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Print all possible strings that can be made by placing spaces
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Print all paths from a given source to a destination

Last Updated : 22 Apr, 2025
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Given a directed acyclic graph, a source vertex src and a destination vertex dest, print all paths from given src to dest. 

Examples:

Input: V = 4, edges[ ][ ] = [[0, 1], [1, 2], [1, 3], [2, 3]], src = 0, dest = 3
Output: [[0, 1, 2, 3], [0, 1, 3]]
Explanation: There are two ways to reach at 3 from 0. These are: 0 -> 1 -> 3 and 0 -> 1 -> 2 -> 3.

Print-all-paths-2

Input: V = 4, edges[ ][ ] = [[0, 3], [0, 1], [1, 3], [2, 1], [2, 0]], src = 2, dest = 3
Output: [[2, 1, 3], [2, 0, 3], [2, 0, 1, 3]]
Explanation: There are three ways to reach at 3 from 2. These are: 2 -> 1 -> 3, 2 -> 0 -> 3 and 2 -> 0 -> 1 -> 3.

Print-all-paths-1

Table of Content

  • [Approach 1] Using DFS - O( 2^V) time and O(V + E) space
  • [Approach 2] Using BFS - O( 2^V) time and O(V + E) space

[Approach 1] Using DFS

The main idea uses DFS to explore all paths from the source to the destination in a directed graph. It recursively builds paths, stores them when the destination is reached, and backtracks to explore alternative routes.

C++ 
// C++ Program to print all paths // from source to destination   #include <iostream> #include <vector> using namespace std;  void dfs(int src, int dest, vector<vector<int>> &graph, vector<int> &path,                                 vector<vector<int>> &allPaths){                                          // Add the current vertex to the path     path.push_back(src);      // Store the path when destination is reached     if (src == dest){         allPaths.push_back(path);     }     else{         for (int adj_node:graph[src]){             dfs(adj_node, dest, graph, path, allPaths);         }     }      // remove the current vertex from the path     path.pop_back(); }  vector<vector<int>> findPaths(int v, vector<vector<int>> &edges, int src, int dest){     vector<vector<int>> graph(v);      // Build the graph from edges     for (const auto &edge : edges){         graph[edge[0]].push_back(edge[1]);     }      vector<vector<int>> allPaths;     vector<int> path;      dfs(src, dest, graph, path, allPaths);      return allPaths; }  int main(){     vector<vector<int>> edges = {{0, 3}, {0, 1}, {1, 3}, {2, 0}, {2, 1}};     int src = 2, dest = 3;     int v = 4;      vector<vector<int>> paths = findPaths(v, edges, src, dest);      for (const auto &path : paths){         for (int vtx : path){             cout << vtx << " ";         }         cout << endl;     }     return 0; }
Java 
// Java Program to print all paths // from source to destination   import java.util.ArrayList; import java.util.List;   class GfG {      static ArrayList<ArrayList<Integer>> dfs(int src, int dest,                     List<List<Integer>> graph, ArrayList<Integer> path,                             ArrayList<ArrayList<Integer>> allPaths) {                  // Add the current vertex to the path         path.add(src);          // Store the path when destination is reached         if (src == dest) {             allPaths.add(new ArrayList<>(path));         } else {             for (int adjNode : graph.get(src)) {                 dfs(adjNode, dest, graph, path, allPaths);             }         }          // remove the current vertex from the path         path.remove(path.size() - 1);         return allPaths;     }       static ArrayList<ArrayList<Integer>> findPaths(int v, int[][] edges,                             int src, int dest) {         List<List<Integer>> graph = new ArrayList<>();          // Build the graph from edges         for (int i = 0; i < v; i++) {             graph.add(new ArrayList<>());         }         for (int[] edge : edges) {             graph.get(edge[0]).add(edge[1]);         }          ArrayList<ArrayList<Integer>> allPaths = new ArrayList<>();         ArrayList<Integer> path = new ArrayList<>();          dfs(src, dest, graph, path, allPaths);          return allPaths;     }      public static void main(String[] args) {         int[][] edges = {{0, 3}, {0, 1}, {1, 3}, {2, 0}, {2, 1}};         int src = 2, dest = 3;         int v = 4;          ArrayList<ArrayList<Integer>> paths = findPaths(v, edges, src, dest);          for (ArrayList<Integer> path : paths) {             for (int vtx : path) {                 System.out.print(vtx + " ");             }             System.out.println();         }     } }
Python 
# Python Program to print all paths # from source to destination   def dfs(src, dest, graph, path, allPaths):     # Add the current vertex to the path     path.append(src)      # Store the path when destination is reached     if src == dest:         allPaths.append(path.copy())     else:         for adj_node in graph[src]:             dfs(adj_node, dest, graph, path, allPaths)      # remove the current vertex from the path     path.pop()  def findPaths(v, edges, src, dest):     graph = [[] for _ in range(v)]      # Build the graph from edges     for edge in edges:         graph[edge[0]].append(edge[1])      allPaths = []     path = []      dfs(src, dest, graph, path, allPaths)      return allPaths  if __name__ == "__main__":     edges = [[0, 3], [0, 1], [1, 3], [2, 0], [2, 1]]     src = 2     dest = 3     v = 4      paths = findPaths(v, edges, src, dest)      for path in paths:         for vtx in path:             print(vtx, end=" ")         print()
C# 
using System; using System.Collections.Generic;  class GfG {     static void dfs(int src, int dest, int[,] graph, bool[] visited,         List<int> path,         List<List<int>> allPaths) {         // Add the current vertex to the path         path.Add(src);          // If destination is reached, store the path         if (src == dest) {             allPaths.Add(new List<int>(path));         }         else {                          // Recurse for all adjacent vertices             for (int adjNode = 0; adjNode < graph.GetLength(0); adjNode++) {                 if (graph[src, adjNode] == 1 && !visited[adjNode]) {                     visited[adjNode] = true;                     dfs(adjNode, dest, graph, visited, path, allPaths);                     visited[adjNode] = false;                 }             }         }          // Remove the current vertex from path         path.RemoveAt(path.Count - 1);     }      public static List<List<int>> FindPaths(int v, int[,] edges, int src, int dest) {         int[,] graph = new int[v, v];          // Build the graph from edges         for (int i = 0; i < edges.GetLength(0); i++) {             int u = edges[i, 0];             int vtx = edges[i, 1];              // mark the edge between u and vtx             graph[u, vtx] = 1;         }          bool[] visited = new bool[v];         List<int> path = new List<int>();         List<List<int>> allPaths = new List<List<int>>();          visited[src] = true;         dfs(src, dest, graph, visited, path, allPaths);          return allPaths;     }      public static void Main(string[] args) {         int[,] edges = new int[,]         {             { 0, 3 }, { 0, 1 }, { 1, 3 }, { 2, 0 }, { 2, 1 }         };         int src = 2, dest = 3;         int v = 4;          List<List<int>> paths = FindPaths(v, edges, src, dest);          foreach (List<int> path in paths) {             foreach (int vtx in path) {                 Console.Write(vtx + " ");             }             Console.WriteLine();         }     } }
JavaScript 
// JavaScript Program to print all paths // from source to destination  function dfs(src, dest, graph, path, allPaths){          // Add the current vertex to the path     path.push(src);      // Store the path when destination is reached     if (src === dest) {         allPaths.push([...path ]);     }     else {         for (let adjNode of graph[src]) {             dfs(adjNode, dest, graph, path, allPaths);         }     }      // remove the current vertex from the path     path.pop(); }  function findPaths(v, edges, src, dest){     let graph = Array.from({length : v}, () => []);      // Build the graph from edges     for (let edge of edges) {         graph[edge[0]].push(edge[1]);     }      let allPaths = [];     let path = [];      dfs(src, dest, graph, path, allPaths);      return allPaths; }  // Driver Code const edges =     [ [ 0, 3 ], [ 0, 1 ], [ 1, 3 ], [ 2, 0 ], [ 2, 1 ] ]; const src = 2; const dest = 3; const v = 4;  const paths = findPaths(v, edges, src, dest);  for (const path of paths) {     console.log(path.join(" ")); }

Output
2 0 3  2 0 1 3  2 1 3

Time Complexity: O(2V ), where V is number of vertices. There can be at most 2V paths in the graph
Auxiliary Space: O(V + E)

[Approach 2] Using BFS

The main idea is to use Breadth-First Search (BFS) to find all paths from a source to a destination in a directed graph. It uses a queue to explore all possible paths level by level. Each path is stored and extended by adding adjacent nodes, and when the destination is reached, the current path is added to the result.

C++ 
// C++ Program to find all paths  // from source to destination in a directed graph  #include <iostream> #include <queue> #include <vector> using namespace std;  vector<vector<int>> findPaths(int v, vector<vector<int>> &edges,                                 int src, int dest) {     vector<vector<int>> graph(v);      // Build the graph from edges     for (const auto &edge : edges) {         graph[edge[0]].push_back(edge[1]);     }      vector<vector<int>> allPaths;     queue<vector<int>> q;      // Initialize queue with the starting path     q.push({src});      while (!q.empty()) {         vector<int> path = q.front();         q.pop();          int current = path.back();          // If destination is reached, store the path         if (current == dest) {             allPaths.push_back(path);         }          // Explore all adjacent vertices         for (int adj : graph[current]) {             vector<int> newPath = path;             newPath.push_back(adj);             q.push(newPath);         }     }      return allPaths; }  int main() {     vector<vector<int>> edges = {{0, 3}, {0, 1}, {1, 3}, {2, 0}, {2, 1}};     int src = 2, dest = 3;     int v = 4;      // Find all paths from source to destination     vector<vector<int>> paths = findPaths(v, edges, src, dest);      // Print all the paths     for (const auto &path : paths) {         for (int vtx : path) {             cout << vtx << " ";         }         cout << endl;     }      return 0; }
Java 
// Java Program to find all paths  // from source to destination in a directed graph  import java.util.ArrayList; import java.util.LinkedList; import java.util.Queue;  public class GfG {     public static ArrayList<ArrayList<Integer>> findPaths(int v, int[][] edges, int src, int dest) {         ArrayList<ArrayList<Integer>> graph = new ArrayList<>();         for (int i = 0; i < v; i++) {             graph.add(new ArrayList<>());         }          // Build the graph from edges         for (int[] edge : edges) {             graph.get(edge[0]).add(edge[1]);         }          ArrayList<ArrayList<Integer>> allPaths = new ArrayList<>();         Queue<ArrayList<Integer>> q = new LinkedList<>();          // Initialize queue with the starting path         ArrayList<Integer> initialPath = new ArrayList<>();         initialPath.add(src);         q.add(initialPath);          while (!q.isEmpty()) {             ArrayList<Integer> path = q.poll();             int current = path.get(path.size() - 1);              // If destination is reached, store the path             if (current == dest) {                 allPaths.add(new ArrayList<>(path));             }              // Explore all adjacent vertices             for (int adj : graph.get(current)) {                 ArrayList<Integer> newPath = new ArrayList<>(path);                 newPath.add(adj);                 q.add(newPath);             }         }          return allPaths;     }      public static void main(String[] args) {         int[][] edges = {{0, 3}, {0, 1}, {1, 3}, {2, 0}, {2, 1}};         int src = 2, dest = 3;         int v = 4;          // Find all paths from source to destination         ArrayList<ArrayList<Integer>> paths = findPaths(v, edges, src, dest);          // Print all the paths         for (ArrayList<Integer> path : paths) {             for (int vtx : path) {                 System.out.print(vtx + " ");             }             System.out.println();         }     } }
Python 
# Python Program to find all paths  # from source to destination in a directed graph  from collections import deque  def findPaths(v, edges, src, dest):     graph = [[] for _ in range(v)]      # Build the graph from edges     for edge in edges:         graph[edge[0]].append(edge[1])      allPaths = []     q = deque()      # Initialize queue with the starting path     q.append([src])      while q:         path = q.popleft()         current = path[-1]          # If destination is reached, store the path         if current == dest:             allPaths.append(path)          # Explore all adjacent vertices         for adj in graph[current]:             newPath = list(path)             newPath.append(adj)             q.append(newPath)      return allPaths  if __name__ == "__main__":     edges = [[0, 3], [0, 1], [1, 3], [2, 0], [2, 1]]     src = 2     dest = 3     v = 4      # Find all paths from source to destination     paths = findPaths(v, edges, src, dest)      # Print all the paths     for path in paths:         for vtx in path:             print(vtx, end=" ")         print()
C# 
// C# Program to find all paths // from source to destination in a directed graph using System; using System.Collections.Generic;  class GfG {     public static List<List<int>>     findPaths(int v, int[, ] edges, int src, int dest) {         List<List<int> > graph = new List<List<int> >();         for (int i = 0; i < v; i++) {             graph.Add(new List<int>());         }          // Build the graph from edges         int edgeCount = edges.GetLength(0);         for (int i = 0; i < edgeCount; i++) {             int u = edges[i, 0];             int vtx = edges[i, 1];             graph[u].Add(vtx);         }          List<List<int> > allPaths = new List<List<int> >();         Queue<List<int> > q = new Queue<List<int> >();          // Initialize queue with the starting path         q.Enqueue(new List<int>{ src });          while (q.Count > 0) {             List<int> path = q.Dequeue();             int current = path[path.Count - 1];              // If destination is reached, store the path             if (current == dest) {                 allPaths.Add(new List<int>(path));             }              // Explore all adjacent vertices             foreach(int adj in graph[current]) {                 List<int> newPath = new List<int>(path);                 newPath.Add(adj);                 q.Enqueue(newPath);             }         }          return allPaths;     }      static void Main(){         int[, ] edges = {             { 0, 3 }, { 0, 1 }, { 1, 3 }, { 2, 0 }, { 2, 1 }         };         int src = 2, dest = 3;         int v = 4;          // Find all paths from source to destination         var paths = findPaths(v, edges, src, dest);          // Print all the paths         foreach(var path in paths) {             Console.WriteLine(string.Join(" ", path));         }     } }
JavaScript 
// JavaScript Program to find all paths  // from source to destination in a directed graph  function findPaths(v, edges, src, dest) {     const graph = Array.from({ length: v }, () => []);      // Build the graph from edges     for (const edge of edges) {         graph[edge[0]].push(edge[1]);     }      const allPaths = [];     const q = [];      // Initialize queue with the starting path     q.push([src]);      while (q.length > 0) {         const path = q.shift();         const current = path[path.length - 1];          // If destination is reached, store the path         if (current === dest) {             allPaths.push(path);         }          // Explore all adjacent vertices         for (const adj of graph[current]) {             const newPath = [...path, adj];             q.push(newPath);         }     }      return allPaths; }  // Driver Code const edges = [[0, 3], [0, 1], [1, 3], [2, 0], [2, 1]]; const src = 2, dest = 3; const v = 4;  // Find all paths from source to destination const paths = findPaths(v, edges, src, dest);  // Print all the paths for (const path of paths) {     console.log(path.join(' ')); }

Output
2 0 3  2 1 3  2 0 1 3

Time Complexity: O(2V), where V is number of vertices. There can be at most 2V paths in the graph
Auxiliary Space: O(V + E)


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Article Tags :
  • Graph
  • Backtracking
  • DSA
  • DFS
Practice Tags :
  • Backtracking
  • DFS
  • Graph

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