mirror of
https://github.com/mfocko/blog.git
synced 2024-11-14 01:59:42 +01:00
142 lines
59 KiB
HTML
142 lines
59 KiB
HTML
|
<!doctype html>
|
|||
|
|
<html lang="en" dir="ltr" class="docs-wrapper plugin-docs plugin-id-algorithms docs-version-current docs-doc-page docs-doc-id-hash-tables/2023-11-28-breaking/python" data-has-hydrated="false">
|
|||
|
|
<head>
|
|||
|
|
<meta charset="UTF-8">
|
|||
|
|
<meta name="generator" content="Docusaurus v3.0.0">
|
|||
|
|
<title data-rh="true">Breaking Python | mf</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:url" content="https://blog.mfocko.xyz/algorithms/hash-tables/breaking/python/"><meta data-rh="true" property="og:locale" content="en"><meta data-rh="true" name="docusaurus_locale" content="en"><meta data-rh="true" name="docsearch:language" content="en"><meta data-rh="true" name="docusaurus_version" content="current"><meta data-rh="true" name="docusaurus_tag" content="docs-algorithms-current"><meta data-rh="true" name="docsearch:version" content="current"><meta data-rh="true" name="docsearch:docusaurus_tag" content="docs-algorithms-current"><meta data-rh="true" property="og:title" content="Breaking Python | mf"><meta data-rh="true" name="description" content="Actually getting the worst-case time complexity in Python.
|
|||
|
|
"><meta data-rh="true" property="og:description" content="Actually getting the worst-case time complexity in Python.
|
|||
|
|
"><link data-rh="true" rel="icon" href="/img/favicon.ico"><link data-rh="true" rel="canonical" href="https://blog.mfocko.xyz/algorithms/hash-tables/breaking/python/"><link data-rh="true" rel="alternate" href="https://blog.mfocko.xyz/algorithms/hash-tables/breaking/python/" hreflang="en"><link data-rh="true" rel="alternate" href="https://blog.mfocko.xyz/algorithms/hash-tables/breaking/python/" hreflang="x-default"><link data-rh="true" rel="preconnect" href="https://0VXRFPR4QF-dsn.algolia.net" crossorigin="anonymous"><link rel="search" type="application/opensearchdescription+xml" title="mf" href="/opensearch.xml">
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
<link rel="alternate" type="application/rss+xml" href="/blog/rss.xml" title="mf RSS Feed">
|
|||
|
|
<link rel="alternate" type="application/atom+xml" href="/blog/atom.xml" title="mf Atom Feed">
|
|||
|
|
<link rel="alternate" type="application/json" href="/blog/feed.json" title="mf JSON Feed">
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.13.24/dist/katex.min.css" integrity="sha384-odtC+0UGzzFL/6PNoE8rX/SPcQDXBJ+uRepguP4QkPCm2LBxH3FA3y+fKSiJ+AmM" crossorigin="anonymous"><link rel="stylesheet" href="/assets/css/styles.0f577c26.css">
|
|||
|
|
<script src="/assets/js/runtime~main.f17742ff.js" defer="defer"></script>
|
|||
|
|
<script src="/assets/js/main.a809bb25.js" defer="defer"></script>
|
|||
|
|
</head>
|
|||
|
|
<body class="navigation-with-keyboard">
|
|||
|
|
<script>!function(){function t(t){document.documentElement.setAttribute("data-theme",t)}var e=function(){try{return new URLSearchParams(window.location.search).get("docusaurus-theme")}catch(t){}}()||function(){try{return localStorage.getItem("theme")}catch(t){}}();t(null!==e?e:"light")}(),function(){try{const c=new URLSearchParams(window.location.search).entries();for(var[t,e]of c)if(t.startsWith("docusaurus-data-")){var a=t.replace("docusaurus-data-","data-");document.documentElement.setAttribute(a,e)}}catch(t){}}()</script><div id="__docusaurus"><div role="region" aria-label="Skip to main content"><a class="skipToContent_fXgn" href="#__docusaurus_skipToContent_fallback">Skip to main content</a></div><nav aria-label="Main" class="navbar navbar--fixed-top"><div class="navbar__inner"><div class="navbar__items"><button aria-label="Toggle navigation bar" aria-expanded="false" class="navbar__toggle clean-btn" type="button"><svg width="30" height="30" viewBox="0 0 30 30" aria-hidden="true"><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></button><a class="navbar__brand" href="/"><b class="navbar__title text--truncate">mf</b></a><div class="navbar__item dropdown dropdown--hoverable"><a href="#" aria-haspopup="true" aria-expanded="false" role="button" class="navbar__link">Additional FI MU materials</a><ul class="dropdown__menu"><li><a aria-current="page" class="dropdown__link dropdown__link--active" href="/algorithms/">Algorithms</a></li><li><a class="dropdown__link" href="/c/">C</a></li><li><a class="dropdown__link" href="/cpp/">C++</a></li></ul></div><a class="navbar__item navbar__link" href="/contributions/">Contributions</a><a class="navbar__item navbar__link" href="/talks/">Talks</a></div><div class="navbar__items navbar__items--right"><a class="navbar__item navbar__link" href="/blog/">Blog</a><div class="toggle_vylO colorModeToggle_DEke"><button class="clean-btn toggleButton_gllP toggleButtonDisabled_aARS" type="button" disabled="" title="Switch between dark and light mode (currently light mode)" aria-label="Switch between dark and light mode (currently light mode)" aria-live="polite"><svg viewBox="0 0 24 24" width="24" height="24" class="lightToggleIcon_pyhR"><path fill="currentColor" d="M12,9c1.65,0,3,1.35,3,3s-1.35,3-3,3s-3-1.35-3-3S10.35,9,12,9 M12,7c-2.76,0-5,2.24-5,5s2.24,5,5,5s5-2.24,5-5 S14.76,7,12,7L12,7z M2,13l2,0c0.55,0,1-0.45,1-1s-0.45-1-1-1l-2,0c-0.55,0-1,0.45-1,1S1.45,13,2,13z M20,13l2,0c0.55,0,1-0.45,1-1 s-0.45-1-1-1l-2,0c-0.55,0-1,0.45-1,1S19.45,13,20,13z M11,2v2c0,0.55,0.45,1,1,1s1-0.45,1-1V2c0-0.55-0.45-1-1-1S11,1.45,11,2z M11,20v2c0,0.55,0.45,1,1,1s1-0.45,1-1v-2c0-0.55-0.45-1-1-1C11.45,19,11,19.45,11,20z M5.99,4.58c-0.39-0.39-1.03-0.39-1.41,0 c-0.39,0.39-0.39,1.03,0,1.41l1.06,1.06c0.39,0.39,1.03,0.39,1.41,0s0.39-1.03,0-1.41L5.99,4.58z M18.36,16.95 c-0.39-0.39-1.03-0.39-1.41,0c-0.39,0.39-0.39,1.03,0,1.41l1.06,1.06c0.39,0.39,1.03,0.39,1.41,0c0.39-0.39,0.39-1.03,0-1.41 L18.36,16.95z M19.42,5.99c0.39-0.39,0.39-1.03,0-1.41c-0.39-0.39-1.03-0.39-1.41,0l-1.06,1.06c-0.39,0.39-0.39,1.03,0,1.41 s1.03,0.39,1.41,0L19.42,5.99z M7.05,18.36c0.39-0.39,0.39-1.03,0-1.41c-0.39-0.39-1.03-0.39-1.41,0l-1.06,1.06 c-0.39,0.39-0.39,1.03,0,1.41s1.03,0.39,1.41,0L7.05,18.36z"></path></svg><svg viewBox="0 0 24 24" width="24" height="24" class="darkToggleIcon_wfgR"><path fill="currentColor" d="M9.37,5.51C9.19,6.15,9.1,6.82,9.1,7.5c0,4.08,3.32,7.4,7.4,7.4c0.68,0,1.35-0.09,1.99-0.27C17.45,17.19,14.93,19,12,19 c-3.86,0-7-3.14-7-7C5,9.07,6.81,6.55,9.37,5.51z M12,3c-4.97,0-9,4.03-9,9s4.03,9,9,9s9-4.03,9-9c0-0.46-0.04-0.92-0.1-1.36 c-0.98,1.37-2.58,2.26-4.4,2.26c-2.98,0-5.4-2.42-5.4-5.4c0-1.81,0.89-3.42,2.26-4.4C12.92,3.04,12.46,3,12,3L12,3z"></path></svg></button></div><div class="navbarSearchContainer_Bca1"><button type="button" class="DocSearch DocSearch-Button" aria-label="Search"><span class="DocSearch-Button-Container"><svg width="20" height="20" class="DocSearch-Search-Icon" viewBox="0 0 20 20"><path d="M14.386 14.386l4.0877 4.0877-4.0877-4.0877c-2.
|
|||
|
|
<p>Our language of choice for bringing the worst out of the hash table is <em>Python</em>.</p>
|
|||
|
|
<p>Let's start by talking about the hash function and why we've chosen Python for
|
|||
|
|
this. Hash function for integers in Python is simply <em>identity</em>, as you might've
|
|||
|
|
guessed, there's no avalanche effect. Another thing that helps us is the fact
|
|||
|
|
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
|
|||
|
|
more pressure on the hashing function.</p>
|
|||
|
|
<p>From the perspective of the implementation, it is a hash table that uses probing
|
|||
|
|
to resolve conflicts. This also means that it's a contiguous space in memory.
|
|||
|
|
Indexing works like in the provided example above. When the hash table reaches
|
|||
|
|
a <em>breaking point</em> (defined somewhere in the C code), it reallocates the table
|
|||
|
|
and rehashes everything.</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>Resizing and rehashing can reduce the conflicts. That is coming from the fact
|
|||
|
|
that the position in the table is determined by the hash and the size of the
|
|||
|
|
table itself.</p></div></div>
|
|||
|
|
<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>
|
|||
|
|
<p>Knowing the things above, it is not that hard to construct a method how to cause
|
|||
|
|
as many conflicts as possible. Let's go over it:</p>
|
|||
|
|
<ol>
|
|||
|
|
<li>We know that integers are hashed to themselves.</li>
|
|||
|
|
<li>We also know that from that hash we use only lower bits that are used as
|
|||
|
|
indices.</li>
|
|||
|
|
<li>We also know that there's a rehashing on resize that could possibly fix the
|
|||
|
|
conflicts.</li>
|
|||
|
|
</ol>
|
|||
|
|
<p>We will test with different sequences:</p>
|
|||
|
|
<ol>
|
|||
|
|
<li>ordered one, numbers through 1 to N</li>
|
|||
|
|
<li>ordered one in a reversed order, numbers through N back to 1</li>
|
|||
|
|
<li>numbers that are shifted to the left, so they create conflicts until resize</li>
|
|||
|
|
<li>numbers that are shifted to the left, but resizing helps only in the end</li>
|
|||
|
|
<li>numbers that are shifted to the left, but they won't be taken in account even
|
|||
|
|
after final resize</li>
|
|||
|
|
</ol>
|
|||
|
|
<p>For each of these sequences, we will insert 10⁷ elements and look each of them
|
|||
|
|
up for 10 times in a row.</p>
|
|||
|
|
<p>As a base of our benchmark, we will use a <code>Strategy</code> class and then for each
|
|||
|
|
strategy we will just implement the sequence of numbers that it uses:</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">class</span><span class="token plain"> </span><span class="token class-name">Strategy</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">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</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"> data_structure</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">set</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">_table </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> data_structure</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" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token decorator annotation punctuation" style="color:#393A34">@cached_property</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">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">elements</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 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">raise</span><span class="token plain"> NotImplementedError</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">"Implement for each strategy"</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" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token decorator annotation punctuation" style="color:#393A34">@property</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">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">name</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 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" styl
|
|||
|
|
<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>
|
|||
|
|
<p>Let's have a look at how we generate the numbers to be inserted:</p>
|
|||
|
|
<ul>
|
|||
|
|
<li>ordered sequence (ascending)<!-- -->
|
|||
|
|
<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 plain">x </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> x </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 plain">N_ELEMENTS</span><span class="token punctuation" style="color:#393A34">)</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>ordered sequence (descending)<!-- -->
|
|||
|
|
<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 plain">x </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> x </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">reversed</span><span class="token punctuation" style="color:#393A34">(</span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">N_ELEMENTS</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</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-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 punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34"><<</span><span class="token plain"> </span><span class="token builtin">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">bit_length</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 punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> x </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 plain">N_ELEMENTS</span><span class="token punctuation" style="color:#393A34">)</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-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 punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34"><<</span><span class="token plain"> </span><span class="token builtin">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">bit_length</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 punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> x </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">reversed</span><span class="token punctuation" style="color:#393A34">(</span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">N_ELEMENTS</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</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-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 plain">x </span><span class="token operator" style="color:#393A34"><<</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">32</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> x </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 plain">N_ELEMENTS</span><span class="token punctuation" style="color:#393A34">)</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="path:///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="path:///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>
|
|||
|
|
</section></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/cpp/">cpp</a></li><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/hash-tables/">hash-tables</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/12-hash-tables/2023-11-28-breaking/01-python.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="2023-11-28T00:00:00.000Z">Nov 28, 2023</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/hash-tables/breaking/"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">Breaking Hash Table</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/algorithms/hash-tables/breaking/mitigations/"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Possible Mitigations</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="#breaking-the-hash-table-in-python" class="table-of-contents__link toc-highlight">Breaking the Hash Table in Python</a></li><li><a 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 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" target="_blank" rel="noopener noreferrer" class="footer__link-item">GitLab<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://git.mfocko.xyz/mfocko" target="_blank" rel="noopener noreferrer" class="footer__link-item">Gitea (self-hosted)<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></ul></d
|
|||
|
|
</body>
|
|||
|
|
</html>
|