Print the DFS traversal step-wise (Backtracking also)

Given a graph, the task is to print the DFS traversal of a graph which includes the 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 whose all the adjacent node has 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.

Below is the implementation of the above approach:

// 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 th 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-travesal stepwise
void dfs(int node)
{
  
    // Create a array of visited ndoe
    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;
}

Output:

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


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