Depth First Traversal (or Search) for a graph is similar to Depth First Traversal (DFS) of a tree. The only catch here is, unlike trees, graphs may contain cycles, so a node might be visited twice. To avoid processing a node more than once, use a boolean visited array.
Example:
Input: n = 4, e = 6
0 -> 1, 0 -> 2, 1 -> 2, 2 -> 0, 2 -> 3, 3 -> 3
Output: DFS from vertex 1 : 1 2 0 3
Explanation:
DFS Diagram:
Input: n = 4, e = 6
2 -> 0, 0 -> 2, 1 -> 2, 0 -> 1, 3 -> 3, 1 -> 3
Output: DFS from vertex 2 : 2 0 1 3
Explanation:
DFS Diagram:
The recursive implementation of DFS is already discussed: previous post.
Solution:
- Approach: Depth-first search is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. So the basic idea is to start from the root or any arbitrary node and mark the node and move to the adjacent unmarked node and continue this loop until there is no unmarked adjacent node. Then backtrack and check for other unmarked nodes and traverse them. Finally print the nodes in the path.
The only difference between iterative DFS and recursive DFS is that the recursive stack is replaced by a stack of nodes. - Algorithm:
- Created a stack of nodes and visited array.
- Insert the root in the stack.
- Run a loop till the stack is not empty.
- Pop the element from the stack and print the element.
- For every adjacent and unvisited node of current node, mark the node and insert it in the stack.
- Implementation of Iterative DFS: This is similar to BFS, the only difference is queue is replaced by stack.
C++
// An Iterative C++ program to do DFS traversal from// a given source vertex. DFS(int s) traverses vertices// reachable from s.#include<bits/stdc++.h>using namespace std;// This class represents a directed graph using adjacency// list representationclass Graph{ int V; // No. of vertices list<int> *adj; // adjacency listspublic: Graph(int V); // Constructor void addEdge(int v, int w); // to add an edge to graph void DFS(int s); // prints all vertices in DFS manner // from a given source.};Graph::Graph(int V){ this->V = V; adj = new list<int>[V];}void Graph::addEdge(int v, int w){ adj[v].push_back(w); // Add w to v’s list.}// prints all not yet visited vertices reachable from svoid Graph::DFS(int s){ // Initially mark all vertices as not visited vector<bool> visited(V, false); // Create a stack for DFS stack<int> stack; // Push the current source node. stack.push(s); while (!stack.empty()) { // Pop a vertex from stack and print it int s = stack.top(); stack.pop(); // Stack may contain same vertex twice. So // we need to print the popped item only // if it is not visited. if (!visited[s]) { cout << s << " "; visited[s] = true; } // Get all adjacent vertices of the popped vertex s // If a adjacent has not been visited, then push it // to the stack. for (auto i = adj[s].begin(); i != adj[s].end(); ++i) if (!visited[*i]) stack.push(*i); }}// Driver program to test methods of graph classint main(){ Graph g(5); // Total 5 vertices in graph g.addEdge(1, 0); g.addEdge(0, 2); g.addEdge(2, 1); g.addEdge(0, 3); g.addEdge(1, 4); cout << "Following is Depth First Traversal\n"; g.DFS(0); return 0;} |
Java
//An Iterative Java program to do DFS traversal from//a given source vertex. DFS(int s) traverses vertices//reachable from s.import java.util.*;public class GFG { // This class represents a directed graph using adjacency // list representation static class Graph { int V; //Number of Vertices LinkedList<Integer>[] adj; // adjacency lists //Constructor Graph(int V) { this.V = V; adj = new LinkedList[V]; for (int i = 0; i < adj.length; i++) adj[i] = new LinkedList<Integer>(); } //To add an edge to graph void addEdge(int v, int w) { adj[v].add(w); // Add w to v’s list. } // prints all not yet visited vertices reachable from s void DFS(int s) { // Initially mark all vertices as not visited Vector<Boolean> visited = new Vector<Boolean>(V); for (int i = 0; i < V; i++) visited.add(false); // Create a stack for DFS Stack<Integer> stack = new Stack<>(); // Push the current source node stack.push(s); while(stack.empty() == false) { // Pop a vertex from stack and print it s = stack.peek(); stack.pop(); // Stack may contain same vertex twice. So // we need to print the popped item only // if it is not visited. if(visited.get(s) == false) { System.out.print(s + " "); visited.set(s, true); } // Get all adjacent vertices of the popped vertex s // If a adjacent has not been visited, then push it // to the stack. Iterator<Integer> itr = adj[s].iterator(); while (itr.hasNext()) { int v = itr.next(); if(!visited.get(v)) stack.push(v); } } } } // Driver program to test methods of graph class public static void main(String[] args) { // Total 5 vertices in graph Graph g = new Graph(5); g.addEdge(1, 0); g.addEdge(0, 2); g.addEdge(2, 1); g.addEdge(0, 3); g.addEdge(1, 4); System.out.println("Following is the Depth First Traversal"); g.DFS(0); }} |
Python3
# An Iterative Python program to do DFS traversal from # a given source vertex. DFS(int s) traverses vertices # reachable from s. # This class represents a directed graph using adjacency # list representation class Graph: def __init__(self,V): # Constructor self.V = V # No. of vertices self.adj = [[] for i in range(V)] # adjacency lists def addEdge(self,v, w): # to add an edge to graph self.adj[v].append(w) # Add w to v’s list. # prints all not yet visited vertices reachable from s def DFS(self,s): # prints all vertices in DFS manner from a given source. # Initially mark all vertices as not visited visited = [False for i in range(self.V)] # Create a stack for DFS stack = [] # Push the current source node. stack.append(s) while (len(stack)): # Pop a vertex from stack and print it s = stack[-1] stack.pop() # Stack may contain same vertex twice. So # we need to print the popped item only # if it is not visited. if (not visited[s]): print(s,end=' ') visited[s] = True # Get all adjacent vertices of the popped vertex s # If a adjacent has not been visited, then push it # to the stack. for node in self.adj[s]: if (not visited[node]): stack.append(node) # Driver program to test methods of graph class g = Graph(5); # Total 5 vertices in graph g.addEdge(1, 0); g.addEdge(0, 2); g.addEdge(2, 1); g.addEdge(0, 3); g.addEdge(1, 4); print("Following is Depth First Traversal") g.DFS(0)# This code is contributed by ankush_953 |
C#
// An Iterative C# program to do DFS traversal from// a given source vertex. DFS(int s) traverses vertices// reachable from s.using System; using System.Collections.Generic;class GFG { // This class represents a directed graph using adjacency // list representation public class Graph { public int V; // Number of Vertices public LinkedList<int>[] adj; // adjacency lists // Constructor public Graph(int V) { this.V = V; adj = new LinkedList<int>[V]; for (int i = 0; i < adj.Length; i++) adj[i] = new LinkedList<int>(); } // To add an edge to graph public void addEdge(int v, int w) { adj[v].AddLast(w); // Add w to v’s list. } // prints all not yet visited vertices reachable from s public void DFS(int s) { // Initially mark all vertices as not visited Boolean []visited = new Boolean[V]; // Create a stack for DFS Stack<int> stack = new Stack<int>(); // Push the current source node stack.Push(s); while(stack.Count > 0) { // Pop a vertex from stack and print it s = stack.Peek(); stack.Pop(); // Stack may contain same vertex twice. So // we need to print the popped item only // if it is not visited. if(visited[s] == false) { Console.Write(s + " "); visited[s] = true; } // Get all adjacent vertices of the popped vertex s // If a adjacent has not been visited, then push it // to the stack. foreach(int v in adj[s]) { if(!visited[v]) stack.Push(v); } } } } // Driver code public static void Main(String []args) { // Total 5 vertices in graph Graph g = new Graph(5); g.addEdge(1, 0); g.addEdge(0, 2); g.addEdge(2, 1); g.addEdge(0, 3); g.addEdge(1, 4); Console.Write("Following is the Depth First Traversal\n"); g.DFS(0); }}// This code is contributed by Arnasb Kundu |
Javascript
<script>// An Iterative Javascript program to // do DFS traversal from a given source// vertex. DFS(int s) traverses vertices// reachable from s.// This class represents a directed graph// using adjacency list representationclass Graph{ constructor(V){ this.V = V; this.adj = new Array(V); for(let i = 0; i < this.adj.length; i++) this.adj[i] = [];}// To add an edge to graphaddEdge(v, w){ // Add w to v’s list. this.adj[v].push(w); }// Prints all not yet visited // vertices reachable from sDFS(s){ // Initially mark all vertices as not visited let visited = []; for(let i = 0; i < this.V; i++) visited.push(false); // Create a stack for DFS let stack = []; // Push the current source node stack.push(s); while(stack.length != 0) { // Pop a vertex from stack and print it s = stack.pop(); // Stack may contain same vertex twice. So // we need to print the popped item only // if it is not visited. if (visited[s] == false) { document.write(s + " "); visited[s] = true; } // Get all adjacent vertices of the // popped vertex s. If a adjacent has // not been visited, then push it // to the stack. for(let node = 0; node < this.adj[s].length; node++) { if (!visited[this.adj[s][node]]) stack.push(this.adj[s][node]) } }}}// Driver code// Total 5 vertices in graphlet g = new Graph(5);g.addEdge(1, 0);g.addEdge(0, 2);g.addEdge(2, 1);g.addEdge(0, 3);g.addEdge(1, 4);document.write("Following is the Depth " + "First Traversal<br>");g.DFS(0);// This code is contributed by rag2127</script> |
Output
Following is Depth First Traversal 0 3 2 1 4
- Complexity Analysis:
- Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.
- Space Complexity: O(V). Since an extra visited array is needed of size V.
Modification of the above Solution: Note that the above implementation prints only vertices that are reachable from a given vertex. For example, if the edges 0-3 and 0-2 are removed, then the above program would only print 0. To print all vertices of a graph, call DFS for every unvisited vertex.
Implementation:
C++
// An Iterative C++ program to do DFS traversal from// a given source vertex. DFS(int s) traverses vertices// reachable from s.#include<bits/stdc++.h>using namespace std;// This class represents a directed graph using adjacency// list representationclass Graph{ int V; // No. of vertices list<int> *adj; // adjacency listspublic: Graph(int V); // Constructor void addEdge(int v, int w); // to add an edge to graph void DFS(); // prints all vertices in DFS manner // prints all not yet visited vertices reachable from s void DFSUtil(int s, vector<bool> &visited);};Graph::Graph(int V){ this->V = V; adj = new list<int>[V];}void Graph::addEdge(int v, int w){ adj[v].push_back(w); // Add w to v’s list.}// prints all not yet visited vertices reachable from svoid Graph::DFSUtil(int s, vector<bool> &visited){ // Create a stack for DFS stack<int> stack; // Push the current source node. stack.push(s); while (!stack.empty()) { // Pop a vertex from stack and print it int s = stack.top(); stack.pop(); // Stack may contain same vertex twice. So // we need to print the popped item only // if it is not visited. if (!visited[s]) { cout << s << " "; visited[s] = true; } // Get all adjacent vertices of the popped vertex s // If a adjacent has not been visited, then push it // to the stack. for (auto i = adj[s].begin(); i != adj[s].end(); ++i) if (!visited[*i]) stack.push(*i); }}// prints all vertices in DFS mannervoid Graph::DFS(){ // Mark all the vertices as not visited vector<bool> visited(V, false); for (int i = 0; i < V; i++) if (!visited[i]) DFSUtil(i, visited);}// Driver program to test methods of graph classint main(){ Graph g(5); // Total 5 vertices in graph g.addEdge(1, 0); g.addEdge(2, 1); g.addEdge(3, 4); g.addEdge(4, 0); cout << "Following is Depth First Traversal\n"; g.DFS(); return 0;} |
Java
//An Iterative Java program to do DFS traversal from//a given source vertex. DFS() traverses vertices//reachable from s.import java.util.*;public class GFG { // This class represents a directed graph using adjacency // list representation static class Graph { int V; //Number of Vertices LinkedList<Integer>[] adj; // adjacency lists //Constructor Graph(int V) { this.V = V; adj = new LinkedList[V]; for (int i = 0; i < adj.length; i++) adj[i] = new LinkedList<Integer>(); } //To add an edge to graph void addEdge(int v, int w) { adj[v].add(w); // Add w to v’s list. } // prints all not yet visited vertices reachable from s void DFSUtil(int s, Vector<Boolean> visited) { // Create a stack for DFS Stack<Integer> stack = new Stack<>(); // Push the current source node stack.push(s); while(stack.empty() == false) { // Pop a vertex from stack and print it s = stack.peek(); stack.pop(); // Stack may contain same vertex twice. So // we need to print the popped item only // if it is not visited. if(visited.get(s) == false) { System.out.print(s + " "); visited.set(s, true); } // Get all adjacent vertices of the popped vertex s // If a adjacent has not been visited, then push it // to the stack. Iterator<Integer> itr = adj[s].iterator(); while (itr.hasNext()) { int v = itr.next(); if(!visited.get(v)) stack.push(v); } } } // prints all vertices in DFS manner void DFS() { Vector<Boolean> visited = new Vector<Boolean>(V); // Mark all the vertices as not visited for (int i = 0; i < V; i++) visited.add(false); for (int i = 0; i < V; i++) if (!visited.get(i)) DFSUtil(i, visited); } } // Driver program to test methods of graph class public static void main(String[] args) { Graph g = new Graph(5); g.addEdge(1, 0); g.addEdge(2, 1); g.addEdge(3, 4); g.addEdge(4, 0); System.out.println("Following is Depth First Traversal"); g.DFS(); }} |
Python3
# An Iterative Python3 program to do DFS # traversal from a given source vertex. # DFS(s) traverses vertices reachable from s.class Graph: def __init__(self, V): self.V = V self.adj = [[] for i in range(V)] def addEdge(self, v, w): self.adj[v].append(w) # Add w to v’s list. # prints all not yet visited vertices # reachable from s def DFSUtil(self, s, visited): # Create a stack for DFS stack = [] # Push the current source node. stack.append(s) while (len(stack) != 0): # Pop a vertex from stack and print it s = stack.pop() # Stack may contain same vertex twice. # So we need to print the popped item only # if it is not visited. if (not visited[s]): print(s, end = " ") visited[s] = True # Get all adjacent vertices of the # popped vertex s. If a adjacent has not # been visited, then push it to the stack. i = 0 while i < len(self.adj[s]): if (not visited[self.adj[s][i]]): stack.append(self.adj[s][i]) i += 1 # prints all vertices in DFS manner def DFS(self): # Mark all the vertices as not visited visited = [False] * self.V for i in range(self.V): if (not visited[i]): self.DFSUtil(i, visited)# Driver Codeif __name__ == '__main__': g = Graph(5) # Total 5 vertices in graph g.addEdge(1, 0) g.addEdge(2, 1) g.addEdge(3, 4) g.addEdge(4, 0) print("Following is Depth First Traversal") g.DFS()# This code is contributed by PranchalK |
C#
// An Iterative C# program to do DFS traversal from// a given source vertex. DFS() traverses vertices// reachable from s.using System;using System.Collections.Generic;class GFG { // This class represents a directed graph using adjacency // list representation class Graph { public int V; // Number of Vertices public List<int>[] adj; // adjacency lists // Constructor public Graph(int V) { this.V = V; adj = new List<int>[V]; for (int i = 0; i < adj.Length; i++) adj[i] = new List<int>(); } // To add an edge to graph public void addEdge(int v, int w) { adj[v].Add(w); // Add w to v’s list. } // prints all not yet visited vertices reachable from s public void DFSUtil(int s, List<Boolean> visited) { // Create a stack for DFS Stack<int> stack = new Stack<int>(); // Push the current source node stack.Push(s); while(stack.Count != 0) { // Pop a vertex from stack and print it s = stack.Peek(); stack.Pop(); // Stack may contain same vertex twice. So // we need to print the popped item only // if it is not visited. if(visited[s] == false) { Console.Write(s + " "); visited[s] = true; } // Get all adjacent vertices of the popped vertex s // If a adjacent has not been visited, then push it // to the stack. foreach(int itr in adj[s]) { int v = itr; if(!visited[v]) stack.Push(v); } } } // prints all vertices in DFS manner public void DFS() { List<Boolean> visited = new List<Boolean>(V); // Mark all the vertices as not visited for (int i = 0; i < V; i++) visited.Add(false); for (int i = 0; i < V; i++) if (!visited[i]) DFSUtil(i, visited); } } // Driver code public static void Main(String[] args) { Graph g = new Graph(5); g.addEdge(1, 0); g.addEdge(2, 1); g.addEdge(3, 4); g.addEdge(4, 0); Console.WriteLine("Following is Depth First Traversal"); g.DFS(); }}// This code is contributed by 29AjayKumar |
Javascript
<script>//An Iterative Javascript program to do DFS traversal from//a given source vertex. DFS() traverses vertices//reachable from s.// This class represents a directed graph using adjacency // list representationclass Graph{ //Constructor constructor(V) { this.V=V; this.adj = new Array(V); for (let i = 0; i < this.adj.length; i++) this.adj[i] = []; } //To add an edge to graph addEdge(v,w) { this.adj[v].push(w); // Add w to v’s list. } // prints all not yet visited vertices reachable from s DFSUtil(s,visited) { // Create a stack for DFS let stack = []; // Push the current source node stack.push(s); while(stack.length != 0) { // Pop a vertex from stack and print it s = stack.pop(); // Stack may contain same vertex twice. So // we need to print the popped item only // if it is not visited. if(visited[s] == false) { document.write(s + " "); visited[s] = true; } // Get all adjacent vertices of the popped vertex s // If a adjacent has not been visited, then push it // to the stack. for (let itr=0;itr<this.adj[s].length;itr++) { let v = this.adj[s][itr]; if(!visited[v]) stack.push(v); } } } // prints all vertices in DFS manner DFS() { let visited = [] // Mark all the vertices as not visited for (let i = 0; i < this.V; i++) visited.push(false); for (let i = 0; i < this.V; i++) if (!visited[i]) this.DFSUtil(i, visited); } }// Driver program to test methods of graph classlet g = new Graph(5);g.addEdge(1, 0);g.addEdge(2, 1);g.addEdge(3, 4);g.addEdge(4, 0);document.write("Following is Depth First Traversal<br>");g.DFS();// This code is contributed by avanitrachhadiya2155</script> |
Output
Following is Depth First Traversal 0 1 2 3 4
Time complexity: O(V+E), The time complexity of DFS is O (V+E). Here V is the number of vertices and E is the number of edges.
Auxiliary Space: O(V), The space complexity of DFS is O(V). The space is consumed by the recursion stack and the visited array.
This article is contributed by Shivam. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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