{"id":11222,"date":"2025-11-24T14:27:45","date_gmt":"2025-11-24T08:57:45","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=11222"},"modified":"2025-11-24T17:17:50","modified_gmt":"2025-11-24T11:47:50","slug":"allpathsfromsourcetotarget","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/allpathsfromsourcetotarget\/","title":{"rendered":"All Paths from Source to Target"},"content":{"rendered":"\n<!-- Inorder & Postorder recursive approach: 4 -->\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: #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\n    <h1 class=\"wp_blog_main-heading\"><\/h1>\n    <div class=\"wp_blog_explanation\">\n        <h2>Problem Statement<\/h2>\n        <p>\n            Given a directed acyclic graph <strong>(DAG)<\/strong> of n nodes labeled from <code>0<\/code> to <code>n - 1<\/code>, find all possible paths from node 0 to node n &#8211; 1 and return them in any order.\n        <\/p>\n\n        <p>\n            The graph is given as follows: <code>graph[i]<\/code> is a list of all nodes you can visit from node i (i.e., there is a directed edge from node i to node <code>graph[i][j]<\/code>).\n        <\/p>\n                <h2>Example 1:<\/h2>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/11\/Screenshot-2025-11-24-at-2.00.53-PM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> graph = [[1,2],[3],[3],[]]<\/p>\n                <p><strong>Output:<\/strong> [[0,1,3],[0,2,3]]<\/p>\n                <p><strong>Explanation:<\/strong> There are two paths: 0 -> 1 -> 3 and 0 -> 2 -> 3.\n&#8211; 0 \u2192 1 \u2192 2\n&#8211; 0 \u2192 2<\/p>\n            \n                <h2>Example 2:<\/h2>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/11\/Screenshot-2025-11-24-at-2.24.51-PM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> graph = [[4,3,1],[3,2,4],[3],[4],[]]\n                <p><strong>Output:<\/strong> [[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4],[0,1,4]]<\/p>\n\n                    <h2>Constraints:<\/h2>\n                   <ul>\n                    <li><code>n == graph.length<\/code><\/li>\n                    <li><code>2 <= n <= 15<\/code><\/li>\n                    <li><code>0 <= graph[i][j] < n<\/code><\/li>\n                    <li><code>graph[i][j] != i<\/code> (i.e., there will be no self-loops).<\/li>\n                    <li>All the elements of <code>graph[i]<\/code> are <strong>unique<\/strong>.<\/li>\n                    <li>The input graph is <strong>guranteed<\/strong> to be a <strong>DAG.<\/strong><\/li>\n                   <\/ul>\n\n                <h2>Approach<\/h2>\n            <ul>\n                <li>Treat the graph as a directed adjacency list.<\/li>\n                <li>Start DFS from node 0 and aim to reach the last node (n \u2212 1).<\/li>\n                <li>Maintain a current path list to track the nodes visited on the current route.<\/li>\n                <li>Whenever we reach the target node, store a copy of the current path in the result.<\/li>\n                <li>For each neighbor of the current node,\n                    <ul><code>\n                        <li>add the neighbor to the path,<\/li>\n                        <li>recursively explore it,<\/li>\n                        <li>then backtrack by removing the neighbor after returning.<\/li>\n                    <\/code>\n                    <\/ul>\n                <\/li>\n                <li><strong>Return<\/strong> the list of all valid paths.<\/li>\n            <\/ul>\n\n                <!-- <h2>Time Complexity:<\/h2>\n                <li>\n                  <p><strong>Time Complexity = O(n)<\/strong>\n                  <\/li>\n                <h2>Space Complexity:<\/h2>\n                <li>\n                  <p><strong>Space Complexity = O(n)<\/strong><\/p>\n                <\/li> -->\n<h2>Dry Run<\/h2> <div style=\"background: var(--light-bg); border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0; color: var(--text-dark);\"> <p><strong>Input:<\/strong> <code>graph = [[1,2],[3],[3],[]]<\/code><\/p> <pre style=\"white-space: pre-wrap; background: var(--code-bg); padding: 1rem; border-radius: 8px; overflow-x: auto; color: var(--code-text);\"> Graph Structure (Adjacency List): 0 \u2192 [1, 2] 1 \u2192 [3] 2 \u2192 [3] 3 \u2192 []\n    Initialize:\n    start = 0\n    end = 3\n    allPaths = [ ]\n\n    Start DFS: dfs(0, [0])\n    \u2022 curr = 0\n    \u2022 neighbors = [1, 2]\n\n    Explore neighbor 1:\n    \u2022 path = [0,1]\n    dfs(1, [0,1])\n    \u2022 curr = 1\n    \u2022 neighbors = [3]\n\n    Explore neighbor 3:\n    \u2022 path = [0,1,3]\n    dfs(3, [0,1,3])\n    \u2022 curr === end \u2192 push [0,1,3] into allPaths\n\n    Backtrack to curr = 0\n\n    Explore neighbor 2:\n    \u2022 path = [0,2]\n    dfs(2, [0,2])\n    \u2022 curr = 2\n    \u2022 neighbors = [3]\n\n    Explore neighbor 3:\n    \u2022 path = [0,2,3]\n    dfs(3, [0,2,3])\n    \u2022 curr === end \u2192 push [0,2,3] into allPaths\n\n    All neighbors of 0 explored\n\n    Final Answer:\n    allPaths = [[0,1,3], [0,2,3]]\n<\/pre> \n<p><strong>Output:<\/strong> <code>[[0,1,3],[0,2,3]]<\/code><\/p>\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 allPathsSourceTarget = function(graph) {\n    let start = 0;\n    let end = graph.length - 1;\n    let allPaths = [];\n    let dfs = (curr, path) => {\n        if(curr === end){\n            allPaths.push([...path]);\n            return;\n        }\n        for(let neighbor of graph[curr]){\n            path.push(neighbor)\n            dfs(neighbor, path);\n            path.pop();\n        }\n    }\n\n    dfs(0, [0])\n    return allPaths;\n};\n     <\/code><\/pre>\n        <\/div>\n\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n            <pre><code class=\"language-python\">\nfrom typing import List\n\ndef allPathsSourceTarget(graph: List[List[int]]) -> List[List[int]]:\n    target = len(graph) - 1\n    res = []\n    path = []\nimport java.util.*;\n\npublic class Solution {\n    public List<List<Integer>> allPathsSourceTarget(int[][] graph) {\n        int target = graph.length - 1;\n        List<List<Integer>> res = new ArrayList<>();\n        LinkedList<Integer> path = new LinkedList<>();\n\n        dfs(0, target, graph, path, res);\n        return res;\n    }\n\n    private void dfs(int node, int target, int[][] graph, LinkedList<Integer> path, List<List<Integer>> res) {\n        path.add(node);\n        if (node == target) {\n            res.add(new ArrayList<>(path));\n        } else {\n            for (int nei : graph[node]) {\n                dfs(nei, target, graph, path, res);\n            }\n        }\n        path.removeLast();\n    }\n}\n    def dfs(node):\n        path.append(node)\n        if node == target:\n            res.append(path.copy())\n        else:\n            for nei in graph[node]:\n                dfs(nei)\n        path.pop()\n\n    dfs(0)\n    return res\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\">\nimport java.util.*;\npublic class Solution {\n    public List<List<Integer>> allPathsSourceTarget(int[][] graph) {\n        int target = graph.length - 1;\n        List<List<Integer>> res = new ArrayList<>();\n        LinkedList<Integer> path = new LinkedList<>();\n\n        dfs(0, target, graph, path, res);\n        return res;\n    }\n    private void dfs(int node, int target, int[][] graph, LinkedList<Integer> path, List<List<Integer>> res) {\n        path.add(node);\n        if (node == target) {\n            res.add(new ArrayList<>(path));\n        } else {\n            for (int nei : graph[node]) {\n                dfs(nei, target, graph, path, res);\n            }\n        }\n        path.removeLast();\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\">\n#include &lt;bits\/stdc++.h&gt;              \nusing namespace std;\n\nvector<vector<int>> allPathsSourceTarget(vector<vector<int>>& graph) {\n    int target = graph.size() - 1;\n    vector<vector<int>> allPaths;\n    vector<int> path;\n\n    function<void(int)> dfs = [&](int node) {\n        path.push_back(node);\n        if (node == target) {\n            allPaths.push_back(path);\n        } else {\n            for (int nei : graph[node]) {\n                dfs(nei);\n            }\n        }\n        path.pop_back();\n    };\n\n    dfs(0);\n    return allPaths;\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\">\n#include &lt;stdlib.h&gt;\n#include &lt;stdio.h&gt;\n\nstatic int **results = NULL;\nstatic int *resultsCols = NULL;\nstatic int resultsCount = 0;\nstatic int resultsCap = 0;\n\nvoid add_result(int *path, int len) {\n    if (resultsCount == resultsCap) {\n        resultsCap = resultsCap == 0 ? 8 : resultsCap * 2;\n        results = (int**)realloc(results, resultsCap * sizeof(int*));\n        resultsCols = (int*)realloc(resultsCols, resultsCap * sizeof(int));\n    }\n    int *copy = (int*)malloc(len * sizeof(int));\n    for (int i = 0; i < len; ++i) copy[i] = path[i];\n    results[resultsCount] = copy;\n    resultsCols[resultsCount] = len;\n    resultsCount++;\n}\n\nvoid dfs_c(int node, int target, int *path, int pathLen, int **graph, int *graphColSize) {\n    path[pathLen++] = node;\n    if (node == target) {\n        add_result(path, pathLen);\n    } else {\n        for (int i = 0; i < graphColSize[node]; ++i) {\n            int nei = graph[node][i];\n            dfs_c(nei, target, path, pathLen, graph, graphColSize);\n        }\n    }\n}\n\nint** allPathsSourceTarget(int** graph, int graphSize, int* graphColSize, int* returnSize, int** returnColumnSizes) {\n    \/\/ reset globals\n    results = NULL;\n    resultsCols = NULL;\n    resultsCount = 0;\n    resultsCap = 0;\n\n    int target = graphSize - 1;\n    int *path = (int*)malloc((graphSize + 5) * sizeof(int)); \/\/ max depth = graphSize\n    dfs_c(0, target, path, 0, graph, graphColSize);\n    free(path);\n\n    *returnSize = resultsCount;\n    *returnColumnSizes = resultsCols;\n    return results;\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\">\nusing System;\nusing System.Collections.Generic;\n\npublic class Solution {\n    public IList<IList<int>> AllPathsSourceTarget(int[][] graph) {\n        int target = graph.Length - 1;\n        var res = new List<IList<int>>();\n        var path = new List<int>();\n\n        void Dfs(int node) {\n            path.Add(node);\n            if (node == target) {\n                res.Add(new List<int>(path));\n            } else {\n                foreach (var nei in graph[node]) {\n                    Dfs(nei);\n                }\n            }\n            path.RemoveAt(path.Count - 1);\n        }\n\n        Dfs(0);\n        return res;\n    }\n}\n       <\/code><\/pre>\n        <\/div>\n    <\/div>\n<\/div>\n\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","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Problem Statement Given a directed acyclic graph (DAG) of n nodes labeled from 0 to n &#8211; 1, find all possible paths from node 0 to node n &#8211; 1 and return them in any order. The graph is given as follows: graph[i] is a list of all nodes you can visit from node<\/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":[210,322,260,176,175,211,811,810,174,172,173],"tags":[],"class_list":{"0":"post-11222","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-algorithms-and-data-structures","8":"category-c-c-plus-plus","9":"category-csharp","10":"category-cplusplus","11":"category-data-structures","12":"category-data-structures-and-algorithms","13":"category-dsa","14":"category-java","15":"category-javascript","16":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11222","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=11222"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11222\/revisions"}],"predecessor-version":[{"id":11226,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11222\/revisions\/11226"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=11222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=11222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=11222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}