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class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">Algorithms</span><meta itemprop="position" content="1"></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">Sorting</span><meta itemprop="position" content="2"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Bubble Sort</span><meta itemprop="position" content="3"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><header><h1>Bubble Sort</h1></header><h2 class="anchor anchorWithStickyNavbar_LWe7" id="idea">Idea<a href="#idea" class="hash-link" aria-label="Direct link to Idea" title="Direct link to Idea"></a></h2><ul><li>compare each item wth the item next to it, and swap positions if required</li><li>the largest element will be bubbled to the end of the array</li><li>algorithm repeats until we have a pass without swapping any elements</li></ul><h2 class="anchor anchorWithStickyNavbar_LWe7" id="visualization">Visualization<a href="#visualization" class="hash-link" aria-label="Direct link to Visualization" title="Direct link to Visualization"></a></h2><br><h2 class="anchor anchorWithStickyNavbar_LWe7" id="implementation">Implementation<a href="#implementation" class="hash-link" aria-label="Direct link to Implementation" title="Direct link to Implementation"></a></h2><ul><li>for every step, move largest element in left unsorted array to the end; in this caes, avoid inner loop to iterate through right sorted subarray</li><li>for every step, swap unordered adjacent pair until no swap is needed </li><li>note that in one pass, more than one element can be placed into their final positions, so the position after last swap is sorted and do not need to traverse again</li></ul><div class="language-java codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-java codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">void</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">bubbleSort</span><span class="token punctuation" style="color:#393A34">(</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> arr</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 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">int</span><span class="token plain"> n </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> arr</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">length</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 punctuation" style="color:#393A34">(</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> i </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> i </span><span class="token operator" style="color:#393A34"><</span><span class="token plain"> n</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> i</span><span class="token operator" 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 punctuation" style="color:#393A34">(</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> j </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> j </span><span class="token operator" style="color:#393A34"><</span><span class="token plain"> n</span><span class="token operator" style="color:#393A34">-</span><span class="token plain">i</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> j</span><span class="token operator" 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 punctuation" style="color:#393A34">(</span><span class="token plain">arr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">j</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 plain"> arr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">j</span><span class="token operator" style="color:#393A34">+</span><span class="token number" style="color:#36acaa">1</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 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">// swap arr[j+1] and arr[i] </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">int</span><span class="token plain"> temp </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> arr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">j</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"> arr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">j</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 plain"> arr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">j</span><span class="token operator" style="color:#393A34">+</span><span class="token number" style="color:#36acaa">1</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"> arr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">j</span><span class="token operator" style="color:#393A34">+</span><span class="token number" style="color:#36acaa">1</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 plain"> temp</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 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 punctuation" style="color:#393A34">}</span><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><h2 class="anchor anchorWithStickyNavbar_LWe7" id="time-and-space-analysis">Time and Space Analysis<a href="#time-and-space-analysis" class="hash-link" aria-label="Direct link to Time and Space Analysis" title="Direct link to Time and Space Analysis"></a></h2><ul><li>Time O(n^2)</li><li>Space O(1)</li></ul><h2 class="anchor anchorWithStickyNavbar_LWe7" id="properties">Properties<a href="#properties" class="hash-link" aria-label="Direct link to Properties" title="Direct link to Properties"></a></h2><ul><li>the algorithm garantees that the list is sorted</li><li>Turtle and Hare Problem:<ul><li>larger elements at the beginning get swapped to the end quickly, but small elements at the end get swapped very slowly to the beginning</li><li>this property is good to find k largest elements - use outer loop of bubble sort for k times</li></ul></li></ul><h2 class="anchor anchorWithStickyNavbar_LWe7" id="variants">Variants<a href="#variants" class="hash-link" aria-label="Direct link to Variants" title="Direct link to Variants"></a></h2><ul><li><a href="https://www.geeksforgeeks.org/odd-even-sort-brick-sort/" target="_blank" rel="noopener noreferrer">Odd Even Sort / Brick Sort</a></li><li><a href="https://www.geeksforgeeks.org/cocktail-sort/" target="_blank" rel="noopener noreferrer">Cocktail Sort</a></li></ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages"><a class="pagination-nav__link pagination-nav__link--next" href="/Algorithms/Sorting/InsertionSort"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Insertion Sort</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="#idea" class="table-of-contents__link toc-highlight">Idea</a></li><li><a href="#visualization" class="table-of-contents__link toc-highlight">Visualization</a></li><li><a href="#implementation" class="table-of-contents__link toc-highlight">Implementation</a></li><li><a href="#time-and-space-analysis" class="table-of-contents__link toc-highlight">Time and Space Analysis</a></li><li><a href="#properties" class="table-of-contents__link toc-highlight">Properties</a></li><li><a href="#variants" class="table-of-contents__link toc-highlight">Variants</a></li></ul></div></div></div></div></main></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">Links</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://docusaurus.io" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path 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