;/span>&lt;span class="lnt">12
&lt;/span>&lt;span class="lnt">13
&lt;/span>&lt;span class="lnt">14
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&lt;/span>&lt;span class="lnt">19
&lt;/span>&lt;span class="lnt">20
&lt;/span>&lt;span class="lnt">21
&lt;/span>&lt;span class="lnt">22
&lt;/span>&lt;span class="lnt">23
&lt;/span>&lt;span class="lnt">24
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-python" data-lang="python">&lt;span class="line">&lt;span class="cl">&lt;span class="kn">import&lt;/span> &lt;span class="nn">urllib.request&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kn">import&lt;/span> &lt;span class="nn">tempfile&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kn">import&lt;/span> &lt;span class="nn">os&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kn">import&lt;/span> &lt;span class="nn">webbrowser&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kn">import&lt;/span> &lt;span class="nn">time&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">url&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="s2">&amp;#34;https://www.aomori-ringo.or.jp/kids/wp-content/uploads/2021/11/apple.png&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">try&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">with&lt;/span> &lt;span class="n">urllib&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">request&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">urlopen&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">url&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="k">as&lt;/span> &lt;span class="n">response&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">img_data&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">response&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">read&lt;/span>&lt;span class="p">()&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1"># Save to a temporary file and display&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">with&lt;/span> &lt;span class="n">tempfile&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">NamedTemporaryFile&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">delete&lt;/span>&lt;span class="o">=&lt;/span>&lt;span class="kc">False&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">suffix&lt;/span>&lt;span class="o">=&lt;/span>&lt;span class="s2">&amp;#34;.png&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="k">as&lt;/span> &lt;span class="n">tmp&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">tmp&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">write&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">img_data&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">f&lt;/span>&lt;span class="s2">&amp;#34;file://&lt;/span>&lt;span class="si">{&lt;/span>&lt;span class="n">tmp&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">name&lt;/span>&lt;span class="si">}&lt;/span>&lt;span class="s2">&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">webbrowser&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">open&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">f&lt;/span>&lt;span class="s2">&amp;#34;file://&lt;/span>&lt;span class="si">{&lt;/span>&lt;span class="n">tmp&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">name&lt;/span>&lt;span class="si">}&lt;/span>&lt;span class="s2">&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">time&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">sleep&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="mi">3&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">except&lt;/span> &lt;span class="ne">Exception&lt;/span> &lt;span class="k">as&lt;/span> &lt;span class="n">e&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">print&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">f&lt;/span>&lt;span class="s2">&amp;#34;An error occurred: &lt;/span>&lt;span class="si">{&lt;/span>&lt;span class="n">e&lt;/span>&lt;span class="si">}&lt;/span>&lt;span class="s2">&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">finally&lt;/span>&lt;span class="p">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="s1">&amp;#39;tmp&amp;#39;&lt;/span> &lt;span class="ow">in&lt;/span> &lt;span class="nb">locals&lt;/span>&lt;span class="p">():&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">os&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">unlink&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">tmp&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">name&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="c1"># Delete temporary file&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div></description></item><item><title>How to draw graphs using Python (matplotlib.pyplot)</title><link>http://kenji.blog/en/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/</link><pubDate>Sun, 09 Apr 2023 01:02:19 +0900</pubDate><guid>http://kenji.blog/en/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/</guid><description>&lt;img src="http://kenji.blog/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img.png" alt="Featured image of post How to draw graphs using Python (matplotlib.pyplot)" />&lt;p>&lt;img src="http://kenji.blog/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img_1.png"
width="1200"
height="288"
srcset="http://kenji.blog/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img_1_hue3f23818eeeec9c43d6452cc0f61fb52_43864_480x0_resize_box_3.png 480w, http://kenji.blog/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img_1_hue3f23818eeeec9c43d6452cc0f61fb52_43864_1024x0_resize_box_3.png 1024w"
loading="lazy"
alt="img_1.png"
class="gallery-image"
data-flex-grow="416"
data-flex-basis="1000px"
>&lt;/p>
&lt;h1 id="requirements">Requirements
&lt;/h1>&lt;ul>
&lt;li>Google Account&lt;/li>
&lt;/ul>
&lt;h1 id="steps">Steps
&lt;/h1>&lt;ol>
&lt;li>Access &lt;a class="link" href="https://colab.research.google.com/" target="_blank" rel="noopener"
>https://colab.research.google.com/&lt;/a>&lt;/li>
&lt;li>Select &amp;ldquo;File&amp;rdquo; -&amp;gt; &amp;ldquo;New notebook&amp;rdquo;&lt;/li>
&lt;li>Paste and run the following code&lt;/li>
&lt;/ol>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-python" data-lang="python">&lt;span class="line">&lt;span class="cl">&lt;span class="kn">import&lt;/span> &lt;span class="nn">matplotlib.pyplot&lt;/span> &lt;span class="k">as&lt;/span> &lt;span class="nn">plt&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kn">import&lt;/span> &lt;span class="nn">numpy&lt;/span> &lt;span class="k">as&lt;/span> &lt;span class="nn">np&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">x&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">np&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">linspace&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="mi">0&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">2&lt;/span>&lt;span class="o">*&lt;/span>&lt;span class="n">np&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">pi&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">500&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">plt&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">plot&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">x&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">np&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">sin&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">x&lt;/span>&lt;span class="p">),&lt;/span> &lt;span class="n">label&lt;/span>&lt;span class="o">=&lt;/span>&lt;span class="s2">&amp;#34;sin curve&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">plt&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">plot&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">x&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">np&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">cos&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">x&lt;/span>&lt;span class="p">),&lt;/span> &lt;span class="n">label&lt;/span>&lt;span class="o">=&lt;/span>&lt;span class="s2">&amp;#34;cos curve&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">plt&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">legend&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="c1"># Show legend&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">plt&lt;/span>&lt;span class="o">.&lt;/span>&lt;span class="n">show&lt;/span>&lt;span class="p">()&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;h1 id="execution-result">Execution Result
&lt;/h1>&lt;p>&lt;img src="http://kenji.blog/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img.png"
width="568"
height="413"
srcset="http://kenji.blog/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img_hucdb24ab588d845f9f7a56ef99be2c709_27745_480x0_resize_box_3.png 480w, http://kenji.blog/p/pythonmatplotlib.pyplot%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6%E3%82%B0%E3%83%A9%E3%83%95%E3%82%92%E6%8F%8F%E7%94%BB%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img_hucdb24ab588d845f9f7a56ef99be2c709_27745_1024x0_resize_box_3.png 1024w"
loading="lazy"
alt="img.png"
class="gallery-image"
data-flex-grow="137"
data-flex-basis="330px"
>&lt;/p>
&lt;h1 id="references">References
&lt;/h1>&lt;ul>
&lt;li>&lt;a class="link" href="https://matplotlib.org/3.5.3/api/_as_gen/matplotlib.pyplot.html" target="_blank" rel="noopener"
>matplotlib.pyplot — Matplotlib 3.5.3 documentation&lt;/a>&lt;/li>
&lt;/ul></description></item></channel></rss>