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padding-bottom--lg"><div class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><nav class="theme-doc-breadcrumbs breadcrumbsContainer_Z_bl" aria-label="Breadcrumbs"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="Home page" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/algorithms/category/recursion/"><span itemprop="name">Recursion</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Recursion and backtracking with Robot Karel</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><header><h1>Recursion and backtracking with Robot Karel</h1></header><ul>
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<li><a href="/files/algorithms/recursion/karel-1.tar.gz" target="_blank" rel="noopener noreferrer">Sources</a></li>
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</ul>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="introduction">Introduction<a href="#introduction" class="hash-link" aria-label="Direct link to Introduction" title="Direct link to Introduction"></a></h2>
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<p>In this exercise we will be working with a Robot Karel and with a »very« limited
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resources. The point of this exercise is to show how powerful recursion and
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backtracking can be even without anything else at your hand.</p>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="your-environment-and-problem-description">Your environment and problem description<a href="#your-environment-and-problem-description" class="hash-link" aria-label="Direct link to Your environment and problem description" title="Direct link to Your environment and problem description"></a></h2>
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<h3 class="anchor anchorWithStickyNavbar_LWe7" id="environment">Environment<a href="#environment" class="hash-link" aria-label="Direct link to Environment" title="Direct link to Environment"></a></h3>
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<p>You are given a robot that is present in a maze and is looking for an exit. Maze
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consists of different walls and exit is marked with a single so-called “beeper”.</p>
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<p>Walking into a wall results in a permanent damage of the robot.</p>
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<h3 class="anchor anchorWithStickyNavbar_LWe7" id="interface">Interface<a href="#interface" class="hash-link" aria-label="Direct link to Interface" title="Direct link to Interface"></a></h3>
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<p>You can control the robot using the following interface:</p>
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<ul>
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<li>actions — you can use them to change the current state of the robot and its
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surroundings<!-- -->
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<ul>
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<li><code>robot.step()</code> — moves robot one step further</li>
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<li><code>robot.turn_left()</code> — turns robot 90-degrees counter-clockwise<!-- -->
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<ul>
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<li>notice that you are not given <code>turn_right</code> or <code>turn_around</code>, but feel free
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to implement them yourself</li>
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</ul>
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</li>
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<li><code>robot.pick_beeper()</code> and opposite operation <code>robot.put_beeper()</code> — that
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allows you to either pick or put “beeper” from or onto the current position</li>
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</ul>
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</li>
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<li>queries — you can use them to check the current state of the robot and its
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surroundings<!-- -->
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<ul>
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<li><code>robot.beepers_present()</code> — to check if there are any beepers at the robot's
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current location</li>
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<li><code>robot.left_is_clear()</code> — to check if you can step to the left<!-- -->
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<ul>
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<li>analogically for <code>front</code> and <code>right</code></li>
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</ul>
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</li>
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</ul>
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</li>
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||
</ul>
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||
<div class="theme-admonition theme-admonition-caution admonition_xJq3 alert alert--warning"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>caution</div><div class="admonitionContent_BuS1"><p>Helper functions / procedures are allowed. Return values are allowed.</p><p><strong>Variables are prohibited!</strong></p></div></div>
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||
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="problem">Problem<a href="#problem" class="hash-link" aria-label="Direct link to Problem" title="Direct link to Problem"></a></h3>
|
||
<p>Your task is to decide whether there is an exit from the maze or not. You can see
|
||
an example of a maze here:</p>
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||
<p><img loading="lazy" alt="Image of the maze" src="/assets/images/maze-a374d908bc9445061e15faeddc71641e.png" width="770" height="839" class="img_ev3q"></p>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="simple-problem-to-get-familiar-with-the-robot">Simple problem to get familiar with the robot<a href="#simple-problem-to-get-familiar-with-the-robot" class="hash-link" aria-label="Direct link to Simple problem to get familiar with the robot" title="Direct link to Simple problem to get familiar with the robot"></a></h2>
|
||
<p>If you feel completely lost after the previous description, let me start you off
|
||
with a simpler problem.</p>
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||
<p>You are standing in front of the stairs, your task is to walk up the stairs.</p>
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||
<p>You can see an example of such map here:</p>
|
||
<p><img loading="lazy" alt="Image of the stairs" src="/assets/images/stairs-5ee5d03905645aeb13eeaa7774451a64.png" width="1058" height="1161" class="img_ev3q"></p>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="brainstorm-the-idea">Brainstorm the idea<a href="#brainstorm-the-idea" class="hash-link" aria-label="Direct link to Brainstorm the idea" title="Direct link to Brainstorm the idea"></a></h2>
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||
<p>As a first step write down any ideas and things that you have noticed or came to
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||
your mind. Ideally:</p>
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||
<ol>
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||
<li>Write down a nested list of the problems</li>
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||
<li>Write down list of problems that can happen</li>
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||
<li>Write down <strong>anything</strong> you consider important to solving the problem</li>
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||
</ol>
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||
<div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Example</div><div class="admonitionContent_BuS1"><p><strong>Problem</strong>: I want to find out whether the display on smartphone should rotate.</p><ul>
|
||
<li>nested list of problems<!-- -->
|
||
<ul>
|
||
<li>Check if display has been rotated<!-- -->
|
||
<ul>
|
||
<li>Read data from some sensor<!-- -->
|
||
<ul>
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||
<li>From what sensor</li>
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||
</ul>
|
||
</li>
|
||
<li>In what format are the data I have read?</li>
|
||
<li>How do I communicate with the sensor?</li>
|
||
<li>What is the meaning of the data that I got?</li>
|
||
<li>How can I process it?</li>
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li>any problems that can happen<!-- -->
|
||
<ul>
|
||
<li>What if the sensor doesn't work?</li>
|
||
<li>What if the data doesn't conform to the specification?</li>
|
||
<li>What if my formulas are wrong?</li>
|
||
</ul>
|
||
</li>
|
||
<li>anything important<!-- -->
|
||
<ul>
|
||
<li>I could probably use gyroscope.</li>
|
||
<li>I should probably look up the datasheet for that module.</li>
|
||
<li>I could write some tests to verify that my computations are correct.</li>
|
||
</ul>
|
||
</li>
|
||
</ul></div></div>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="rough-pseudocode">»Rough« pseudocode<a href="#rough-pseudocode" class="hash-link" aria-label="Direct link to »Rough« pseudocode" title="Direct link to »Rough« pseudocode"></a></h2>
|
||
<p>As a next step write a <strong>mock up</strong> of a pseudocode solving the problem, you are
|
||
allowed to use comments as placeholders for bigger chunks of code.</p>
|
||
<p>Those comments are also a very good hints for decomposition and short, but
|
||
descriptive, commnets (if they are short enough and you decide not to factor them
|
||
out to separate functions).</p>
|
||
<div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>tip</div><div class="admonitionContent_BuS1"><p>The smaller the function is, the easier it is to test it and argue about its
|
||
correctness.</p></div></div>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="proper-pseudocode">»Proper« pseudocode<a href="#proper-pseudocode" class="hash-link" aria-label="Direct link to »Proper« pseudocode" title="Direct link to »Proper« pseudocode"></a></h2>
|
||
<p>If you are satisfied with the <em>»rough« pseudocode</em>, it's time to convert it into
|
||
a proper one. Get rid of the uncertain pieces of functionality and replace them
|
||
with proper pseudocode, i.e. list of the things that should happen in its place.</p>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="library">Library<a href="#library" class="hash-link" aria-label="Direct link to Library" title="Direct link to Library"></a></h2>
|
||
<p>If you got here, and you <strong>actually</strong> wrote down the pseudocode, you can try your
|
||
solution after downloading the sources linked at the beginning. If you download
|
||
the ZIP-file, you can there:</p>
|
||
<ul>
|
||
<li>
|
||
<p><code>generate_mazes.py</code> - that was used to generate the same maze with beepers in
|
||
different locations</p>
|
||
</li>
|
||
<li>
|
||
<p><code>karel_tk.py</code> - library which can run Karel given the his world</p>
|
||
<ul>
|
||
<li>documentation can be found <a href="https://www.fi.muni.cz/~xfocko/ib111/10/docs/" target="_blank" rel="noopener noreferrer">here</a></li>
|
||
<li>also requires Tk Python library to be installed (it should be included in
|
||
majority of Python installations)</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p><code>*.kw</code> - which represent multiple worlds for Karel I have prepared</p>
|
||
</li>
|
||
<li>
|
||
<p><code>skeleton.py</code> - skeleton for your solution, needs to be put in the same directory
|
||
as <code>karel_tk.py</code> and takes path to the world as a first argument, example usage:</p>
|
||
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ python3 skeleton.py stairs.kw</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<ul>
|
||
<li>of course, this file can be renamed ;)</li>
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="solution">Solution<a href="#solution" class="hash-link" aria-label="Direct link to Solution" title="Direct link to Solution"></a></h2>
|
||
<p>Solution to this problem will be released as a second part, so that you can try
|
||
it out by yourself without any influence of “example solution”.</p>
|
||
<p>If you want to get any feedback, feel free to mail me your solution (including
|
||
all the steps that lead to your final solution, if you wish to get feedback on
|
||
those too).</p></div><footer class="theme-doc-footer docusaurus-mt-lg"><div class="theme-doc-footer-tags-row row margin-bottom--sm"><div class="col"><b>Tags:</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/algorithms/tags/python/">python</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/algorithms/tags/karel/">karel</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/algorithms/tags/recursion/">recursion</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/algorithms/tags/backtracking/">backtracking</a></li></ul></div></div><div class="theme-doc-footer-edit-meta-row row"><div class="col"><a href="https://github.com/mfocko/blog/tree/main/algorithms/04-recursion/2022-11-29-karel/index.md" target="_blank" rel="noopener noreferrer" class="theme-edit-this-page"><svg fill="currentColor" height="20" width="20" viewBox="0 0 40 40" class="iconEdit_Z9Sw" aria-hidden="true"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="col lastUpdated_vwxv"><span class="theme-last-updated">Last updated<!-- --> on <b><time datetime="2022-11-29T00:00:00.000Z">Nov 29, 2022</time></b></span></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages"><a class="pagination-nav__link pagination-nav__link--prev" href="/algorithms/category/recursion/"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">Recursion</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/algorithms/recursion/karel/solution/"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Solution to the problem</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#introduction" class="table-of-contents__link toc-highlight">Introduction</a></li><li><a href="#your-environment-and-problem-description" class="table-of-contents__link toc-highlight">Your environment and problem description</a><ul><li><a href="#environment" class="table-of-contents__link toc-highlight">Environment</a></li><li><a href="#interface" class="table-of-contents__link toc-highlight">Interface</a></li><li><a href="#problem" class="table-of-contents__link toc-highlight">Problem</a></li></ul></li><li><a href="#simple-problem-to-get-familiar-with-the-robot" class="table-of-contents__link toc-highlight">Simple problem to get familiar with the robot</a></li><li><a href="#brainstorm-the-idea" class="table-of-contents__link toc-highlight">Brainstorm the idea</a></li><li><a href="#rough-pseudocode" class="table-of-contents__link toc-highlight">»Rough« pseudocode</a></li><li><a href="#proper-pseudocode" class="table-of-contents__link toc-highlight">»Proper« pseudocode</a></li><li><a href="#library" class="table-of-contents__link toc-highlight">Library</a></li><li><a href="#solution" class="table-of-contents__link toc-highlight">Solution</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer footer--dark"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">Git</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://github.com/mfocko" target="_blank" rel="noopener noreferrer" class="footer__link-item">GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://gitlab.com/mfocko" 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