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<title data-rh="true">Segment Tree Data Structure | Patternize.io</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" property="og:url" content="https://patternize.github.io/DataStructures/Tree/SegmentTree"><meta data-rh="true" name="docusaurus_locale" content="en"><meta data-rh="true" name="docsearch:language" content="en"><meta data-rh="true" name="og:type" content="website"><meta data-rh="true" name="og:title" content="Patternize.io - Algorithm Visualizations"><meta data-rh="true" name="og:description" content="Learn algorithms and data structures through interactive visualizations"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" name="canonical" content="https://patternize.github.io/docs/Applications/ReactFiber/intro-to-react-fiber"><meta data-rh="true" name="google-site-verification" content="JN9CClo-YacOkqWq94rsPvJaScJJpeowfQaO7TF6Dvw"><meta data-rh="true" name="docusaurus_version" content="current"><meta data-rh="true" name="docusaurus_tag" content="docs-default-current"><meta data-rh="true" name="docsearch:version" content="current"><meta data-rh="true" name="docsearch:docusaurus_tag" content="docs-default-current"><meta data-rh="true" property="og:title" content="Segment Tree Data Structure | Patternize.io"><meta data-rh="true" name="description" content="Learn about Segment Tree data structure - how it works, range queries, updates, and time complexity. Includes implementation examples in Java and common use cases."><meta data-rh="true" property="og:description" content="Learn about Segment Tree data structure - how it works, range queries, updates, and time complexity. Includes implementation examples in Java and common use cases."><meta data-rh="true" name="keywords" content="segment tree,data structure,range queries,range updates,tree data structure,segment tree implementation,java segment tree"><link data-rh="true" rel="icon" href="/img/favicon.ico"><link data-rh="true" rel="canonical" href="https://patternize.github.io/DataStructures/Tree/SegmentTree"><link data-rh="true" rel="alternate" href="https://patternize.github.io/DataStructures/Tree/SegmentTree" hreflang="en"><link data-rh="true" rel="alternate" href="https://patternize.github.io/DataStructures/Tree/SegmentTree" hreflang="x-default"><link data-rh="true" rel="preconnect" href="https://BL2GDNRTKH-dsn.algolia.net" crossorigin="anonymous"><link rel="search" type="application/opensearchdescription+xml" title="Patternize.io" href="/opensearch.xml">

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class="hash-link" aria-label="Direct link to Idea" title="Direct link to Idea"></a></h2><ul><li>This is mostly used for mutable range sum.</li><li>For general segment tree built against a array of <code>n</code> length, the segment tree is <code>2n</code> because <code> (n+n/2+n/4+n/8+…+1≈2n)</code></li><li>Segment Tree is only good when you have consistent interval updates and queries. It is not useful if you have to print or give analytics over all data points</li></ul><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><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">class SegmentTree { int st[]; // The array that stores segment tree nodes int n; SegmentTree(int arr[]) { n = arr.length; int x = (int) (Math.ceil(Math.log(n) / Math.log(2))); //Maximum size of segment tree int max_size = 2 * (int) Math.pow(2, x) - 1; st = new int[max_size]; // Memory allocation constructTree(arr, 0, n - 1, 0); } // A recursive function that constructs Segment Tree for array[ss..se]. // si is index of current node in segment tree st int constructTree(int arr[], int ss, int se, int si) { // If there is one element in array, store it in current node of // segment tree and return if (ss == se) { st[si] = arr[ss]; return arr[ss]; } // If there are more than one elements, then recur for left and // right subtrees and store the sum of values in this node int mid = ss + (se - ss) / 2; st[si] = constructTree(arr, ss, mid, si * 2 + 1) + constructTree(arr, mid + 1, se, si * 2 + 2); return st[si]; } int getSumUtil(int ss, int se, int qs, int qe, int si) { // If segment of this node is a part of given range, then return // the sum of the segment if (qs <= ss && qe >= se) return st[si]; // If segment of this node is outside the given range if (se < qs || ss > qe) return 0; // If a part of this segment overlaps with the given range int mid = ss + (se - ss) / 2; return getSumUtil(ss, mid, qs, qe, 2 * si + 1) + getSumUtil(mid + 1, se, qs, qe, 2 * si + 2); } void updateValueUtil(int ss, int se, int i, int diff, int si) { // Base Case: If the input index lies outside the range of // this segment if (i < ss || i > se) return; // If the input index is in range of this node, then update the // value of the node and its children st[si] = st[si] + diff; if (se != ss) { int mid = ss + (se - ss) / 2; updateValueUtil(ss, mid, i, diff, 2 * si + 1); updateValueUtil(mid + 1, se, i, diff, 2 * si + 2); } } // The function to update a value in input array and segment tree. // It uses updateValueUtil() to update the value in segment tree void updateValue(int arr[], int n, int i, int new_val) { // Check for erroneous input index if (i < 0 || i > n - 1) { return; } // Get the difference between new value and old value int diff = new_val - arr[i]; // Update the value in array arr[i] = new_val; // Update the values of nodes in segment tree updateValueUtil(0, n - 1, i, diff, 0); } // Return sum of elements in range from index qs (quey start) to // qe (query end). It mainly uses getSumUtil() int getSum(int n, int qs, int qe) { // Check for erroneous input values if (qs < 0 || qe > n - 1 || qs > qe) { return -1; } return getSumUtil(0, n - 1, qs, qe, 0); } } </code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><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></button></div></div></div><h2 class="anchor anchorWithStickyNavbar_LWe7" id="runtime-analysis">Runtime Analysis<a href="#runtime-analysis" class="hash-link" aria-label="Direct link to Runtime Analysis" title="Direct link to Runtime Analysis"></a></h2><ul><li>Build the tree: O(n)</li><li>Update Tree: O(log n)</li><li>Query: O(log n)</li></ul><h2 class="anchor anchorWithStickyNavbar_LWe7" id="reference">Reference<a href="#reference" class="hash-link" aria-label="Direct link to Reference" title="Direct link to Reference"></a></h2><ul><li><a href="https://www.geeksforgeeks.org/segment-tree-set-1-sum-of-given-range/" target="_blank" rel="noopener noreferrer">GeeksForGeeks Implement</a></li></ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages"></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="#implementation" class="table-of-contents__link toc-highlight">Implementation</a></li><li><a href="#runtime-analysis" class="table-of-contents__link toc-highlight">Runtime Analysis</a></li><li><a href="#reference" class="table-of-contents__link toc-highlight">Reference</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 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://airbnb.io/visx" target="_blank" rel="noopener noreferrer" class="footer__link-item">airbnb/visx<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></div><div class="col footer__col"><div class="footer__title">Resources</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://cs229.stanford.edu/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Stanford CS229 Machine Learning</a></li><li class="footer__item"><a href="https://stanford-cs161.github.io/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Stanford CS161 Introduction to Algorithms</a></li></ul></div><div class="col footer__col"><div class="footer__title">Follow Us</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://github.com/patternize" target="_blank" rel="noopener noreferrer" class="footer__link-item">Patternize.io<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></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2025 Patternize.io</div></div></div></footer></div>

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