blog/content/post/1970-01-01-00000053.md

---
title: クレジットカードの判別アルゴリズム
author: kazu634
date: 1969-12-31
url: /1970/01/01/_61/
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categories:
  - gauche
  - Lisp

---
<div class="section">
<p>
    この前「<a href="http://d.hatena.ne.jp/kkomiyama/20090429/1240996163" onclick="__gaTracker('send', 'event', 'outbound-article', 'http://d.hatena.ne.jp/kkomiyama/20090429/1240996163', 'あなたのクレジットカード番号に潜む規則性 &#8211; モスマン');" target="_blank">あなたのクレジットカード番号に潜む規則性 &#8211; モスマン</a>」を読んでいて、いつか実装しようと思っていたのだけれど、ついに完成。
</p>

<p>
    基本的なアルゴリズムは
</p>

<blockquote title="あなたのクレジットカード番号に潜む規則性 - モスマン" cite="http://d.hatena.ne.jp/kkomiyama/20090429/1240996163">
<ol>
<li>
        クレジットカード番号の後ろから数えて*1奇数桁だけを合計する。
</li>
<li>
        クレジットカード番号の後ろから数えて偶数桁を2倍して合計する。2倍して10以上になるときは9を引く。
</li>
<li>
        1と2の数字を合計する
</li>
</ol>

<p>
      正しいカード番号ならこの合計が10で割り切れる。
</p>

<p>
<cite><a href="http://d.hatena.ne.jp/kkomiyama/20090429/1240996163" onclick="__gaTracker('send', 'event', 'outbound-article', 'http://d.hatena.ne.jp/kkomiyama/20090429/1240996163', 'あなたのクレジットカード番号に潜む規則性 &#8211; モスマン');" target="_blank">あなたのクレジットカード番号に潜む規則性 &#8211; モスマン</a></cite>
</p>
</blockquote>

<p>
    です。gaucheで順番に考えていきました。
</p>

<h4>
    16桁かどうか？の判別
</h4>

<p>
    とりあえずカード番号は16桁だから、与えられた引数が16桁の数字かどうかを調べようと考えました。
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>chkdigit <span class="synStatement">number</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synConstant">16</span>digit? <span class="synStatement">number</span><span class="synSpecial">)</span>
<span class="synComment">;; 16桁だったら処理を開始</span>
#f <span class="synComment">;; 16桁じゃないから終了))</span>
</pre>

<p>
    gaucheだと16桁かどうかというのは、正規表現を使えばいいと考えたのでrxmatchを使います。
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span><span class="synConstant">16</span>digit? <span class="synStatement">number</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span>rxmatch #/\d\d\d\d\d\d\d\d\d\d\d\d\d\d\d\d/ <span class="synSpecial">(</span>number-&#62;string <span class="synStatement">number</span><span class="synSpecial">))</span>
#t
#f<span class="synSpecial">))</span>
</pre>

<h4>
    奇数桁だけを合計する・偶数桁を2倍して合計するetc
</h4>

<p>
    これらはおそらくfoldとmapを使えばできる。
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>fold <span class="synStatement">+</span> <span class="synConstant"></span> 奇数桁を集めたリスト<span class="synSpecial">)</span>
<span class="synSpecial">(</span>fold <span class="synStatement">+</span> <span class="synConstant"></span> <span class="synSpecial">(</span><span class="synStatement">map</span> <span class="synSpecial">(</span><span class="synStatement">lambda</span> <span class="synSpecial">(</span>n<span class="synSpecial">)</span> <span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">))</span> 偶数桁を集めたリスト<span class="synSpecial">))</span>
</pre>

<h4>
    リストから奇数桁・偶数桁だけを取り出す
</h4>

<p>
    与えられた16桁の数字をリストに変換しようと思ったので、この前Shiroさんに教えていただいた手続きをそのまま使います。
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>number-&#62;list n<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">let</span> <span class="synStatement">loop</span> <span class="synSpecial">((</span>n n<span class="synSpecial">)</span> <span class="synSpecial">(</span>r <span class="synSpecial">'()))</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synStatement">&#60;</span> n <span class="synConstant">10</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">cons</span> n r<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">loop</span> <span class="synSpecial">(</span>quotient n <span class="synConstant">10</span><span class="synSpecial">)</span> <span class="synSpecial">(</span><span class="synStatement">cons</span> <span class="synSpecial">(</span>modulo n <span class="synConstant">10</span><span class="synSpecial">)</span> r<span class="synSpecial">)))))</span>
</pre>

<p>
    これで数字をリストに変換できたので、奇数桁と偶数桁だけを取り出す部分を考えます。
</p>

<p>
    奇数桁というのは、リストの要素数が偶数の時の(car リスト)の結果になります。偶数桁というのは、リストの要素数が奇数の時の(car list)の結果になります。それを一つのリストにすればいいので:
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>even_list source<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">cond</span>
[<span class="synSpecial">(</span><span class="synStatement">null</span>? source<span class="synSpecial">)</span> <span class="synSpecial">'()</span>]
[<span class="synSpecial">(</span>even? <span class="synSpecial">(</span><span class="synStatement">length</span> source<span class="synSpecial">))</span> <span class="synSpecial">(</span>even_list <span class="synSpecial">(</span><span class="synStatement">cdr</span> source<span class="synSpecial">))</span>]
[<span class="synSpecial">(</span>odd? <span class="synSpecial">(</span><span class="synStatement">length</span> source<span class="synSpecial">))</span> <span class="synSpecial">(</span><span class="synStatement">cons</span> <span class="synSpecial">(</span><span class="synStatement">car</span> source<span class="synSpecial">)</span> <span class="synSpecial">(</span>even_list <span class="synSpecial">(</span><span class="synStatement">cdr</span> source<span class="synSpecial">)))</span>]<span class="synSpecial">))</span>
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>odd_list source<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">cond</span>
[<span class="synSpecial">(</span><span class="synStatement">null</span>? source<span class="synSpecial">)</span> <span class="synSpecial">'()</span>]
[<span class="synSpecial">(</span>even? <span class="synSpecial">(</span><span class="synStatement">length</span> source<span class="synSpecial">))</span> <span class="synSpecial">(</span><span class="synStatement">cons</span> <span class="synSpecial">(</span><span class="synStatement">car</span> source<span class="synSpecial">)</span> <span class="synSpecial">(</span>odd_list <span class="synSpecial">(</span><span class="synStatement">cdr</span> source<span class="synSpecial">)))</span>]
[<span class="synSpecial">(</span>odd? <span class="synSpecial">(</span><span class="synStatement">length</span> source<span class="synSpecial">))</span> <span class="synSpecial">(</span>odd_list <span class="synSpecial">(</span><span class="synStatement">cdr</span> source<span class="synSpecial">))</span>]<span class="synSpecial">))</span>
</pre>

<p>
    このような形になるかと思います。
</p>

<h4>
    奇数桁だけを合計する・偶数桁を2倍して合計するetc
</h4>

<p>
    奇数桁だけを合計するというのは、foldを使えばできそうです。
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>proc_odd <span class="synStatement">list</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span>fold <span class="synStatement">+</span> <span class="synConstant"></span> <span class="synSpecial">(</span>odd_list リスト<span class="synSpecial">)))</span>
</pre>

<p>
    「偶数桁を2倍して合計する。2倍して10以上になるときは9を引く」というのは、
</p>

<ol>
<li>
      偶数桁のそれぞれを2倍する。2倍して10以上になるときは9を引く
</li>
<li>
      その結果を足し合わせる
</li>
</ol>

<p>
    足し合わせる部分はfoldを使えばできそうです:
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>proc_even <span class="synStatement">list</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span>fold <span class="synStatement">+</span> <span class="synConstant"></span> 偶数桁のそれぞれを2倍する。2倍して10以上になるときは9を引いたリスト<span class="synSpecial">)</span>
</pre>

<p>
    問題は「偶数桁のそれぞれを2倍する。2倍して10以上になるときは9を引く」の部分になります。この部分はmapを使えばいいはず。こんな感じで:
</p>

<pre class="syntax-highlight">
gosh&#62; <span class="synSpecial">(</span><span class="synStatement">map</span>
<span class="synSpecial">(</span><span class="synStatement">lambda</span> <span class="synSpecial">(</span>n<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synStatement">&#60;=</span> <span class="synConstant">10</span> <span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">))</span>
<span class="synSpecial">(</span><span class="synStatement">-</span> <span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">)</span> <span class="synConstant">9</span><span class="synSpecial">)</span> <span class="synComment">;; 10以上なら9を引く</span>
<span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">)))</span> <span class="synComment">;; そうでなければ、2倍する</span>
<span class="synSpecial">'(</span>1 2 3 4 5<span class="synSpecial">))</span> <span class="synComment">;; 処理対象のリスト</span>
<span class="synSpecial">(</span><span class="synConstant">2</span> <span class="synConstant">4</span> <span class="synConstant">6</span> <span class="synConstant">8</span> <span class="synConstant">1</span><span class="synSpecial">)</span>
</pre>

<p>
    だから結局、
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>proc_even <span class="synStatement">list</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span>fold <span class="synStatement">+</span> <span class="synConstant"></span> <span class="synSpecial">(</span><span class="synStatement">map</span>
<span class="synSpecial">(</span><span class="synStatement">lambda</span> <span class="synSpecial">(</span>n<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synStatement">&#60;=</span> <span class="synConstant">10</span> <span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">))</span>
<span class="synSpecial">(</span><span class="synStatement">-</span> <span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">)</span> <span class="synConstant">9</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">)))</span>
偶数桁のリスト<span class="synSpecial">)))</span>
</pre>

<p>
    となります。
</p>

<h4>
    正しいカード番号ならこの合計が10で割り切れる
</h4>

<p>
    ここまででだいぶ部品ができてきたので、それを一つにまとめます:
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>judge_card リスト<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">let</span> <span class="synSpecial">((</span>temp
<span class="synSpecial">(</span><span class="synStatement">+</span> <span class="synSpecial">(</span>proc_odd リスト<span class="synSpecial">)</span> <span class="synSpecial">(</span>proc_even リスト<span class="synSpecial">))))</span> <span class="synComment">;; ローカル変数tempに各桁の合計を代入</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synStatement">=</span> <span class="synSpecial">(</span>modulo temp <span class="synConstant">10</span><span class="synSpecial">)</span> <span class="synConstant"></span><span class="synSpecial">)</span> <span class="synComment">;; tempが10で割り切れる？</span>
#t <span class="synComment">;; 割り切れたらカード番号は正しい</span>
#f<span class="synSpecial">)))</span> <span class="synComment">;; そうでなければカード番号は不正</span>
</pre>

<h4>
    まとめ
</h4>

<p>
    一番上位の手続きはchkdigitなので、それにこれまでの結果をまとめます。後、カード番号を逆順にするのも忘れずに:
</p>

<pre class="syntax-highlight">
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>chkdigit <span class="synStatement">number</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">let</span> <span class="synSpecial">((</span>temp <span class="synSpecial">(</span><span class="synStatement">reverse</span> <span class="synSpecial">(</span>number-&#62;list <span class="synStatement">number</span><span class="synSpecial">))))</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synConstant">16</span>digit? <span class="synStatement">number</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span>judge_card temp<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">print</span> <span class="synConstant">&#34;Card Number must be 16 digits.&#34;</span><span class="synSpecial">)</span>
<span class="synSpecial">)))</span>
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>number-&#62;list n<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">let</span> <span class="synStatement">loop</span> <span class="synSpecial">((</span>n n<span class="synSpecial">)</span> <span class="synSpecial">(</span>r <span class="synSpecial">'()))</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synStatement">&#60;</span> n <span class="synConstant">10</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">cons</span> n r<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">loop</span> <span class="synSpecial">(</span>quotient n <span class="synConstant">10</span><span class="synSpecial">)</span> <span class="synSpecial">(</span><span class="synStatement">cons</span> <span class="synSpecial">(</span>modulo n <span class="synConstant">10</span><span class="synSpecial">)</span> r<span class="synSpecial">)))))</span>
<span class="synSpecial">(</span>define <span class="synSpecial">(</span><span class="synConstant">16</span>digit? <span class="synStatement">number</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span>rxmatch #/\d\d\d\d\d\d\d\d\d\d\d\d\d\d\d\d/ <span class="synSpecial">(</span>number-&#62;string <span class="synStatement">number</span><span class="synSpecial">))</span>
#t
#f<span class="synSpecial">))</span>
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>even_list source<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">cond</span>
[<span class="synSpecial">(</span><span class="synStatement">null</span>? source<span class="synSpecial">)</span> <span class="synSpecial">'()</span>]
[<span class="synSpecial">(</span>even? <span class="synSpecial">(</span><span class="synStatement">length</span> source<span class="synSpecial">))</span> <span class="synSpecial">(</span>even_list <span class="synSpecial">(</span><span class="synStatement">cdr</span> source<span class="synSpecial">))</span>]
[<span class="synSpecial">(</span>odd? <span class="synSpecial">(</span><span class="synStatement">length</span> source<span class="synSpecial">))</span> <span class="synSpecial">(</span><span class="synStatement">cons</span> <span class="synSpecial">(</span><span class="synStatement">car</span> source<span class="synSpecial">)</span> <span class="synSpecial">(</span>even_list <span class="synSpecial">(</span><span class="synStatement">cdr</span> source<span class="synSpecial">)))</span>]<span class="synSpecial">))</span>
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>odd_list source<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">cond</span>
[<span class="synSpecial">(</span><span class="synStatement">null</span>? source<span class="synSpecial">)</span> <span class="synSpecial">'()</span>]
[<span class="synSpecial">(</span>even? <span class="synSpecial">(</span><span class="synStatement">length</span> source<span class="synSpecial">))</span> <span class="synSpecial">(</span><span class="synStatement">cons</span> <span class="synSpecial">(</span><span class="synStatement">car</span> source<span class="synSpecial">)</span> <span class="synSpecial">(</span>odd_list <span class="synSpecial">(</span><span class="synStatement">cdr</span> source<span class="synSpecial">)))</span>]
[<span class="synSpecial">(</span>odd? <span class="synSpecial">(</span><span class="synStatement">length</span> source<span class="synSpecial">))</span> <span class="synSpecial">(</span>odd_list <span class="synSpecial">(</span><span class="synStatement">cdr</span> source<span class="synSpecial">))</span>]<span class="synSpecial">))</span>
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>proc_odd <span class="synStatement">list</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span>fold <span class="synStatement">+</span> <span class="synConstant"></span> <span class="synSpecial">(</span>odd_list <span class="synStatement">list</span><span class="synSpecial">)))</span>
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>proc_even <span class="synStatement">list</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span>fold <span class="synStatement">+</span> <span class="synConstant"></span> <span class="synSpecial">(</span><span class="synStatement">map</span>
<span class="synSpecial">(</span><span class="synStatement">lambda</span> <span class="synSpecial">(</span>n<span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synStatement">&#60;=</span> <span class="synConstant">10</span> <span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">))</span>
<span class="synSpecial">(</span><span class="synStatement">-</span> <span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">)</span> <span class="synConstant">9</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">*</span> <span class="synConstant">2</span> n<span class="synSpecial">)))</span>
<span class="synSpecial">(</span>even_list <span class="synStatement">list</span><span class="synSpecial">))))</span>
<span class="synSpecial">(</span>define <span class="synSpecial">(</span>judge_card <span class="synStatement">list</span><span class="synSpecial">)</span>
<span class="synSpecial">(</span><span class="synStatement">let</span> <span class="synSpecial">((</span>temp
<span class="synSpecial">(</span><span class="synStatement">+</span> <span class="synSpecial">(</span>proc_odd <span class="synStatement">list</span><span class="synSpecial">)</span> <span class="synSpecial">(</span>proc_even <span class="synStatement">list</span><span class="synSpecial">))))</span>
<span class="synSpecial">(</span><span class="synStatement">if</span> <span class="synSpecial">(</span><span class="synStatement">=</span> <span class="synSpecial">(</span>modulo temp <span class="synConstant">10</span><span class="synSpecial">)</span> <span class="synConstant"></span><span class="synSpecial">)</span>
#t
#f<span class="synSpecial">)))</span>
</pre>

<h4>
    「gauche」に関連する最近のエントリ
</h4>

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