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tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><h1>Breaking the Hash Table in Python</h1>
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<p>Our language of choice for bringing the worst out of the hash table is <em>Python</em>.</p>
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<p>Let's start by talking about the hash function and why we've chosen Python for
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this. Hash function for integers in Python is simply <em>identity</em>, as you might've
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guessed, there's no avalanche effect. Another thing that helps us is the fact
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that integers in Python are technically <code>BigInt</code>s<sup><a href="#user-content-fn-1" id="user-content-fnref-1" data-footnote-ref="true" aria-describedby="footnote-label">1</a></sup>. This allows us to put bit
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more pressure on the hashing function.</p>
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<p>From the perspective of the implementation, it is a hash table that uses probing
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to resolve conflicts. This also means that it's a contiguous space in memory.
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Indexing works like in the provided example above. When the hash table reaches
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a <em>breaking point</em> (defined somewhere in the C code), it reallocates the table
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and rehashes everything.</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>tip</div><div class="admonitionContent_BuS1"><p>Resizing and rehashing can reduce the conflicts. That is coming from the fact
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that the position in the table is determined by the hash and the size of the
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table itself.</p></div></div>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="preparing-the-attack">Preparing the attack<a href="#preparing-the-attack" class="hash-link" aria-label="Direct link to Preparing the attack" title="Direct link to Preparing the attack"></a></h2>
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<p>Knowing the things above, it is not that hard to construct a method how to cause
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as many conflicts as possible. Let's go over it:</p>
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<ol>
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<li>We know that integers are hashed to themselves.</li>
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<li>We also know that from that hash we use only lower bits that are used as
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indices.</li>
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<li>We also know that there's a rehashing on resize that could possibly fix the
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conflicts.</li>
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</ol>
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<p>We will test with different sequences:</p>
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<ol>
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<li>ordered one, numbers through 1 to N</li>
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<li>ordered one in a reversed order, numbers through N back to 1</li>
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<li>numbers that are shifted to the left, so they create conflicts until resize</li>
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<li>numbers that are shifted to the left, but resizing helps only in the end</li>
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<li>numbers that are shifted to the left, but they won't be taken in account even
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after final resize</li>
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</ol>
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<p>For each of these sequences, we will insert 10⁷ elements and look each of them
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up for 10 times in a row.</p>
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<p>As a base of our benchmark, we will use a <code>Strategy</code> class and then for each
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strategy we will just implement the sequence of numbers that it uses:</p>
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<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">class</span><span class="token plain"> </span><span class="token class-name" style="color:hsl(35, 99%, 36%)">Strategy</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">def</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">__init__</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">self</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> data_structure</span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">set</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> self</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">_table </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> data_structure</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token decorator annotation punctuation" style="color:hsl(119, 34%, 47%)">@cached_property</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">def</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">elements</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">self</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">raise</span><span class="token plain"> NotImplementedError</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Implement for each strategy"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token decorator annotation punctuation" style="color:hsl(119, 34%, 47%)">@property</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">def</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">name</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">self</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">raise</span><span class="token plain"> NotImplementedError</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Implement for each strategy"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">def</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">run</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">self</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string-interpolation string" style="color:hsl(119, 34%, 47%)">f"\nBenchmarking:\t\t</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token string-interpolation interpolation">self</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token string-interpolation interpolation">name</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token string-interpolation string" style="color:hsl(119, 34%, 47%)">"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)"># Extract the elements here, so that the evaluation of them does not</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)"># slow down the relevant part of benchmark</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> elements </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">elements</span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)"># Insertion phase</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> start </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> monotonic_ns</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> elements</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> self</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">_table</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">add</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> after_insertion </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> monotonic_ns</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string-interpolation string" style="color:hsl(119, 34%, 47%)">f"Insertion phase:\t</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string-interpolation interpolation">after_insertion </span><span class="token string-interpolation interpolation operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token string-interpolation interpolation"> start</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation operator" style="color:hsl(221, 87%, 60%)">/</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation number" style="color:hsl(35, 99%, 36%)">1000000</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token string-interpolation interpolation format-spec">.2f</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token string-interpolation string" style="color:hsl(119, 34%, 47%)">ms"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)"># Lookup phase</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> start </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> monotonic_ns</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> _ </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">range</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">LOOPS</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> elements</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">assert</span><span class="token plain"> x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> self</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">_table</span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> after_lookups </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> monotonic_ns</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string-interpolation string" style="color:hsl(119, 34%, 47%)">f"Lookup phase:\t\t</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string-interpolation interpolation">after_lookups </span><span class="token string-interpolation interpolation operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token string-interpolation interpolation"> start</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation operator" style="color:hsl(221, 87%, 60%)">/</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation number" style="color:hsl(35, 99%, 36%)">1000000</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token string-interpolation interpolation format-spec">.2f</span><span class="token string-interpolation interpolation punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token string-interpolation string" style="color:hsl(119, 34%, 47%)">ms"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</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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<h3 class="anchor anchorWithStickyNavbar_LWe7" id="sequences">Sequences<a href="#sequences" class="hash-link" aria-label="Direct link to Sequences" title="Direct link to Sequences"></a></h3>
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<p>Let's have a look at how we generate the numbers to be inserted:</p>
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<ul>
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<li>ordered sequence (ascending)<!-- -->
|
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<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain">x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">range</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">N_ELEMENTS</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</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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</li>
|
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<li>ordered sequence (descending)<!-- -->
|
||
<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain">x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">reversed</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">range</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">N_ELEMENTS</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</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>
|
||
</li>
|
||
<li>progressive sequence that “heals” on resize<!-- -->
|
||
<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><<</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">max</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">5</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">bit_length</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">range</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">N_ELEMENTS</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</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>
|
||
</li>
|
||
<li>progressive sequence that “heals” in the end<!-- -->
|
||
<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><<</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">max</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">5</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">bit_length</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">reversed</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">range</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">N_ELEMENTS</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</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>
|
||
</li>
|
||
<li>conflicts everywhere<!-- -->
|
||
<div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:hsl(230, 8%, 24%)"><span class="token plain">x </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><<</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">32</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> x </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">range</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">N_ELEMENTS</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</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>
|
||
</li>
|
||
</ul>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="results">Results<a href="#results" class="hash-link" aria-label="Direct link to Results" title="Direct link to Results"></a></h2>
|
||
<p>Let's have a look at the obtained results after running the code:</p>
|
||
<table><thead><tr><th style="text-align:center">Technique</th><th style="text-align:right">Insertion phase</th><th style="text-align:right">Lookup phase</th></tr></thead><tbody><tr><td style="text-align:center">ordered sequence (ascending)</td><td style="text-align:right"><code>558.60ms</code></td><td style="text-align:right"><code>3304.26ms</code></td></tr><tr><td style="text-align:center">ordered sequence (descending)</td><td style="text-align:right"><code>554.08ms</code></td><td style="text-align:right"><code>3365.84ms</code></td></tr><tr><td style="text-align:center">progressive sequence that “heals” on resize</td><td style="text-align:right"><code>3781.30ms</code></td><td style="text-align:right"><code>28565.71ms</code></td></tr><tr><td style="text-align:center">progressive sequence that “heals” in the end</td><td style="text-align:right"><code>3280.38ms</code></td><td style="text-align:right"><code>26494.61ms</code></td></tr><tr><td style="text-align:center">conflicts everywhere</td><td style="text-align:right"><code>4027.54ms</code></td><td style="text-align:right"><code>29132.92ms</code></td></tr></tbody></table>
|
||
<p>You can see a noticable “jump” in the time after switching to the “progressive”
|
||
sequence. The last sequence that has conflicts all the time has the worst time,
|
||
even though it's rather comparable with the first progressive sequence with
|
||
regards to the insertion phase.</p>
|
||
<p>If we were to compare the <em>always conflicting</em> one with the first one, we can
|
||
see that insertion took over 7× longer and lookups almost 9× longer.</p>
|
||
<p>You can have a look at the code <a href="/files/algorithms/hash-tables/breaking/benchmark.py" target="_blank" rel="noopener noreferrer">here</a>.</p>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="comparing-with-the-tree">Comparing with the tree<a href="#comparing-with-the-tree" class="hash-link" aria-label="Direct link to Comparing with the tree" title="Direct link to Comparing with the tree"></a></h2>
|
||
<div class="theme-admonition theme-admonition-danger admonition_xJq3 alert alert--danger"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>danger</div><div class="admonitionContent_BuS1"><p>Source code can be found <a href="/files/algorithms/hash-tables/breaking/benchmark.cpp" target="_blank" rel="noopener noreferrer">here</a>.</p><p><em>Viewer discretion advised.</em></p></div></div>
|
||
<p>Python doesn't have a tree structure for sets/maps implemented, therefore for
|
||
a comparison we will run a similar benchmark in C++. By running the same
|
||
sequences on both hash table and tree (RB-tree) we will obtain the following
|
||
results:</p>
|
||
<table><thead><tr><th style="text-align:center">Technique</th><th style="text-align:right">Insertion (hash)</th><th style="text-align:right">Lookup (hash)</th><th style="text-align:right">Insertion (tree)</th><th style="text-align:right">Lookup (tree)</th></tr></thead><tbody><tr><td style="text-align:center">ordered (ascending)</td><td style="text-align:right"><code>316ms</code></td><td style="text-align:right"><code>298ms</code></td><td style="text-align:right"><code>2098ms</code></td><td style="text-align:right"><code>5914ms</code></td></tr><tr><td style="text-align:center">ordered (descending)</td><td style="text-align:right"><code>259ms</code></td><td style="text-align:right"><code>315ms</code></td><td style="text-align:right"><code>1958ms</code></td><td style="text-align:right"><code>14747ms</code></td></tr><tr><td style="text-align:center">progressive a)</td><td style="text-align:right"><code>1152ms</code></td><td style="text-align:right"><code>6021ms</code></td><td style="text-align:right"><code>2581ms</code></td><td style="text-align:right"><code>16074ms</code></td></tr><tr><td style="text-align:center">progressive b)</td><td style="text-align:right"><code>1041ms</code></td><td style="text-align:right"><code>6096ms</code></td><td style="text-align:right"><code>2770ms</code></td><td style="text-align:right"><code>15986ms</code></td></tr><tr><td style="text-align:center">conflicts</td><td style="text-align:right"><code>964ms</code></td><td style="text-align:right"><code>1633ms</code></td><td style="text-align:right"><code>2559ms</code></td><td style="text-align:right"><code>13285ms</code></td></tr></tbody></table>
|
||
<div class="theme-admonition theme-admonition-note admonition_xJq3 alert alert--secondary"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>note</div><div class="admonitionContent_BuS1"><p>We can't forget that implementation details be involved. Hash function is still
|
||
the identity, to my knowledge.</p></div></div>
|
||
<p>One interesting thing to notice is the fact that the progressive sequences took
|
||
the most time in lookups (which is not same as in the Python).</p>
|
||
<p>Now, if we have a look at the tree implementation, we can notice two very
|
||
distinctive things:</p>
|
||
<ol>
|
||
<li>Tree implementations are not affected by the input, therefore (except for the
|
||
first sequence) we can see <strong>very consistent</strong> times.</li>
|
||
<li>Compared to the hash table the times are much higher and not very ideal.</li>
|
||
</ol>
|
||
<p>The reason for the 2nd point may not be very obvious. From the technical
|
||
perspective it makes some sense. Let's dive into it!</p>
|
||
<p>If we take a hash table, it is an array in a memory, therefore it is contiguous
|
||
piece of memory. (For more information I'd suggest looking into the 1st blog
|
||
post below in references section by <em>Bjarne Stroustrup</em>)</p>
|
||
<p>On the other hand, if we take a look at the tree, each node holds some
|
||
attributes and pointers to the left and right descendants of itself. Even if we
|
||
maintain a reasonable height of the tree (keep the tree balanced), we still need
|
||
to follow the pointers which point to the nodes <em>somewhere</em> on the heap. When
|
||
traversing the tree, we get a consistent time complexity, but at the expense of
|
||
jumping between the nodes on the heap which takes some time.</p>
|
||
<div class="theme-admonition theme-admonition-danger admonition_xJq3 alert alert--danger"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>danger</div><div class="admonitionContent_BuS1"><p>This is not supposed to leverage the hash table and try to persuade people not
|
||
to use the tree representations. There are benefits coming from the respective
|
||
data structures, even if the time is not the best.</p><p>Overall if we compare the worst-case time complexities of the tree and hash
|
||
table, tree representation comes off better.</p></div></div>
|
||
<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>Challenge</div><div class="admonitionContent_BuS1"><p>Try to benchmark with the similar approach in the Rust. Since Rust uses
|
||
different hash function, it would be the best to just override the hash, this
|
||
way you can also avoid the hard part of this attack (making up the numbers that
|
||
will collide).</p></div></div>
|
||
<hr>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="references">References<a href="#references" class="hash-link" aria-label="Direct link to References" title="Direct link to References"></a></h2>
|
||
<ol>
|
||
<li>Bjarne Stroustrup.
|
||
<a href="https://www.stroustrup.com/bs_faq.html#list" target="_blank" rel="noopener noreferrer">Are lists evil?</a></li>
|
||
</ol>
|
||
<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>
|
||
<ol>
|
||
<li id="user-content-fn-1">
|
||
<p>Arbitrary-sized integers, they can get as big as your memory allows. <a href="#user-content-fnref-1" data-footnote-backref="" aria-label="Back to reference 1" class="data-footnote-backref">↩</a></p>
|
||
</li>
|
||
</ol>
|
||
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href="#preparing-the-attack" class="table-of-contents__link toc-highlight">Preparing the attack</a><ul><li><a href="#sequences" class="table-of-contents__link toc-highlight">Sequences</a></li></ul></li><li><a href="#results" class="table-of-contents__link toc-highlight">Results</a></li><li><a href="#comparing-with-the-tree" class="table-of-contents__link toc-highlight">Comparing with the tree</a></li><li><a href="#references" class="table-of-contents__link toc-highlight">References</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 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