Print the DFS traversal step-wise (Backtracking also) - GeeksforGeeks

14 Sep, 2021
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.
Below is the implementation of the above approach:
C++
Java
Python3
C#
Javascript
// 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-traversalvoid 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-traversal stepwisevoid 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 Graphvoid insertEdge(int u, int v){    adj[u].push_back(v);    adj[v].push_back(u);} // Driver Codeint 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 program to print the complete// DFS-traversal of graph// using back-trackingimport 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 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.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 program to print the# complete DFS-traversal of graph# using back-trackingN = 1000adj = [[] for i in range(N)] # Function to print the complete DFS-traversaldef dfsUtil(u, node,visited,            road_used, parent, it):    c = 0     # Check if all th 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 stepwisedef 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 Graphdef insertEdge(u, v):         adj[u].append(v)    adj[v].append(u) # Driver Codeif __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# program for the above approachusing 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 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.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
<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 th 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
0 1 5 1 6 7 8 7 6 1 0 2 4 2 9 3 10
 
mohit kumar 29
avanitrachhadiya2155
rag2127
unknown2108
khushboogoyal499
surinderdawra388
gulshankumarar231
cpp-vector
DFS
Advanced Data Structure
Backtracking
Graph
DFS
Graph
Backtracking
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