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Euler Tour of Tree
  • Difficulty Level : Easy
  • Last Updated : 20 Jul, 2020

A Tree is a generalization of connected graph where it has N nodes that will have exactly N-1 edges, i.e one edge between every pair of vertices. Find the Euler tour of tree represented by adjacency list.
Examples:
Input : 
 

Output : 1 2 3 2 4 2 1
Input : 
 

Output : 1 5 4 2 4 3 4 5 1
 



Euler tour is defined as a way of traversing tree such that each vertex is added to the tour when we visit it (either moving down from parent vertex or returning from child vertex). We start from root and reach back to root after visiting all vertices.
It requires exactly 2*N-1 vertices to store Euler tour.
Approach: We will run DFS(Depth first search) algorithm on Tree as: 
 

(1) Visit root node, i.e 1 
vis[1]=1, Euler[0]=1 
run dfs() for all unvisited adjacent nodes(2) 
(2) Visit node 2 
vis[2]=1, Euler[1]=2 
run dfs() for all unvisited adjacent nodes(3, 4) 
(3) Visit node 3 
vis[3]=1, Euler[2]=3 
All adjacent nodes are already visited, return to parent node 
and add parent to Euler tour Euler[3]=2 
(4) Visit node 4 
vis[4]=1, Euler[4]=4 
All adjacent nodes are already visited, return to parent node 
and add parent to Euler tour, Euler[5]=2 
(5) Visit node 2 
All adjacent nodes are already visited, return to parent node 
and add parent to Euler tour, Euler[6]=1 
(6) Visit node 1 
All adjacent nodes are already visited, and node 1 is root node 
so, we stop our recursion here. 
Similarly, for example 2: 
 

 

 

C++




// C++ program to print Euler tour of a
// tree.
#include <bits/stdc++.h>
using namespace std;
  
#define MAX 1001
  
// Adjacency list representation of tree
vector<int> adj[MAX]; 
  
// Visited array to keep track visited 
// nodes on tour
int vis[MAX]; 
  
// Array to store Euler Tour
int Euler[2 * MAX]; 
  
// Function to add edges to tree
void add_edge(int u, int v)
{
    adj[u].push_back(v);
    adj[v].push_back(u);
}
  
// Function to store Euler Tour of tree
void eulerTree(int u, int &indx)
{
    vis[u] = 1;
    Euler[indx++] = u;
    for (auto it : adj[u]) {
        if (!vis[it]) {
            eulerTree(it, indx);
            Euler[indx++] = u;
        }
    }
}
  
// Function to print Euler Tour of tree
void printEulerTour(int root, int N)
{
    int index = 0;  
    eulerTree(root, index);
    for (int i = 0; i < (2*N-1); i++)
        cout << Euler[i] << " ";
}
  
// Driver code
int main()
{
    int N = 4;
  
    add_edge(1, 2);
    add_edge(2, 3);
    add_edge(2, 4);
  
    // Consider 1 as root and print
    // Euler tour 
    printEulerTour(1, N);
  
    return 0;
}

Java




// Java program to print Euler tour of a
// tree.
import java.util.*;
  
class GFG{
  
static final int MAX = 1001;
static int indx = 0;
  
// Adjacency list representation of tree
static ArrayList<
       ArrayList<Integer>> adj = new ArrayList<>();
  
// Visited array to keep track visited
// nodes on tour
static int vis[] = new int[MAX];
  
// Array to store Euler Tour
static int Euler[] = new int[2 * MAX];
  
// Function to add edges to tree
static void add_edge(int u, int v)
{
    adj.get(u).add(v);
    adj.get(v).add(u);
}
  
// Function to store Euler Tour of tree
static void eulerTree(int u)
{
    vis[u] = 1;
    Euler[indx++] = u;
      
    for(int it : adj.get(u))
    {
        if (vis[it] == 0
        {
            eulerTree(it);
            Euler[indx++] = u;
        }
    }
}
  
// Function to print Euler Tour of tree
static void printEulerTour(int root, int N)
{
    eulerTree(root);
    for(int i = 0; i < (2 * N - 1); i++)
        System.out.print(Euler[i] + " ");
}
  
// Driver code
public static void main(String[] args)
{
    int N = 4;
      
    for(int i = 0; i <= N; i++)
        adj.add(new ArrayList<>());
          
    add_edge(1, 2);
    add_edge(2, 3);
    add_edge(2, 4);
  
    // Consider 1 as root and print
    // Euler tour
    printEulerTour(1, N);
}
}
  
// This code is contributed by jrishabh99
Output: 
1 2 3 2 4 2 1

 

Auxiliary Space :O(N) 
Time Complexity: O(N)
 

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