Iterative Depth First Traversal of Graph

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 we may come to the same node again. To avoid processing a node more than once, we use a boolean visited array.

For example, a DFS of below graph is “0 3 4 2 1”, other possible DFS is “0 2 1 3 4”.

We have discussed recursive implementation of DFS in previous in previous post. In the post, iterative DFS is discussed. The recursive implementation uses function call stack. In iterative implementation, an explicit stack is used to hold visited vertices.

Below is implementation of Iterative DFS. The implementation 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 representation 
class Graph 
{ 
    int V;    // No. of vertices 
    list<int> *adj;    // adjacency lists 
public: 
    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 s 
void Graph::DFS(int s) 
{ 
    // Initially mark all verices 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 
        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 puah 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 class 
int 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 puah 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); 
    } 
} 

Output:

Following is Depth First Traversal
0 3 2 1 4

Note that the above implementation prints only vertices that are reachable from a given vertex. For example, if we remove edges 0-3 and 0-2, the above program would only print 0. To print all vertices of a graph, we need to call DFS for every vertex. Below is implementation for the same.

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 representation 
class Graph 
{ 
    int V;    // No. of vertices 
    list<int> *adj;    // adjacency lists 
public: 
    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 s 
void Graph::DFSUtil(int s, vector<bool> &visited) 
{ 
    // Create a stack for DFS 
    stack<int> stack; 
  
    // Puah the current source node. 
    stack.push(s); 
  
    while (!stack.empty()) 
    { 
        // Pop a vertex from stack and print it 
        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 puah 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 manner 
void 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 class 
int 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 puah 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 Python 3 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 prit  
            s = stack.pop() 
      
            # Stack may contain same vertex twice.  
            # So we need to prthe 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 Code 
if __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 

Output:

Following is Depth First Traversal
0 1 2 3 4

Like recursive traversal, time complexity of iterative implementation is O(V + E).

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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