{"id":11300,"date":"2025-12-08T20:00:45","date_gmt":"2025-12-08T14:30:45","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=11300"},"modified":"2026-01-11T19:24:31","modified_gmt":"2026-01-11T13:54:31","slug":"shortest-path-in-unweighted-graph-bfs","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/shortest-path-in-unweighted-graph-bfs\/","title":{"rendered":"Shortest Path in Unweighted Graph BFS"},"content":{"rendered":"\n<!-- Shortest Path in unweighted graph -->\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  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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    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n    <pre>\n      function shortestDistance(graph, src){\n        let n = graph.length;\n        const dist = new Array(n).fill(Infinity);\n        dist[src] = 0;\n\n        let q = [src];\n        while(q.length) {\n          let curr = q.shift();\n          for(let neighbor of graph[curr]) {\n            if(dist[neighbor] == Infinity) {\n              dist[neighbor] = dist[curr] + 1;\n              q.push(neighbor);\n            }\n          }\n        }\n        return dist;\n      }\n\n      const graph = [\n        [1, 2],   \/\/ 0\n        [3],      \/\/ 1\n        [4],      \/\/ 2\n        [5],      \/\/ 3\n        [3],      \/\/ 4\n        []        \/\/ 5\n      ];\n    <\/pre>\n    <\/div>\n     <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre>\nfrom collections import deque\n\ndef shortest_distance(graph, src):\n    n = len(graph)\n    dist = [float('inf')] * n\n    dist[src] = 0\n\n    q = deque([src])\n\n    while q:\n        curr = q.popleft()\n        for neighbor in graph[curr]:\n            if dist[neighbor] == float('inf'):\n                dist[neighbor] = dist[curr] + 1\n                q.append(neighbor)\n\n    return dist\n\n\ngraph = [\n    [1, 2],   # 0\n    [3],      # 1\n    [4],      # 2\n    [5],      # 3\n    [3],      # 4\n    []        # 5\n]\n\nprint(shortest_distance(graph, 0))\n    <\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre>import java.util.*;\n\nclass Solution {\n    static int[] shortestDistance(List<List<Integer>> graph, int src) {\n        int n = graph.size();\n        int[] dist = new int[n];\n        Arrays.fill(dist, Integer.MAX_VALUE);\n        dist[src] = 0;\n\n        Queue<Integer> q = new LinkedList<>();\n        q.add(src);\n\n        while (!q.isEmpty()) {\n            int curr = q.poll();\n            for (int neighbor : graph.get(curr)) {\n                if (dist[neighbor] == Integer.MAX_VALUE) {\n                    dist[neighbor] = dist[curr] + 1;\n                    q.add(neighbor);\n                }\n            }\n        }\n        return dist;\n    }\n\n    public static void main(String[] args) {\n        List<List<Integer>> graph = new ArrayList<>();\n\n        graph.add(Arrays.asList(1, 2));\n        graph.add(Arrays.asList(3));\n        graph.add(Arrays.asList(4));\n        graph.add(Arrays.asList(5));\n        graph.add(Arrays.asList(3));\n        graph.add(new ArrayList<>());\n\n        System.out.println(Arrays.toString(shortestDistance(graph, 0)));\n    }\n}\n  <\/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\nvector<int> shortestDistance(vector<vector<int>>& graph, int src) {\n    int n = graph.size();\n    vector<int> dist(n, INT_MAX);\n    dist[src] = 0;\n\n    queue<int> q;\n    q.push(src);\n\n    while (!q.empty()) {\n        int curr = q.front();\n        q.pop();\n\n        for (int neighbor : graph[curr]) {\n            if (dist[neighbor] == INT_MAX) {\n                dist[neighbor] = dist[curr] + 1;\n                q.push(neighbor);\n            }\n        }\n    }\n    return dist;\n}\n\nint main() {\n    vector<vector<int>> graph = {\n        {1, 2},\n        {3},\n        {4},\n        {5},\n        {3},\n        {}\n    };\n\n    vector<int> res = shortestDistance(graph, 0);\n    for (int x : res) cout << x << \" \";\n}\n<\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre>\n#include &lt;stdio.h&gt;\n#include &lt;limits.h&gt;\n\nint graph[6][2] = {\n    {1, 2},\n    {3},\n    {4},\n    {5},\n    {3},\n    {}\n};\n\nint size[] = {2, 1, 1, 1, 1, 0};\n\nint main() {\n    int n = 6, src = 0;\n    int dist[6];\n\n    for (int i = 0; i < n; i++)\n        dist[i] = INT_MAX;\n\n    dist[src] = 0;\n\n    int queue[6], front = 0, rear = 0;\n    queue[rear++] = src;\n\n    while (front < rear) {\n        int curr = queue[front++];\n\n        for (int i = 0; i < size[curr]; i++) {\n            int neighbor = graph[curr][i];\n            if (dist[neighbor] == INT_MAX) {\n                dist[neighbor] = dist[curr] + 1;\n                queue[rear++] = neighbor;\n            }\n        }\n    }\n\n    for (int i = 0; i < n; i++)\n        printf(\"%d \", dist[i]);\n\n    return 0;\n}\n<\/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    static int[] ShortestDistance(List<int>[] graph, int src) {\n        int n = graph.Length;\n        int[] dist = new int[n];\n        Array.Fill(dist, int.MaxValue);\n        dist[src] = 0;\n\n        Queue<int> q = new Queue<int>();\n        q.Enqueue(src);\n\n        while (q.Count > 0) {\n            int curr = q.Dequeue();\n            foreach (int neighbor in graph[curr]) {\n                if (dist[neighbor] == int.MaxValue) {\n                    dist[neighbor] = dist[curr] + 1;\n                    q.Enqueue(neighbor);\n                }\n            }\n        }\n        return dist;\n    }\n\n    static void Main() {\n        List<int>[] graph = new List<int>[] {\n            new List<int>{1, 2},\n            new List<int>{3},\n            new List<int>{4},\n            new List<int>{5},\n            new List<int>{3},\n            new List<int>()\n        };\n\n        var result = ShortestDistance(graph, 0);\n        Console.WriteLine(string.Join(\" \", result));\n    }\n}\n<\/pre>\n    <\/div>\n  <\/div>\n\n    <h2>Time Complexity: <code>O(V + E)<\/code> <\/h2>\n    <h2>Space Complexity: <code>O(E)<\/code> <\/h2>\n\n    <h4>Here: V = Vertices, E = Edges<\/h4>\n    \n    <h2><strong>Note:<\/strong><\/h2>\n    <p><strong><code>If you have an undirected graph, you can represent it as a directed graph by adding edges in both directions.<\/code><\/strong><\/p>\n<\/div>  \n<\/div>\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) => 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neighbor of graph[curr]) { if(dist[neighbor] == Infinity) { 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