{"id":11246,"date":"2025-11-26T12:17:14","date_gmt":"2025-11-26T06:47:14","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=11246"},"modified":"2026-01-11T18:56:59","modified_gmt":"2026-01-11T13:26:59","slug":"topological-sort-dfs","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/topological-sort-dfs\/","title":{"rendered":"Topological Sort DFS"},"content":{"rendered":"\n<!-- PrismJS for Syntax Highlighting -->\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\" rel=\"stylesheet\">\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: #030302;\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\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\n.wp_blog_explanation code {\n  background: #fef9f4; 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\/* makes it the reference for absolute children *\/\n}\n\n.wp_blog_toggle-btn {\n  position: absolute;\n  top: 1rem;\n  right: 1rem;\n  z-index: 9999;\n  padding: 0.5rem 0.8rem;\n  border-radius: 10%;\n  background: var(--primary);\n  color: white;\n  font-weight: bold;\n  cursor: pointer;\n  border: none;\n  box-shadow: var(--shadow);\n  transition: background 0.3s, transform 0.2s;\n}\n\n.wp_blog_toggle-btn:hover {\n  background: #cc772e;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_code-tabs-container {\n  background: #1e1e1e;\n}\n<\/style>\n\n<div class=\"wp_blog_container wp_blog_theme\">\n  <button id=\"blogNotesThemeToggle\" class=\"wp_blog_toggle-btn\">\ud83c\udf19<\/button>\n  <h1 class=\"wp_blog_main-heading\"><\/h1>\n\n  <div class=\"wp_blog_explanation\">\n    <h2>Topological Sort<\/h2>\n    <p><strong><code>\n      It is a linear ordering of nodes of a DAG(Directed Acyclic Graph) such that for every directed edge (u -> v), node u comes before v.\n    <\/code><\/strong><\/p>\n\n    <h3>Example<\/h3>\n    <p><strong>An adjacency list represents a graph.<\/strong><\/p>\n    <p>\n      <pre>\n        const adj = [\n            [],          \/\/ 0\n            [],          \/\/ 1\n            [3],         \/\/ 2 -> 3\n            [1],         \/\/ 3 -> 1\n            [0, 1],      \/\/ 4 -> 0, 1\n            [0, 2]       \/\/ 5 -> 0, 2 \n        ]\n      <\/pre>\n    <\/p>\n\n    <h2>Representation<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/11\/Screenshot-2025-11-26-at-11.51.35-AM.png\" alt=\"\">\n    <p>\n      <strong>\n        <code>5, 0, 2, 3, 1, 4<\/code>    \n      <\/strong>\n    <\/p>\n\n    <h2>Code<\/h2>\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 <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n    <pre>\n    function topologicalSortDFS(n, graph) {\n    let ans = [];\n    let visited = new Set();\n\n    function dfs(curr) {\n        visited.add(curr);\n\n        for (let neighbor of graph[curr]) {\n            if (!visited.has(neighbor)) {\n                dfs(neighbor);\n            }\n        }\n\n        ans.push(curr);\n    }\n\n    for (let i = 0; i < n; i++) {\n        if (!visited.has(i)) {\n            dfs(i);\n        }\n    }\n\n    return ans.reverse();\n}\n\nconst n = 6;\nconst adj = [\n    [],        \/\/ 0\n    [],        \/\/ 1\n    [3],       \/\/ 2 -> 3\n    [1],       \/\/ 3 -> 1\n    [0, 1],    \/\/ 4 -> 0, 1\n    [0, 2]     \/\/ 5 -> 0, 2\n];\n\nconsole.log(topologicalSortDFS(n, adj));\n\n    <\/pre>\n<\/div> \n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre>\ndef topological_sort_dfs(n, graph):\n    visited = [False] * n\n    ans = []\n\n    def dfs(curr):\n        visited[curr] = True\n        for neighbor in graph[curr]:\n            if not visited[neighbor]:\n                dfs(neighbor)\n        ans.append(curr)\n\n    for i in range(n):\n        if not visited[i]:\n            dfs(i)\n\n    return ans[::-1]\n\n\nn = 6\nadj = [\n    [],        # 0\n    [],        # 1\n    [3],       # 2 -> 3\n    [1],       # 3 -> 1\n    [0, 1],    # 4 -> 0, 1\n    [0, 2]     # 5 -> 0, 2\n]\n\nprint(topological_sort_dfs(n, adj))\n\n      <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre>\nimport java.util.*;\n\nclass Solution {\n\n    static void dfs(int curr,\n                    List<List<Integer>> graph,\n                    boolean[] visited,\n                    List<Integer> ans) {\n\n        visited[curr] = true;\n\n        for (int neighbor : graph.get(curr)) {\n            if (!visited[neighbor]) {\n                dfs(neighbor, graph, visited, ans);\n            }\n        }\n\n        ans.add(curr);\n    }\n\n    static List<Integer> topologicalSort(int n, List<List<Integer>> graph) {\n        boolean[] visited = new boolean[n];\n        List<Integer> ans = new ArrayList<>();\n\n        for (int i = 0; i < n; i++) {\n            if (!visited[i]) {\n                dfs(i, graph, visited, ans);\n            }\n        }\n\n        Collections.reverse(ans);\n        return ans;\n    }\n\n    public static void main(String[] args) {\n        int n = 6;\n        List<List<Integer>> graph = new ArrayList<>();\n\n        for (int i = 0; i < n; i++) {\n            graph.add(new ArrayList<>());\n        }\n\n        graph.get(2).add(3);\n        graph.get(3).add(1);\n        graph.get(4).add(0);\n        graph.get(4).add(1);\n        graph.get(5).add(0);\n        graph.get(5).add(2);\n\n        System.out.println(topologicalSort(n, graph));\n    }\n}\n    <\/code><\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n      <pre>\n#include &lt;bits\/stdc++.h&gt;\nusing namespace std;\n\nvoid dfs(\n    int curr,\n    vector<vector<int>>& graph,\n    vector<bool>& visited,\n    vector<int>& ans\n) {\n    visited[curr] = true;\n\n    for (int neighbor : graph[curr]) {\n        if (!visited[neighbor]) {\n            dfs(neighbor, graph, visited, ans);\n        }\n    }\n\n    ans.push_back(curr);\n}\n\nvector<int> topologicalSort(int n, vector<vector<int>>& graph) {\n    vector<bool> visited(n, false);\n    vector<int> ans;\n\n    for (int i = 0; i < n; i++) {\n        if (!visited[i]) {\n            dfs(i, graph, visited, ans);\n        }\n    }\n\n    reverse(ans.begin(), ans.end());\n    return ans;\n}\n\nint main() {\n    int n = 6;\n    vector<vector<int>> graph(n);\n\n    graph[2].push_back(3);\n    graph[3].push_back(1);\n    graph[4].push_back(0);\n    graph[4].push_back(1);\n    graph[5].push_back(0);\n    graph[5].push_back(2);\n\n    vector<int> result = topologicalSort(n, graph);\n\n    for (int x : result) {\n        cout << x << \" \";\n    }\n\n    return 0;\n}\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre>\n#include &lt;stdio.h&gt;\n\nint graph[6][2] = {\n    {},        \/\/ 0\n    {},        \/\/ 1\n    {3},       \/\/ 2 -> 3\n    {1},       \/\/ 3 -> 1\n    {0, 1},    \/\/ 4 -> 0, 1\n    {0, 2}     \/\/ 5 -> 0, 2\n};\n\nint size[6] = {0, 0, 1, 1, 2, 2};\nint visited[6] = {0};\nint ans[6];\nint idx = 0;\n\nvoid dfs(int curr)\n{\n    visited[curr] = 1;\n\n    for (int i = 0; i < size[curr]; i++)\n    {\n        int neighbor = graph[curr][i];\n        if (!visited[neighbor])\n        {\n            dfs(neighbor);\n        }\n    }\n\n    ans[idx++] = curr;\n}\n\nint main()\n{\n    for (int i = 0; i < 6; i++)\n    {\n        if (!visited[i])\n        {\n            dfs(i);\n        }\n    }\n\n    \/* Reverse and print result *\/\n    for (int i = 5; i >= 0; i--)\n    {\n        printf(\"%d \", ans[i]);\n    }\n\n    return 0;\n}\n\n <\/code><\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n    <pre>\nusing System;\nusing System.Collections.Generic;\n\nclass Solution\n{\n    static void DFS(\n        int curr,\n        List<int>[] graph,\n        bool[] visited,\n        List<int> ans)\n    {\n        visited[curr] = true;\n\n        foreach (int neighbor in graph[curr])\n        {\n            if (!visited[neighbor])\n            {\n                DFS(neighbor, graph, visited, ans);\n            }\n        }\n\n        ans.Add(curr);\n    }\n\n    static List<int> TopologicalSort(int n, List<int>[] graph)\n    {\n        bool[] visited = new bool[n];\n        List<int> ans = new List<int>();\n\n        for (int i = 0; i < n; i++)\n        {\n            if (!visited[i])\n            {\n                DFS(i, graph, visited, ans);\n            }\n        }\n\n        ans.Reverse();\n        return ans;\n    }\n\n    static void Main()\n    {\n        int n = 6;\n        List<int>[] graph = new List<int>[n];\n\n        for (int i = 0; i < n; i++)\n        {\n            graph[i] = new List<int>();\n        }\n\n        graph[2].Add(3);\n        graph[3].Add(1);\n        graph[4].Add(0);\n        graph[4].Add(1);\n        graph[5].Add(0);\n        graph[5].Add(2);\n\n        var result = TopologicalSort(n, graph);\n        Console.WriteLine(string.Join(\" \", result));\n    }\n}\n\n    <\/code><\/pre>\n    <\/div>\n  <\/div>\n\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  const themeToggle = document.getElementById(\"blogNotesThemeToggle\");\n  const themeContainer = document.querySelector(\".wp_blog_theme\");\n\n  themeToggle.addEventListener(\"click\", () => {\n    themeContainer.classList.toggle(\"dark-mode\");\n    themeToggle.textContent =\n      themeContainer.classList.contains(\"dark-mode\") ? \"\u2600\ufe0f\" : \"\ud83c\udf19\";\n  });\n});\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Topological Sort It is a linear ordering of nodes of a DAG(Directed Acyclic Graph) such that for every directed edge (u -> v), node u comes before v. Example An adjacency list represents a graph. const adj = [ [], \/\/ 0 [], \/\/ 1 [3], \/\/ 2 -> 3 [1], \/\/ 3 -><\/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":[210,322,260,176,175,211,811,174,172,173],"tags":[],"class_list":["post-11246","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-c-c-plus-plus","category-csharp","category-cplusplus","category-data-structures","category-data-structures-and-algorithms","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11246","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=11246"}],"version-history":[{"count":3,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11246\/revisions"}],"predecessor-version":[{"id":11435,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11246\/revisions\/11435"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=11246"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=11246"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=11246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}