{"id":8973,"date":"2025-08-05T23:31:13","date_gmt":"2025-08-05T18:01:13","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8973"},"modified":"2025-11-07T15:10:08","modified_gmt":"2025-11-07T09:40:08","slug":"search-in-a-bst","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/search-in-a-bst\/","title":{"rendered":"Search in a BST"},"content":{"rendered":"\n<!-- Search in Binary 3 -->\n<link\n  href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\"\n  rel=\"stylesheet\"\n\/>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/prism.min.js\"><\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/plugins\/autoloader\/prism-autoloader.min.js\"><\/script>\n\n<style>\n.wp_blog_theme {\n  --primary: #E58C32;\n  --secondary: #f8c291;\n  --light-bg: #fef9f4;\n  --text-dark: #2d2d2d;\n  --tab-radius: 12px;\n  --shadow: 0 4px 12px rgba(0, 0, 0, 0.08);\n  --code-bg: #001f3f;\n  --code-text: #d4f1ff;\n}\n\n.wp_blog_container {\n  font-family: 'Segoe UI', sans-serif;\n  background: var(--light-bg);\n  margin: 0;\n  padding: 0;\n  color: var(--text-dark);\n}\n\n\/* Heading *\/\n.wp_blog_main-heading {\n  text-align: center;\n  font-size: 2.4rem;\n  color: var(--primary);\n  margin-top: 2.5rem;\n  font-weight: bold;\n}\n\n\/* Explanation Card *\/\n.wp_blog_explanation,\n.wp_blog_code-tabs-container {\n  max-width: 940px;\n  margin: 2rem auto;\n  padding: 2rem;\n  background: white;\n  border-radius: var(--tab-radius);\n  box-shadow: var(--shadow);\n}\n\n\/* Text and Visuals *\/\n.wp_blog_explanation h2 {\n  font-size: 1.4rem;\n  color: var(--primary);\n  margin-bottom: 0.5rem;\n}\n.wp_blog_explanation h5 {\n  color: var(--primary);\n}\n.wp_blog_explanation p,\n.wp_blog_explanation li {\n  font-size: 1.05rem;\n  line-height: 1.7;\n  margin: 0.5rem 0;\n}\n.wp_blog_explanation code {\n  background: #f9cea6;\n  color: #2d2d2d;\n  padding: 3px 6px;\n  border-radius: 4px;\n  font-family: 'Courier New', monospace;\n}\n.wp_blog_explanation img {\n  max-width: 100%;\n  border-radius: var(--tab-radius);\n  margin-top: 1rem;\n  box-shadow: 0 2px 12px rgba(0, 0, 0, 0.06);\n}\n\n\/* Tab Buttons *\/\n.wp_blog_code-tabs-header {\n  display: flex;\n  flex-wrap: wrap;\n  gap: 0.5rem;\n  margin-bottom: 1rem;\n}\n.wp_blog_code-tab-button {\n  padding: 0.6rem 1.2rem;\n  border: 1px solid var(--primary);\n  background: white;\n  color: var(--primary);\n  border-radius: 50px;\n  font-weight: 600;\n  cursor: pointer;\n  transition: all 0.3s ease;\n}\n.wp_blog_code-tab-button:hover {\n  background: var(--secondary);\n}\n.wp_blog_code-tab-button.active {\n  background: var(--primary);\n  color: white;\n}\n\n\/* Code Content *\/\n.wp_blog_code-tab-content {\n  display: none;\n  background: var(--code-bg);\n  border-radius: var(--tab-radius);\n}\n.wp_blog_code-tab-content.active {\n  display: block;\n}\n.wp_blog_code-tab-content pre {\n  margin: 0;\n  padding: 1.5rem;\n  font-size: 1rem;\n  overflow-x: auto;\n  background: var(--code-bg);\n  border-radius: var(--tab-radius);\n  color: var(--code-text);\n}\n<\/style>\n\n<!-- Approach 1 -->\n<div class=\"wp_blog_container wp_blog_theme\">\n  <h1 class=\"wp_blog_main-heading\"><\/h1>\n  <div class=\"wp_blog_explanation\">\n    <h2>Problem Statement:<\/h2>\n    <p>You are given the <code>root<\/code> of a binary search tree (BST) and an integer <code>val<\/code>.<\/p>\n    <p>Find the node in the BST that the node&#8217;s value equals <code>val<\/code> and return the subtree rooted with that node. If such a node does not exist, return <code>null<\/code>.<\/p>\n\n    <h2>Examples:<\/h2>\n    <h3>Example 1:<\/h3>\n    <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-05-at-8.44.56 PM.png\" alt=\"\">\n    <p><strong>Input:<\/strong> root = [4,2,7,1,3], val = 2<\/p>\n    <p><strong>Output:<\/strong> [2,1,3]<\/p>\n\n    <h3>Example 2:<\/h3>\n    <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-05-at-8.44.56 PM.png\" alt=\"\">\n    <p><strong>Input:<\/strong> root = [4,2,7,1,3], val = 5<\/p>\n    <p><strong>Output:<\/strong> []<\/p>\n\n    <h2>Constraints:<\/h2>\n    <ul>\n      <li>The number of nodes in the tree is in the range <code>[1, 5000]<\/code>.<\/li>\n      <li><code>1 <= Node.val <= 10<sup>7<\/sup><\/code><\/li>\n      <li><code>root<\/code> is a binary search tree.<\/li>\n      <li><code>1 <= val <= 10<sup>7<\/sup><\/code><\/li>\n    <\/ul>\n\n    <h2>Approach 1: Top-Down Method<\/h2>\n    <ul>\n      <li>If the current node&#8217;s value <code>equals<\/code> the target <code>val<\/code>, we store it as the answer.<\/li>\n      <li>If the current value is <code>less<\/code> than the target, we move to the right subtree.<\/li>\n      <li>If the current value is <code>greater<\/code> than the target, we move to the left subtree.<\/li>\n      <li>We <strong>return<\/strong> the node if found, otherwise return <code>null<\/code>.<\/li>\n    <\/ul>\n\n    <h2>Time Complexity:<\/h2>\n    <li><p><strong>Time Complexity = O(log n)<\/strong><\/p><\/li>\n\n    <h2>Space Complexity:<\/h2>\n    <li><p><strong>Space Complexity = O(log n)<\/strong><\/p><\/li>\n\n    <h2>Dry Run<\/h2>\n    <div style=\"background: #f9f9f9; padding: 10px; border: 1px solid #ccc; font-family: monospace;\">\n      <b>Function Call:<\/b> searchBST(root, val = 6) where<br>\n      root = Node(4)<br>\n      \u251c\u2500\u2500 left: Node(2)<br>\n      \u2502&nbsp;&nbsp;&nbsp;&nbsp;\u251c\u2500\u2500 left: Node(1)<br>\n      \u2502&nbsp;&nbsp;&nbsp;&nbsp;\u2514\u2500\u2500 right: Node(3)<br>\n      \u2514\u2500\u2500 right: Node(7)<br>\n      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u251c\u2500\u2500 left: Node(6)<br>\n      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2514\u2500\u2500 right: Node(9)<br><br>\n\n      <b>Step 1:<\/b><br>\n      \u2192 Call traversal(curr = 4)<br>\n      \u2192 curr.val = 4, which is less than val = 6<br>\n      \u2192 So, move to curr.right<br><br>\n\n      \u2192 Call traversal(curr = 7)<br>\n      \u2192 curr.val = 7, which is greater than val = 6<br>\n      \u2192 So, move to curr.left<br><br>\n\n      \u2192 Call traversal(curr = 6)<br>\n      \u2192 curr.val == val (6 == 6)<br>\n      \u2192 ans = curr (Node with value 6)<br><br>\n\n      \u2192 traversal ends<br><br>\n\n      <b>Final Result:<\/b> return Node with value = 6<br>\n    <\/div>\n  <\/div>\n\n  <div class=\"wp_blog_code-tabs-container\">\n    <div class=\"wp_blog_code-tabs-header\">\n      <button class=\"wp_blog_code-tab-button active\" data-lang=\"js\">JavaScript<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"py\">Python<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"java\">Java<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"cpp\">C++<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"c\">C<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"cs\">C#<\/button>\n    <\/div>\n\n    <!-- JavaScript -->\n    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n      <pre><code class=\"language-javascript\">\nvar searchBST = function(root, val) {\n    let ans = null;\n    let traversal = (curr) => {\n        if (curr.val == val) {\n            ans = curr;\n        } else {\n            if (curr.val < val) {\n                curr.right &#038;&#038; traversal(curr.right);\n            } else {\n                curr.left &#038;&#038; traversal(curr.left);\n            }\n        }\n    }\n    traversal(root);\n    return ans;\n};\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- Python -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef searchBST(root, val):\n    ans = None\n    def traversal(curr):\n        nonlocal ans\n        if not curr:\n            return\n        if curr.val == val:\n            ans = curr\n        elif curr.val < val:\n            traversal(curr.right)\n        else:\n            traversal(curr.left)\n    traversal(root)\n    return ans\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- Java -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\npublic TreeNode searchBST(TreeNode root, int val) {\n    TreeNode[] ans = new TreeNode[1];\n    voidTraversal(root, val, ans);\n    return ans[0];\n}\nprivate void voidTraversal(TreeNode curr, int val, TreeNode[] ans) {\n    if (curr == null) return;\n\n    if (curr.val == val) {\n        ans[0] = curr;\n    } else if (curr.val < val) {\n        voidTraversal(curr.right, val, ans);\n    } else {\n        voidTraversal(curr.left, val, ans);\n    }\n}\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- C++ -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n      <pre><code class=\"language-cpp\">\nTreeNode* searchBST(TreeNode* root, int val) {\n    TreeNode* ans = nullptr;\n    function<void(TreeNode*)> traversal = [&](TreeNode* curr) {\n        if (!curr) return;\n        if (curr->val == val) {\n            ans = curr;\n        } else {\n            if (curr->val < val) {\n                traversal(curr->right);\n            } else {\n                traversal(curr->left);\n            }\n        }\n    };\n    traversal(root);\n    return ans;\n}\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- C -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre><code class=\"language-c\">\nTreeNode* searchBST(TreeNode* root, int val) {\n    if (root == NULL) return NULL;\n\n    if (root->val == val)\n        return root;\n    else if (root->val < val)\n        return searchBST(root->right, val);\n    else\n        return searchBST(root->left, val);\n}\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- C# -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n      <pre><code class=\"language-csharp\">\npublic TreeNode SearchBST(TreeNode root, int val) {\n    TreeNode ans = null;\n    void Traversal(TreeNode curr) {\n        if (curr == null) return;\n        if (curr.val == val) {\n            ans = curr;\n        } else {\n            if (curr.val < val)\n                Traversal(curr.right);\n            else\n                Traversal(curr.left);\n        }\n    }   \n    Traversal(root);\n    return ans;\n}\n      <\/code><\/pre>\n    <\/div>\n  <\/div>\n<\/div>\n\n<!-- Approach 2 -->\n<div class=\"wp_blog_container wp_blog_theme\">\n  <h1 class=\"wp_blog_main-heading\"><\/h1>\n  <div class=\"wp_blog_explanation\">\n    <h2>Approach 2: Bottom-Up Method<\/h2>\n    <ul>\n      <li><strong>Best Case:<\/strong> If the current node is <code>null<\/code> or matches the target <code>val<\/code>, return it.<\/li>\n      <li><strong>Recursive Step:<\/strong>\n        <ul>\n          <li>If the current node's value is less than <code>val<\/code>, search in the right <strong>subtree<\/strong>.<\/li>\n          <li>If greater, search in the <strong>left subtree<\/strong>.<\/li>\n        <\/ul>\n      <\/li>\n    <\/ul>\n\n    <h2>Time Complexity:<\/h2>\n    <li>\n      <p><strong>Time Complexity = O(h)<\/strong>, where <code>h<\/code> is the height of the tree.<\/p>\n      <ul>\n        <li>Best: <code>O(log n)<\/code> (balanced tree)<\/li>\n        <li>Worst: <code>O(n)<\/code> (skewed tree)<\/li>\n      <\/ul>\n    <\/li>\n\n    <h2>Space Complexity:<\/h2>\n    <li><p><strong>Space Complexity = O(h)<\/strong><\/p><\/li>\n\n    <h2>Dry Run<\/h2>\n    <div style=\"background: #f9f9f9; padding: 10px; border: 1px solid #ccc; font-family: monospace;\">\n      <b>Function Call:<\/b> searchBST(root, val = 6) where<br>\n      root = Node(4)<br>\n      \u251c\u2500\u2500 left: Node(2)<br>\n      \u2502&nbsp;&nbsp;&nbsp;&nbsp;\u251c\u2500\u2500 left: Node(1)<br>\n      \u2502&nbsp;&nbsp;&nbsp;&nbsp;\u2514\u2500\u2500 right: Node(3)<br>\n      \u2514\u2500\u2500 right: Node(7)<br>\n      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u251c\u2500\u2500 left: Node(6)<br>\n      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2514\u2500\u2500 right: Node(9)<br><br>\n\n      <b>Step 1:<\/b><br>\n      \u2192 searchBST(Node(4), 6)<br>\n      \u2192 4 &lt; 6 \u2192 go right<br><br>\n\n      <b>Step 2:<\/b><br>\n      \u2192 searchBST(Node(7), 6)<br>\n      \u2192 7 &gt; 6 \u2192 go left<br><br>\n\n      <b>Step 3:<\/b><br>\n      \u2192 searchBST(Node(6), 6)<br>\n      \u2192 6 == 6 \u2192 return Node(6)<br><br>\n\n      <b>Final Result:<\/b> return Node with value = 6<br>\n    <\/div>\n  <\/div>\n\n  <div class=\"wp_blog_code-tabs-container\">\n    <div class=\"wp_blog_code-tabs-header\">\n      <button class=\"wp_blog_code-tab-button active\" data-lang=\"js\">JavaScript<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"py\">Python<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"java\">Java<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"cpp\">C++<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"c\">C<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"cs\">C#<\/button>\n    <\/div>\n\n    <!-- JavaScript -->\n    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n      <pre><code class=\"language-javascript\">\nvar searchBST = function(root, val) {\n    if(!root || root.val === val) return root;\n    return root.val < val ?\n        searchBST(root.right, val) :\n        searchBST(root.left, val);\n};\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- Python -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef searchBST(root, val):\n    if not root or root.val == val:\n        return root\n    return searchBST(root.right, val) if root.val < val else searchBST(root.left, val)\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- Java -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\npublic TreeNode searchBST(TreeNode root, int val) {\n    if (root == null || root.val == val) return root;\n    return root.val < val ?\n        searchBST(root.right, val) :\n        searchBST(root.left, val);\n}\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- C++ -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n      <pre><code class=\"language-cpp\">\nTreeNode* searchBST(TreeNode* root, int val) {\n    if (!root || root->val == val) return root;\n    return root->val < val ?\n        searchBST(root->right, val) :\n        searchBST(root->left, val);\n}\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- C -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre><code class=\"language-c\">\nstruct TreeNode {\n    int val;\n    struct TreeNode* left;\n    struct TreeNode* right;\n};\n\nstruct TreeNode* searchBST(struct TreeNode* root, int val) {\n    if (root == NULL || root->val == val) return root;\n    return root->val < val ?\n        searchBST(root->right, val) :\n        searchBST(root->left, val);\n}\n      <\/code><\/pre>\n    <\/div>\n\n    <!-- C# -->\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n      <pre><code class=\"language-csharp\">\npublic TreeNode SearchBST(TreeNode root, int val) {\n    if (root == null || root.val == val) return root;\n    return root.val < val ?\n        SearchBST(root.right, val) :\n        SearchBST(root.left, val);\n}\n      <\/code><\/pre>\n    <\/div>\n  <\/div>\n<\/div>\n\n<script>\ndocument.addEventListener(\"DOMContentLoaded\", () => {\n  const buttons = document.querySelectorAll(\".wp_blog_code-tab-button\");\n  const contents = document.querySelectorAll(\".wp_blog_code-tab-content\");\n\n  buttons.forEach((button) => {\n    button.addEventListener(\"click\", () => {\n      const lang = button.getAttribute(\"data-lang\");\n\n      buttons.forEach((btn) => btn.classList.remove(\"active\"));\n      contents.forEach((content) => content.classList.remove(\"active\"));\n\n      button.classList.add(\"active\");\n      document\n        .querySelector(`.wp_blog_code-tab-content[data-lang=\"${lang}\"]`)\n        .classList.add(\"active\");\n    });\n  });\n});\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Problem Statement: You are given the root of a binary search tree (BST) and an integer val. Find the node in the BST that the node&#8217;s value equals val and return the subtree rooted with that node. If such a node does not exist, return null. Examples: Example 1: Input: root = [4,2,7,1,3], val =<\/p>\n","protected":false},"author":108,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[210,260,176,175,211,810,174,172],"tags":[],"class_list":["post-8973","post","type-post","status-publish","format-standard","category-algorithms","category-c-c-plus-plus","category-csharp","category-cplusplus","category-data-structures","category-dsa","category-java","category-javascript"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8973","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/users\/108"}],"replies":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/comments?post=8973"}],"version-history":[{"count":3,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8973\/revisions"}],"predecessor-version":[{"id":10964,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8973\/revisions\/10964"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}