togakangaroo/daily programmer gcd of strings.html

## daily programmer gcd of strings.html
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<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org9610dd0">1. Greatest Common Divisor of Strings</a>
<ul>
<li><a href="#org86c1d76">1.1. Visulaize moving thorugh <code>examples[1]</code></a></li>
<li><a href="#org1b8699c">1.2. Visualize moving through <code>examples[2]</code></a></li>
</ul>
</li>
<li><a href="#orgc7e5e8e">2. Back to the solution</a></li>
</ul>
</div>
</div>
<div id="outline-container-org9610dd0" class="outline-2">
<h2 id="org9610dd0"><span class="section-number-2">1</span> Greatest Common Divisor of Strings</h2>
<div class="outline-text-2" id="text-1">
<p>
From the <a href="https://operation-code.slack.com/archives/C7JMZ5LAV/p1571058063006200">Operation Code Slack</a>
</p>

<p>
Problem statement:
</p>

<div class="org-src-container">
<pre class="src src-markdown">For strings S and T, we say &#8220;T divides S&#8221; if and only if S = T + ... + T  (T concatenated with itself 1 or more times)
Return the largest string X such that X divides str1 and X divides str2.
<span style="color: #b3b3b3;">```</span>
<span style="color: #8470ff; font-weight: bold;">Input: str1 = "ABCABC", str2 = "ABC"</span>
<span style="color: #8470ff; font-weight: bold;">Output: "ABC"</span>

<span style="color: #8470ff; font-weight: bold;">Input: str1 = "ABABAB", str2 = "ABAB"</span>
<span style="color: #8470ff; font-weight: bold;">Output: "AB"</span>

<span style="color: #8470ff; font-weight: bold;">Input: str1 = "LEET", str2 = "CODE"</span>
<span style="color: #8470ff; font-weight: bold;">Output: ""</span>
<span style="color: #b3b3b3;">```</span>

Note:
&#8226; 1 &lt;= str1.length &lt;= 1000
&#8226; 1 &lt;= str2.length &lt;= 1000
&#8226; str1[i] and str2[i] are English uppercase letters.
</pre>
</div>

<table id="orgfe3f583" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">


<colgroup>
<col  class="org-left" />

<col  class="org-left" />

<col  class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">str1</th>
<th scope="col" class="org-left">str2</th>
<th scope="col" class="org-left">output</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">ABCABC</td>
<td class="org-left">ABC</td>
<td class="org-left">ABC</td>
</tr>

<tr>
<td class="org-left">ABABAB</td>
<td class="org-left">ABAB</td>
<td class="org-left">AB</td>
</tr>

<tr>
<td class="org-left">ABABABB</td>
<td class="org-left">ABAB</td>
<td class="org-left">&#xa0;</td>
</tr>

<tr>
<td class="org-left">LEET</td>
<td class="org-left">CODE</td>
<td class="org-left">&#xa0;</td>
</tr>
</tbody>
</table>

<p>
So lets enumerate conditions where you <b>do</b> get a match.
</p>

<p>
Firstly, we are always comparing the shorter string to the longer one. So lets make sure we know which is which
</p>

<p>
Then the most starightforward one is <code>examples[0]</code> where the shorter string is a proper subset of the longer one
</p>

<p>
There is also the situation on <code>examples[1]</code> where the full shorter string doesn't fit into the the longer one an even amount of times but a shorter substring does.
</p>

<p>
It would seem that anything else would not be a match
</p>


<div class="org-src-container">
<pre class="src src-python"><span style="color: #00ffff;">def</span> <span style="color: #00fa9a; font-size: 110%; font-weight: bold;">get_string_gcd</span><span style="color: #8c8c8c;">(</span>shorter, longer<span style="color: #8c8c8c;">)</span>:
    <span style="color: #00ffff;">if</span> <span style="color: #00ffff;">not</span> shorter:
        <span style="color: #00ffff;">return</span> <span style="color: #8470ff; font-weight: bold;">None</span>
    <span style="color: #00ffff;">if</span> <span style="color: #b0c4de;">len</span><span style="color: #8c8c8c;">(</span>shorter<span style="color: #8c8c8c;">)</span> &gt; <span style="color: #b0c4de;">len</span><span style="color: #8c8c8c;">(</span>longer<span style="color: #8c8c8c;">)</span>:
        <span style="color: #00ffff;">return</span> get_string_gcd<span style="color: #8c8c8c;">(</span>longer, shorter<span style="color: #8c8c8c;">)</span>
</pre>
</div>
</div>

<div id="outline-container-org86c1d76" class="outline-3">
<h3 id="org86c1d76"><span class="section-number-3">1.1</span> Visulaize moving thorugh <code>examples[1]</code></h3>
<div class="outline-text-3" id="text-1-1">
<p>
Lets visualize things physically. We will consider <code>examples[1]</code>. We move through each char one by one, cycling back (starred below) on the short string if need be.
</p>

<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">


<colgroup>
<col  class="org-left" />

<col  class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">longer</th>
<th scope="col" class="org-left">shorter</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">A</td>
<td class="org-left">A</td>
</tr>

<tr>
<td class="org-left">B</td>
<td class="org-left">B</td>
</tr>

<tr>
<td class="org-left">A</td>
<td class="org-left">A</td>
</tr>

<tr>
<td class="org-left">B</td>
<td class="org-left">B</td>
</tr>

<tr>
<td class="org-left">A</td>
<td class="org-left">*A</td>
</tr>

<tr>
<td class="org-left">B</td>
<td class="org-left">B</td>
</tr>
</tbody>
</table>

<p>
If we reach the end of the longer string then we have a match of the substring since last starred
</p>
</div>
</div>

<div id="outline-container-org1b8699c" class="outline-3">
<h3 id="org1b8699c"><span class="section-number-3">1.2</span> Visualize moving through <code>examples[2]</code></h3>
<div class="outline-text-3" id="text-1-2">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">


<colgroup>
<col  class="org-left" />

<col  class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">longer</th>
<th scope="col" class="org-left">shorter</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">A</td>
<td class="org-left">A</td>
</tr>

<tr>
<td class="org-left">B</td>
<td class="org-left">B</td>
</tr>

<tr>
<td class="org-left">A</td>
<td class="org-left">A</td>
</tr>

<tr>
<td class="org-left">B</td>
<td class="org-left">B</td>
</tr>

<tr>
<td class="org-left">A</td>
<td class="org-left">*A</td>
</tr>

<tr>
<td class="org-left">B</td>
<td class="org-left">B</td>
</tr>

<tr>
<td class="org-left">B</td>
<td class="org-left">A!</td>
</tr>
</tbody>
</table>

<p>
Uh oh, we hit a situation where the next step on the left has no match on the right. This means there is no match
</p>
</div>
</div>
</div>


<div id="outline-container-orgc7e5e8e" class="outline-2">
<h2 id="orgc7e5e8e"><span class="section-number-2">2</span> Back to the solution</h2>
<div class="outline-text-2" id="text-2">
<p>
Sounds like what we need to do is move through each string one by one cycling the shorter one but also noting what the most recent cycle is. <code>itertools</code> already has a <code>cycle</code> function but we want more than that. we don't just want the <b>next</b> returned each time but the next <b>and all within this current cycle</b>. So lets implement that
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #00ffff;">def</span> <span style="color: #00fa9a; font-size: 110%; font-weight: bold;">tracked_cycle</span><span style="color: #8c8c8c;">(</span>iterable<span style="color: #8c8c8c;">)</span>:
    <span style="color: #00ffff;">while</span> <span style="color: #8470ff; font-weight: bold;">True</span>:
        <span style="color: #7fffd4;">current_cycle</span> = <span style="color: #8c8c8c;">[]</span>
        <span style="color: #00ffff;">for</span> x <span style="color: #00ffff;">in</span> iterable:
            current_cycle.append<span style="color: #8c8c8c;">(</span>x<span style="color: #8c8c8c;">)</span>
            <span style="color: #00ffff;">yield</span> <span style="color: #8c8c8c;">(</span>x, <span style="color: #b0c4de;">list</span><span style="color: #93a8c6;">(</span>current_cycle<span style="color: #93a8c6;">)</span><span style="color: #8c8c8c;">)</span> <span style="color: #fa8072;">#</span><span style="color: #ff7f24; font-style: italic;">list needed since </span>

</pre>
</div>

<p>
Ok, lets test that
</p>

<div class="org-src-container">
<pre class="src src-python"><span style="color: #00ffff;">from</span> itertools <span style="color: #00ffff;">import</span> islice
<span style="color: #00ffff;">for</span> <span style="color: #8c8c8c;">(</span>_, s, _<span style="color: #8c8c8c;">)</span> <span style="color: #00ffff;">in</span> examples:
    <span style="color: #00ffff;">print</span><span style="color: #8c8c8c;">(</span>
        <span style="color: #b0c4de;">list</span><span style="color: #93a8c6;">(</span>islice<span style="color: #b0b1a3;">(</span>tracked_cycle<span style="color: #97b098;">(</span>s<span style="color: #97b098;">)</span>, <span style="color: #8470ff; font-weight: bold;">0</span>, <span style="color: #8470ff; font-weight: bold;">8</span><span style="color: #b0b1a3;">)</span><span style="color: #93a8c6;">)</span>
    <span style="color: #8c8c8c;">)</span>
</pre>
</div>

<pre class="example">
[('A', ['A']), ('B', ['A', 'B']), ('C', ['A', 'B', 'C']), ('A', ['A']), ('B', ['A', 'B']), ('C', ['A', 'B', 'C']), ('A', ['A']), ('B', ['A', 'B'])]
[('A', ['A']), ('B', ['A', 'B']), ('A', ['A', 'B', 'A']), ('B', ['A', 'B', 'A', 'B']), ('A', ['A']), ('B', ['A', 'B']), ('A', ['A', 'B', 'A']), ('B', ['A', 'B', 'A', 'B'])]
[('A', ['A']), ('B', ['A', 'B']), ('A', ['A', 'B', 'A']), ('B', ['A', 'B', 'A', 'B']), ('A', ['A']), ('B', ['A', 'B']), ('A', ['A', 'B', 'A']), ('B', ['A', 'B', 'A', 'B'])]
[('C', ['C']), ('O', ['C', 'O']), ('D', ['C', 'O', 'D']), ('E', ['C', 'O', 'D', 'E']), ('C', ['C']), ('O', ['C', 'O']), ('D', ['C', 'O', 'D']), ('E', ['C', 'O', 'D', 'E'])]

</pre>

<p>
Ok, seems to work well. Also, hey! That's a cool way of testing things isn't it?
</p>

<p>
Alright, so now that we've got the above working its really a fairly straightforward matter of moving through each one at a time and testing the business logic
</p>

<div class="org-src-container">
<pre class="src src-python"><span style="color: #00ffff;">def</span> <span style="color: #00fa9a; font-size: 110%; font-weight: bold;">get_string_gcd</span><span style="color: #8c8c8c;">(</span>shorter, longer<span style="color: #8c8c8c;">)</span>:
    <span style="color: #00ffff;">if</span> <span style="color: #00ffff;">not</span> shorter:
        <span style="color: #00ffff;">return</span> <span style="color: #8470ff; font-weight: bold;">None</span>
    <span style="color: #00ffff;">if</span> <span style="color: #b0c4de;">len</span><span style="color: #8c8c8c;">(</span>shorter<span style="color: #8c8c8c;">)</span> &gt; <span style="color: #b0c4de;">len</span><span style="color: #8c8c8c;">(</span>longer<span style="color: #8c8c8c;">)</span>:
        <span style="color: #00ffff;">return</span> get_string_gcd<span style="color: #8c8c8c;">(</span>longer, shorter<span style="color: #8c8c8c;">)</span>
    <span style="color: #7fffd4;">current_cycle</span> = <span style="color: #8c8c8c;">[]</span>
    <span style="color: #00ffff;">for</span> <span style="color: #8c8c8c;">(</span><span style="color: #93a8c6;">(</span>s, current_cycle<span style="color: #93a8c6;">)</span>, l<span style="color: #8c8c8c;">)</span> <span style="color: #00ffff;">in</span> <span style="color: #b0c4de;">zip</span><span style="color: #8c8c8c;">(</span>tracked_cycle<span style="color: #93a8c6;">(</span>shorter<span style="color: #93a8c6;">)</span>, longer<span style="color: #8c8c8c;">)</span>:
        <span style="color: #00ffff;">if</span> s != l:
            <span style="color: #00ffff;">return</span> <span style="color: #8470ff; font-weight: bold;">None</span>
    <span style="color: #00ffff;">return</span> <span style="color: #ffc1c1;">''</span>.join<span style="color: #8c8c8c;">(</span>current_cycle<span style="color: #8c8c8c;">)</span>

<span style="color: #00ffff;">for</span> <span style="color: #8c8c8c;">(</span>longer, shorter, desired<span style="color: #8c8c8c;">)</span> <span style="color: #00ffff;">in</span> examples:
    <span style="color: #7fffd4;">desired</span> = desired <span style="color: #00ffff;">or</span> <span style="color: #8470ff; font-weight: bold;">None</span>
    <span style="color: #7fffd4;">gcd</span> = get_string_gcd<span style="color: #8c8c8c;">(</span>shorter, longer<span style="color: #8c8c8c;">)</span>
    <span style="color: #00ffff;">print</span><span style="color: #8c8c8c;">(</span>f<span style="color: #ffc1c1;">'gcd({shorter}, {longer}) = {gcd}'</span><span style="color: #8c8c8c;">)</span>
    <span style="color: #00ffff;">if</span> gcd != desired:
        <span style="color: #00ffff;">print</span><span style="color: #8c8c8c;">(</span>f<span style="color: #ffc1c1;">'FAILBOY! it should be {desired}\n'</span><span style="color: #8c8c8c;">)</span>
</pre>
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<pre class="example">
gcd(ABC, ABCABC) = ABC
gcd(ABAB, ABABAB) = AB
gcd(ABAB, ABABABB) = None
gcd(CODE, LEET) = None

</pre>
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<div id="postamble" class="status">
<p class="author">Author: George Mauer</p>
<p class="date">Created: 2019-10-14 Mon 12:29</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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