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<p>We will go through the given problem the same way as I have suggested in the
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previous post.</p>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="summary-of-the-problem">Summary of the problem<a href="#summary-of-the-problem" class="hash-link" aria-label="Direct link to Summary of the problem" title="Direct link to Summary of the problem"></a></h2>
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<p>We have a robot in some kind of a maze and we have to find our way out that is
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marked with a so-called “beeper”. We've been given a restriction <strong>not to</strong> use
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any variables, we can use just backtracking and recursion.</p>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="brainstorming-the-idea">Brainstorming the idea<a href="#brainstorming-the-idea" class="hash-link" aria-label="Direct link to Brainstorming the idea" title="Direct link to Brainstorming the idea"></a></h2>
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<p>Let's start with some brainstorming of the solution.</p>
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<ul>
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<li>How will I know what I've checked without any variables?<!-- -->
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<ul>
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<li><em>answer</em>: recursion will need to take care of that, cause I'm not allowed
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anything else</li>
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</ul>
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</li>
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<li>How will I pass around the fact I've found the exit?<!-- -->
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<ul>
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<li><em>answer</em>: I can return values from helper functions, so I should be able to
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indicate <em>found</em>/<em>not found</em></li>
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</ul>
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</li>
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<li>How is the exit marked?<!-- -->
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<ul>
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<li><em>answer</em>: there is one “beeper” as a mark</li>
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</ul>
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</li>
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<li>Can I reduce my problem somehow?<!-- -->
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<ul>
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<li><em>answer</em>: I could check each possible direction as a reduced search space</li>
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</ul>
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</li>
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</ul>
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<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>
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<p>We should be able to construct a <em>skeleton</em> of our solution at least. Pseudocode
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follows:</p>
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<div class="language-ruby codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-ruby codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token method-definition function" style="color:#d73a49">find_exit</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> found the exit </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> signal others</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> terminate</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">end</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> check left</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> check front</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> check right</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">end</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>
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<p>As you can see, we only mention what we want to do very roughly, technical
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details are left out, except for the early return (which is the base of our
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recursive function).</p>
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<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>
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<p>In the proper pseudocode we will need to dive into the technical details like
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the way we check for exit, move around, etc.</p>
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<p>We can start by cleaning up and decomposing the function written above:</p>
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<div class="language-ruby codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-ruby codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token method-definition function" style="color:#d73a49">find_exit</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic"># BASE: found exit</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> found_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">true</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">end</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic"># check left</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> left_is_clear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> turn_left</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> step</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> find_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">true</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">end</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-b
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<p>We are missing few of the functions that we use in our pseudocode above:</p>
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<ul>
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<li><code>found_exit()</code></li>
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<li><code>turn_around()</code></li>
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<li><code>turn_right()</code></li>
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</ul>
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<p>We can implement those easily:</p>
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<div class="language-ruby codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-ruby codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token method-definition function" style="color:#d73a49">found_exit</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">not</span><span class="token plain"> beepers_present</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">false</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">end</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> pick_beeper</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> beepers_present</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> put_beeper</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">false</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">end</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> put_beeper</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">true</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">end</span><span class="token plain"></span><br></span><span class="token-line" style="c
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<p>Now we have everything ready for implementing it in Python.</p>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="actual-implementation">Actual implementation<a href="#actual-implementation" class="hash-link" aria-label="Direct link to Actual implementation" title="Direct link to Actual implementation"></a></h2>
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<p>It's just a matter of rewriting the pseudocode into Python<sup><a href="#user-content-fn-1" id="user-content-fnref-1" data-footnote-ref="true" aria-describedby="footnote-label">1</a></sup>:</p>
|
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<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">SuperKarel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Karel</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic"># you can define your own helper functions on Karel here, if you wish to</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">found_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">></span><span class="token plain"> </span><span class="token builtin">bool</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">not</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">beepers_present</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">False</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pick_beeper</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">beepers_present</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">put_beeper</span><span class="token punctuation" style="color:#393A
|
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|
|
<p>We have relatively repetitive code for checking each of the directions, I would
|
|||
|
|
propose to refactor a bit, in a fashion of checkin just forward, so it's more
|
|||
|
|
readable:</p>
|
|||
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<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">find_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">></span><span class="token plain"> </span><span class="token builtin">bool</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">found_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">True</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">turn_left</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> _ </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">front_is_blocked</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">turn_right</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">continue</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="displa
|
|||
|
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<p>We can also notice that turning around takes 2 left turns and turning to right
|
|||
|
|
does 3. We get 5 left turns in total when we turn around and right afterwards…
|
|||
|
|
Taking 4 left turns just rotates us back to our initial direction, therefore it
|
|||
|
|
is sufficient to do just one left turn (<code>5 % 4 == 1</code>). That way we get:</p>
|
|||
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<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">find_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">></span><span class="token plain"> </span><span class="token builtin">bool</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">found_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">True</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">turn_left</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> _ </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">front_is_blocked</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">turn_right</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">continue</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="displa
|
|||
|
|
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="testing">Testing<a href="#testing" class="hash-link" aria-label="Direct link to Testing" title="Direct link to Testing"></a></h2>
|
|||
|
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<p>In the skeleton, with the previous post, I have included multiple mazes that can
|
|||
|
|
be tested. I have tried this solution with all of the given mazes, and it was
|
|||
|
|
successful in finding the exit. However there is one precondition of our
|
|||
|
|
solution that we haven't spoken about.</p>
|
|||
|
|
<p>We are silently expecting the maze <strong>not to</strong> have any loops. Example of such
|
|||
|
|
maze can be the <code>maze666.kw</code>:</p>
|
|||
|
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<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">┌─────────┬─┐</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│. . . . .│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ ┌─────┐ │ │</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│.│. . .│.│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ │ │ │ │ │</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│.│.│. . .│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ │ │ └─┤</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│.│.│. . . 1│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ │ │ │ ┌─┤</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│.│. . .│.│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ └─────┘ │ │</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│. > . . .│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">└─────────┴─┘</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>
|
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<p>If you try running our solution on this map, Karel just loops and never finds
|
|||
|
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the solution. Let's have a look at the loop he gets stuck in:</p>
|
|||
|
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<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">┌─────────┬─┐</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│* * * * *│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ ┌─────┐ │ │</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│*│* * *│*│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ │ │ │ │ │</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│*│*│. * *│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ │ │ └─┤</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│*│*│. * * 1│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ │ │ │ ┌─┤</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│*│* * *│*│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│ └─────┘ │ │</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">│* * * * *│.│</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">└─────────┴─┘</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>
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<p>He walks past the exit, but can't see it, cause there's always a feasible path
|
|||
|
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that is worth trying.</p>
|
|||
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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>Algorithm</div><div class="admonitionContent_BuS1"><p>The algorithm we have written to find the exit is a depth-first search (DFS).
|
|||
|
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However, as opposed to the usual implementation, we have no notion of paths that
|
|||
|
|
are being (or have already been) explored.</p></div></div>
|
|||
|
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="fixing-the-issue">Fixing the issue<a href="#fixing-the-issue" class="hash-link" aria-label="Direct link to Fixing the issue" title="Direct link to Fixing the issue"></a></h2>
|
|||
|
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<p>Since we are not allowed to use variables, the only way to resolve this issue is
|
|||
|
|
to mark the “cells” that we have tried. We can easily use beepers for this, but
|
|||
|
|
we need to be careful <strong>not to</strong> confuse the exit with already visited cell.</p>
|
|||
|
|
<p>To do that we'll use <strong>2</strong> beepers instead of the one. Implementation follows:</p>
|
|||
|
|
<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">visited</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">></span><span class="token plain"> </span><span class="token builtin">bool</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">not</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">beepers_present</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">False</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pick_beeper</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">not</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">beepers_present</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">put_beeper</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">False</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pick_beeper</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" sty
|
|||
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<p>Now our solution works also for mazes that have loops.</p>
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<section data-footnotes="true" class="footnotes"><h2 class="anchor anchorWithStickyNavbar_LWe7 sr-only" id="footnote-label">Footnotes<a href="#footnote-label" class="hash-link" aria-label="Direct link to Footnotes" title="Direct link to Footnotes"></a></h2>
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<ol>
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<li id="user-content-fn-1">
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<p>which is usually very easy matter <a href="#user-content-fnref-1" data-footnote-backref="" aria-label="Back to reference 1" class="data-footnote-backref">↩</a></p>
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</li>
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</ol>
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