Print the DFS traversal step-wise (Backtracking also)

Given a graph, the task is to print the DFS traversal of a graph which includes every step including the backtracking.

1st step:- 0 -> 1
2nd step:- 1 -> 5
3rd step:- 5 -> 1 (backtracking step)
4th step:- 1 -> 6...
and so on till all the nodes are visited.
 
Dfs step-wise(including backtracking) is:
0 1 5 1 6 7 8 7 6 1 0 2 4 2 9 3 10

Note: In this above diagram the weight between the edges has just been added. It does not have any role in DFS-traversal. 

Approach: DFS with Backtracking will be used here. First, visit every node using DFS simultaneously and keep track of the previously used edge and the parent node. If a node comes where all the adjacent nodes have been visited, backtrack using the last used edge and print the nodes. Continue the steps and at every step, the parent node will become the present node. Continue the above steps to find the complete DFS traversal of the graph.

Implementation:

C++

// C++ program to print the complete
// DFS-traversal of graph
// using back-tracking
#include <bits/stdc++.h>
using namespace std;
const int N = 1000;
vector<int> adj[N];

// Function to print the complete DFS-traversal
void dfsUtil(int u, int node, bool visited[],
             vector<pair<int, int> > road_used, int parent,
             int it)
{
    int c = 0;

    // Check if all the node is visited or not
    // and count unvisited nodes
    for (int i = 0; i < node; i++)
        if (visited[i])
            c++;

    // If all the node is visited return;
    if (c == node)
        return;

    // Mark not visited node as visited
    visited[u] = true;

    // Track the current edge
    road_used.push_back({ parent, u });

    // Print the node
    cout << u << " ";

    // Check for not visited node and proceed with it.
    for (int x : adj[u]) {

        // call the DFs function if not visited
        if (!visited[x])
            dfsUtil(x, node, visited, road_used, u, it + 1);
    }

    // Backtrack through the last
    // visited nodes
    for (auto y : road_used)
        if (y.second == u)
            dfsUtil(y.first, node, visited, road_used, u,
                    it + 1);
}

// Function to call the DFS function
// which prints the DFS-traversal stepwise
void dfs(int node)
{

    // Create a array of visited node
    bool visited[node];

    // Vector to track last visited road
    vector<pair<int, int> > road_used;

    // Initialize all the node with false
    for (int i = 0; i < node; i++)
        visited[i] = false;

    // call the function
    dfsUtil(0, node, visited, road_used, -1, 0);
}

// Function to insert edges in Graph
void insertEdge(int u, int v)
{
    adj[u].push_back(v);
    adj[v].push_back(u);
}

// Driver Code
int main()
{
    // number of nodes and edges in the graph
    int node = 11, edge = 13;

    // Function call to create the graph
    insertEdge(0, 1);
    insertEdge(0, 2);
    insertEdge(1, 5);
    insertEdge(1, 6);
    insertEdge(2, 4);
    insertEdge(2, 9);
    insertEdge(6, 7);
    insertEdge(6, 8);
    insertEdge(7, 8);
    insertEdge(2, 3);
    insertEdge(3, 9);
    insertEdge(3, 10);
    insertEdge(9, 10);

    // Call the function to print
    dfs(node);

    return 0;
}

Java

// Java program to print the complete
// DFS-traversal of graph
// using back-tracking
import java.io.*;
import java.util.*;
class GFG
{

    static int N = 1000;
    static ArrayList<ArrayList<Integer>> adj =
      new ArrayList<ArrayList<Integer>>();

    // Function to print the complete DFS-traversal
    static void dfsUtil(int u, int node, boolean visited[],
                        ArrayList<ArrayList<Integer>> road_used,
                        int parent, int it)
    {
        int c = 0;

         // Check if all the node is visited or not
        // and count unvisited nodes
        for (int i = 0; i < node; i++)
            if (visited[i])
                c++;

        // If all the node is visited return;
        if (c == node)
            return;

        // Mark not visited node as visited
        visited[u] = true;

        // Track the current edge
        road_used.add(new ArrayList<Integer>(Arrays.asList( parent, u )));

        // Print the node
        System.out.print(u + " ");

        // Check for not visited node and proceed with it.
        for (int x : adj.get(u))
        {
            // call the DFs function if not visited
            if (!visited[x])
            {
                dfsUtil(x, node, visited, road_used, u, it + 1);
            }
        }

        // Backtrack through the last
        // visited nodes
        for(int y = 0; y < road_used.size(); y++)
        {
            if(road_used.get(y).get(1) == u)
            {
                dfsUtil(road_used.get(y).get(0), node,
                        visited,road_used, u, it + 1);
            }
        }

    }

    // Function to call the DFS function
    // which prints the DFS-traversal stepwise
    static void dfs(int node)
    {

        // Create a array of visited node
        boolean[] visited = new boolean[node];

        // Vector to track last visited road
        ArrayList<ArrayList<Integer>> road_used =
          new ArrayList<ArrayList<Integer>>();

        // Initialize all the node with false
        for (int i = 0; i < node; i++)
        {
            visited[i] = false;
        }

        // call the function
        dfsUtil(0, node, visited, road_used, -1, 0);
    }

    // Function to insert edges in Graph
    static void insertEdge(int u, int v)
    {
        adj.get(u).add(v);
        adj.get(v).add(u);
    }

    // Driver Code
    public static void main (String[] args)
    {

        // number of nodes and edges in the graph
        int node = 11, edge = 13;
        for(int i = 0; i < N; i++)
        {
            adj.add(new ArrayList<Integer>());
        }

        // Function call to create the graph
        insertEdge(0, 1);
        insertEdge(0, 2);
        insertEdge(1, 5);
        insertEdge(1, 6);
        insertEdge(2, 4);
        insertEdge(2, 9);
        insertEdge(6, 7);
        insertEdge(6, 8);
        insertEdge(7, 8);
        insertEdge(2, 3);
        insertEdge(3, 9);
        insertEdge(3, 10);
        insertEdge(9, 10);

        // Call the function to print
        dfs(node);
    }
}

// This code is contributed by avanitrachhadiya2155

Python3

# Python3 program to print the
# complete DFS-traversal of graph
# using back-tracking
N = 1000
adj = [[] for i in range(N)]

# Function to print the complete DFS-traversal
def dfsUtil(u, node,visited,
            road_used, parent, it):
    c = 0

    # Check if all the node is visited
    # or not and count unvisited nodes
    for i in range(node):
        if (visited[i]):
            c += 1

    # If all the node is visited return
    if (c == node):
        return

    # Mark not visited node as visited
    visited[u] = True

    # Track the current edge
    road_used.append([parent, u])

    # Print the node
    print(u, end = " ")

    # Check for not visited node
    # and proceed with it.
    for x in adj[u]:

        # Call the DFs function
        # if not visited
        if (not visited[x]):
            dfsUtil(x, node, visited,
                    road_used, u, it + 1)

    # Backtrack through the last
    # visited nodes
    for y in road_used:
        if (y[1] == u):
            dfsUtil(y[0], node, visited,
                    road_used, u, it + 1)

# Function to call the DFS function
# which prints the DFS-traversal stepwise
def dfs(node):

    # Create a array of visited node
    visited = [False for i in range(node)]

    # Vector to track last visited road
    road_used = []

    # Initialize all the node with false
    for i in range(node):
        visited[i] = False

    # Call the function
    dfsUtil(0, node, visited,
            road_used, -1, 0)

# Function to insert edges in Graph
def insertEdge(u, v):

    adj[u].append(v)
    adj[v].append(u)

# Driver Code
if __name__ == '__main__':

    # Number of nodes and edges in the graph
    node = 11
    edge = 13

    # Function call to create the graph
    insertEdge(0, 1)
    insertEdge(0, 2)
    insertEdge(1, 5)
    insertEdge(1, 6)
    insertEdge(2, 4)
    insertEdge(2, 9)
    insertEdge(6, 7)
    insertEdge(6, 8)
    insertEdge(7, 8)
    insertEdge(2, 3)
    insertEdge(3, 9)
    insertEdge(3, 10)
    insertEdge(9, 10)

    # Call the function to print
    dfs(node)

# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

public class GFG {
    static int N = 1000;
    static List<List<int> > adj = new List<List<int> >();

    // Function to print the complete DFS-traversal
    static void dfsUtil(int u, int node, bool[] visited,
                        List<List<int> > road_used,
                        int parent, int it)
    {
        int c = 0;

        // Check if all the node is visited or not
        // and count unvisited nodes
        for (int i = 0; i < node; i++)
            if (visited[i])
                c++;

        // If all the node is visited return;
        if (c == node)
            return;

        // Mark not visited node as visited
        visited[u] = true;

        // Track the current edge
        road_used.Add(new List<int>() { parent, u });

        // Print the node
        Console.Write(u + " ");

        // Check for not visited node and proceed with it.
        foreach(int x in adj[u])
        {
            // call the DFs function if not visited
            if (!visited[x]) {
                dfsUtil(x, node, visited, road_used, u,
                        it + 1);
            }
        }
        // Backtrack through the last
        // visited nodes
        for (int y = 0; y < road_used.Count; y++) {
            if (road_used[y][1] == u) {
                dfsUtil(road_used[y][0], node, visited,
                        road_used, u, it + 1);
            }
        }
    }

    // Function to call the DFS function
    // which prints the DFS-traversal stepwise
    static void dfs(int node)
    {
        // Create a array of visited node
        bool[] visited = new bool[node];

        // Vector to track last visited road
        List<List<int> > road_used = new List<List<int> >();

        // Initialize all the node with false
        for (int i = 0; i < node; i++) {
            visited[i] = false;
        }

        // call the function
        dfsUtil(0, node, visited, road_used, -1, 0);
    }

    // Function to insert edges in Graph
    static void insertEdge(int u, int v)
    {
        adj[u].Add(v);
        adj[v].Add(u);
    }
    static public void Main()
    {
        // number of nodes and edges in the graph
        int node = 11;
        for (int i = 0; i < N; i++) {
            adj.Add(new List<int>());
        }

        // Function call to create the graph
        insertEdge(0, 1);
        insertEdge(0, 2);
        insertEdge(1, 5);
        insertEdge(1, 6);
        insertEdge(2, 4);
        insertEdge(2, 9);
        insertEdge(6, 7);
        insertEdge(6, 8);
        insertEdge(7, 8);
        insertEdge(2, 3);
        insertEdge(3, 9);
        insertEdge(3, 10);
        insertEdge(9, 10);

        // Call the function to print
        dfs(node);
    }
}
// This code is contributed by rag2127

Javascript

<script>
// Javascript program to print the complete
// DFS-traversal of graph
// using back-tracking

    let N = 1000;
    let adj =[];

    // Function to print the complete DFS-traversal
    function dfsUtil(u,node,visited,road_used,parent,it)
    {
        let c = 0;

        // Check if all the node is visited or not
        // and count unvisited nodes
        for (let i = 0; i < node; i++)
            if (visited[i])
                c++;

        // If all the node is visited return;
        if (c == node)
            return;

        // Mark not visited node as visited
        visited[u] = true;

        // Track the current edge
        road_used.push([ parent, u ]);

        // Print the node
        document.write(u + " ");

        // Check for not visited node and proceed with it.
        for (let x=0;x<adj[u].length;x++)
        {
            // call the DFs function if not visited
            if (!visited[adj[u][x]])
            {
                dfsUtil(adj[u][x], node, visited, road_used, u, it + 1);
            }
        }

        // Backtrack through the last
        // visited nodes
        for(let y = 0; y < road_used.length; y++)
        {
            if(road_used[y][1] == u)
            {
                dfsUtil(road_used[y][0], node,
                        visited,road_used, u, it + 1);
            }
        }
    }

    // Function to call the DFS function
    // which prints the DFS-traversal stepwise
    function dfs(node)
    {
        // Create a array of visited node
        let visited = new Array(node);

        // Vector to track last visited road
        let road_used = [];

        // Initialize all the node with false
        for (let i = 0; i < node; i++)
        {
            visited[i] = false;
        }

        // call the function
        dfsUtil(0, node, visited, road_used, -1, 0);
    }

    // Function to insert edges in Graph
    function insertEdge(u,v)
    {
        adj[u].push(v);
        adj[v].push(u);
    }

     // Driver Code
    let node = 11, edge = 13;
    for(let i = 0; i < N; i++)
        {
            adj.push([]);
        }

        // Function call to create the graph
        insertEdge(0, 1);
        insertEdge(0, 2);
        insertEdge(1, 5);
        insertEdge(1, 6);
        insertEdge(2, 4);
        insertEdge(2, 9);
        insertEdge(6, 7);
        insertEdge(6, 8);
        insertEdge(7, 8);
        insertEdge(2, 3);
        insertEdge(3, 9);
        insertEdge(3, 10);
        insertEdge(9, 10);

        // Call the function to print
        dfs(node);


// This code is contributed by unknown2108
</script>
9

Output

0 1 5 1 6 7 8 7 6 1 0 2 4 2 9 3 10