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Print the lexicographically smallest BFS of the graph starting from 1
  • Difficulty Level : Easy
  • Last Updated : 02 Mar, 2021

Given a connected graph with N vertices and M edges. The task is to print the lexicographically smallest BFS traversal of the graph starting from 1. 
Note: The vertices are numbered from 1 to N.
Examples: 
 

Input: N = 5, M = 5 
       Edges: 
       1 4
       3 4
       5 4
       3 2
       1 5 
Output: 1 4 3 2 5 
Start from 1, go to 4, then to 3 and then to 2 and to 5. 

Input: N = 3, M = 2 
       Edges: 
       1 2 
       1 3 
Output: 1 2 3 

 

Approach: Instead of doing a normal BFS traversal on the graph, we can use a priority queue(min heap) instead of a simple queue. When a node is visited add its adjacent nodes into the priority queue. Every time, we visit a new node, it will be the one with the smallest index in the priority queue. Print the nodes when every time we visit them starting from 1. 
Below is the implementation of the above approach: 
 

CPP




// C++ program to print the lexcicographically
// smallest path starting from 1
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to print the smallest lexicographically
// BFS path starting from 1
void printLexoSmall(vector<int> adj[], int n)
{
    // Visited array
    bool vis[n + 1];
    memset(vis, 0, sizeof vis);
 
    // Minimum Heap
    priority_queue<int, vector<int>, greater<int> > Q;
 
    // First one visited
    vis[1] = true;
    Q.push(1);
 
    // Iterate till all nodes are visited
    while (!Q.empty()) {
 
        // Get the top element
        int now = Q.top();
 
        // Pop the element
        Q.pop();
 
        // Print the current node
        cout << now << " ";
 
        // Find adjacent nodes
        for (auto p : adj[now]) {
 
            // If not visited
            if (!vis[p]) {
 
                // Push
                Q.push(p);
 
                // Mark as visited
                vis[p] = true;
            }
        }
    }
}
 
// Function to insert edges in the graph
void insertEdges(int u, int v, vector<int> adj[])
{
    adj[u].push_back(v);
    adj[v].push_back(u);
}
 
// Driver Code
int main()
{
    int n = 5, m = 5;
    vector<int> adj[n + 1];
 
    // Insert edges
    insertEdges(1, 4, adj);
    insertEdges(3, 4, adj);
    insertEdges(5, 4, adj);
    insertEdges(3, 2, adj);
    insertEdges(1, 5, adj);
 
    // Function call
    printLexoSmall(adj, n);
 
    return 0;
}

Java




// Java program to print the lexcicographically
// smallest path starting from 1
import java.util.*;
public class GFG
{
   
  // Function to print the smallest lexicographically
  // BFS path starting from 1
  static void printLexoSmall(Vector<Vector<Integer>> adj, int n)
  {
    // Visited array
    boolean[] vis = new boolean[n + 1];
 
    // Minimum Heap
    Vector<Integer> Q = new Vector<Integer>();
 
    // First one visited
    vis[1] = true;
    Q.add(1);
 
    // Iterate till all nodes are visited
    while (Q.size() > 0) {
 
      // Get the top element
      int now = Q.get(0);
 
      // Pop the element
      Q.remove(0);
 
      // Print the current node
      System.out.print(now + " ");
 
      // Find adjacent nodes
      for(int p : adj.get(now)) {
 
        // If not visited
        if (!vis[p]) {
 
          // Push
          Q.add(p);
          Collections.sort(Q);
 
          // Mark as visited
          vis[p] = true;
        }
      }
    }
  }
 
  // Function to insert edges in the graph
  static void insertEdges(int u, int v, Vector<Vector<Integer>> adj)
  {
    adj.get(u).add(v);
    adj.get(v).add(u);
  }
 
  // Driver code
  public static void main(String[] args) {
    int n = 5;
    Vector<Vector<Integer>> adj = new Vector<Vector<Integer>>();    
    for(int i = 0; i < n + 1; i++)
    {
      adj.add(new Vector<Integer>());
    }
 
    // Insert edges
    insertEdges(1, 4, adj);
    insertEdges(3, 4, adj);
    insertEdges(5, 4, adj);
    insertEdges(3, 2, adj);
    insertEdges(1, 5, adj);
 
    // Function call
    printLexoSmall(adj, n);
  }
}
 
// This code is contributed by divyeshrabadiya07.

Python3




# Python program to print the lexcicographically
# smallest path starting from 1
 
# Function to print the smallest lexicographically
# BFS path starting from 1
def printLexoSmall(adj, n):
     
    # Visited array
    vis = [False for i in range(n + 1)]
     
    # Minimum Heap
    Q = []
     
    # First one visited
    vis[1] = True;
    Q.append(1)
     
    # Iterate till all nodes are visited
    while(len(Q) != 0):
         
        # Get the top element
        now = Q[0]
         
        # Pop the element
        Q.pop(0)
         
        # Print the current node
        print(now, end = " ")
         
        # Find adjacent nodes
        for p in adj[now]:
             
            # If not visited
            if(not vis[p]):
                 
                # Push
                Q.append(p)
                Q.sort()
                 
                # Mark as visited
                vis[p] = True
 
# Function to insert edges in the graph
def insertEdges(u, v, adj):
    adj[u].append(v)
    adj[v].append(u)
 
# Driver code
n = 5
m = 5
adj = [[] for i in range(n + 1)]
 
# Insert edges
insertEdges(1, 4, adj)
insertEdges(3, 4, adj)
insertEdges(5, 4, adj)
insertEdges(3, 2, adj)
insertEdges(1, 5, adj)
 
# Function call
printLexoSmall(adj, n)
 
# This code is contributed by avanitrachhadiya2155

C#




// C# program to print the lexcicographically
// smallest path starting from 1
using System;
using System.Collections.Generic;
class GFG {
     
    // Function to print the smallest lexicographically
    // BFS path starting from 1
    static void printLexoSmall(List<List<int>> adj, int n)
    {
        // Visited array
        bool[] vis = new bool[n + 1];
       
        // Minimum Heap
        List<int> Q = new List<int>();
       
        // First one visited
        vis[1] = true;
        Q.Add(1);
       
        // Iterate till all nodes are visited
        while (Q.Count > 0) {
       
            // Get the top element
            int now = Q[0];
       
            // Pop the element
            Q.RemoveAt(0);
       
            // Print the current node
            Console.Write(now + " ");
       
            // Find adjacent nodes
            foreach (int p in adj[now]) {
       
                // If not visited
                if (!vis[p]) {
       
                    // Push
                    Q.Add(p);
                    Q.Sort();
       
                    // Mark as visited
                    vis[p] = true;
                }
            }
        }
    }
     
    // Function to insert edges in the graph
    static void insertEdges(int u, int v, List<List<int>> adj)
    {
        adj[u].Add(v);
        adj[v].Add(u);
    }
 
  // Driver code
  static void Main()
  {
    int n = 5;
    List<List<int>> adj = new List<List<int>>();    
    for(int i = 0; i < n + 1; i++)
    {
        adj.Add(new List<int>());
    }
   
    // Insert edges
    insertEdges(1, 4, adj);
    insertEdges(3, 4, adj);
    insertEdges(5, 4, adj);
    insertEdges(3, 2, adj);
    insertEdges(1, 5, adj);
   
    // Function call
    printLexoSmall(adj, n);
  }
}
 
// This code is contributed by divyesh072019.
Output: 
1 4 3 2 5

 




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