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 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:
  1. Created a stack of nodes and visited array.
  2. Insert the root in the stack.
  3. Run a loop till the stack is not empty.
  4. Pop the element from the stack and print the element.
  5. For every adjacent and unvsisted 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++

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  // 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 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 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; }

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  Java

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  //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);     } }

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  Python3

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  # 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 verices 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

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  C#

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  // 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];             for (int i = 0; i < V; i++)                 visited[i] = (false);                    // 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

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  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.

Modifiation 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:

Following is Depth First Traversal
0 1 2 3 4

Like recursive traversal, the 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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