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++ 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 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 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# 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 |
<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 |
0 1 5 1 6 7 8 7 6 1 0 2 4 2 9 3 10