What is Diameter of n-ary tree using BFS?

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N-ary tree refers to the rooted tree in which each node having atmost k child nodes

N-ary tree refers to the rooted tree in which each node having atmost k child nodes. The diameter of n-ary tree is the longest path between two leaf nodes.

Various approaches have already been discussed to compute diameter of tree.

This article discuss another approach for computing diameter tree of n-ary tree using bfs.

Step 1: Run bfs to find the farthest node from rooted tree let say A
Step 2: Then run bfs from A to find farthest node from A let B
Step 3: Distance between node A and B is the diameter of given tree

Implementation:

C++

// C++ Program to find Diameter of n-ary tree
#include <bits/stdc++.h>
using namespace std;
 
// Here 10000 is maximum number of nodes in
// given tree.
int diameter[10001];
 
// The Function to do bfs traversal.
// It uses iterative approach to do bfs
// bfsUtil()
int bfs(int init, vector<int> arr[], int n)
{
    // Initializing queue
    queue<int> q;
    q.push(init);
 
    int visited[n + 1];
    for (int i = 0; i <= n; i++) {
        visited[i] = 0;
        diameter[i] = 0;
    }
 
    // Pushing each node in queue
    q.push(init);
 
    // Mark the traversed node visited
    visited[init] = 1;
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        for (int i = 0; i < arr[u].size(); i++) {
            if (visited[arr[u][i]] == 0) {
                visited[arr[u][i]] = 1;
 
                // Considering weight of edges equal to 1
                diameter[arr[u][i]] += diameter[u] + 1;
                q.push(arr[u][i]);
            }
        }
    }
 
    // return index of max value in diameter
    return int(max_element(diameter + 1,
                           diameter + n + 1)
               - diameter);
}
 
int findDiameter(vector<int> arr[], int n)
{
    int init = bfs(1, arr, n);
    int val = bfs(init, arr, n);
    return diameter[val];
}
 
// Driver Code
int main()
{
    // Input number of nodes
    int n = 6;
 
    vector<int> arr[n + 1];
 
    // Input nodes in adjacency list
    arr[1].push_back(2);
    arr[1].push_back(3);
    arr[1].push_back(6);
    arr[2].push_back(4);
    arr[2].push_back(1);
    arr[2].push_back(5);
    arr[3].push_back(1);
    arr[4].push_back(2);
    arr[5].push_back(2);
    arr[6].push_back(1);
 
    printf("Diameter of n-ary tree is %d\n",
           findDiameter(arr, n));
 
    return 0;
}

Java

// Java Program to find Diameter of n-ary tree
import java.util.*;
 
class GFG
{
     
// Here 10000 is maximum number of nodes in
// given tree.
static int diameter[] = new int[10001];
 
// The Function to do bfs traversal.
// It uses iterative approach to do bfs
// bfsUtil()
static int bfs(int init, 
               Vector<Vector<Integer>>arr, int n)
{
    // Initializing queue
    Queue<Integer> q = new LinkedList<>();
    q.add(init);
 
    int visited[] = new int[n + 1];
    for (int i = 0; i <= n; i++) 
    {
        visited[i] = 0;
        diameter[i] = 0;
    }
 
    // Pushing each node in queue
    q.add(init);
 
    // Mark the traversed node visited
    visited[init] = 1;
    while (q.size() > 0) 
    {
        int u = q.peek();
        q.remove();
        for (int i = 0; 
                 i < arr.get(u).size(); i++) 
        {
            if (visited[arr.get(u).get(i)] == 0)
            {
                visited[arr.get(u).get(i)] = 1;
 
                // Considering weight of edges equal to 1
                diameter[arr.get(u).get(i)] += diameter[u] + 1;
                q.add(arr.get(u).get(i));
            }
        }
    }
    int in = 0;
    for(int i = 0; i <= n; i++)
    {
        if(diameter[i] > diameter[in])
        in = i;
    }
     
    // return index of max value in diameter
    return in;
}
 
static int findDiameter(Vector<Vector<Integer>> arr, int n)
{
    int init = bfs(1, arr, n);
    int val = bfs(init, arr, n);
    return diameter[val];
}
 
// Driver Code
public static void main(String args[])
{
    // Input number of nodes
    int n = 6;
 
    Vector<Vector<Integer>> arr = new
    Vector<Vector<Integer>>();
     
    for(int i = 0; i < n + 1; i++)
    {
        arr.add(new Vector<Integer>());
    }
 
    // Input nodes in adjacency list
    arr.get(1).add(2);
    arr.get(1).add(3);
    arr.get(1).add(6);
    arr.get(2).add(4);
    arr.get(2).add(1);
    arr.get(2).add(5);
    arr.get(3).add(1);
    arr.get(4).add(2);
    arr.get(5).add(2);
    arr.get(6).add(1);
 
    System.out.printf("Diameter of n-ary tree is %d\n",
                                 findDiameter(arr, n));
}
}
 
// This code is contributed by Arnab Kundu

Python3

# Python3 program to find diameter of n-ary tree
      
# Here 10000 is maximum number of nodes in
# given tree.
diameter = [0 for i in range(10001)]
  
# The Function to do bfs traversal.
# It uses iterative approach to do bfs
# bfsUtil()
def bfs(init, arr, n):
 
    # Initializing queue
    q = []
    q.append(init)
  
    visited = [0 for i in range(n + 1)]
     
    for i in range(n + 1):
        visited[i] = 0
        diameter[i] = 0
  
    # Pushing each node in queue
    q.append(init)
  
    # Mark the traversed node visited
    visited[init] = 1
     
    while (len(q) > 0):
        u = q[0]
        q.pop(0)
         
        for i in range(len(arr[u])):
            if (visited[arr[u][i]] == 0):
                visited[arr[u][i]] = 1
  
                # Considering weight of edges equal to 1
                diameter[arr[u][i]] += diameter[u] + 1
                q.append(arr[u][i])
             
    ing = 0
     
    for i in range(n + 1):
        if(diameter[i] > diameter[ing]):
            ing = i
      
    # Return index of max value in diameter
    return ing
 
def findDiameter(arr, n):
 
    init = bfs(1, arr, n)
    val = bfs(init, arr, n)
    return diameter[val]
 
# Driver Code
if __name__=='__main__':
     
    # Input number of nodes
    n = 6
  
    arr = [[] for i in range(n + 1)]
  
    # Input nodes in adjacency list
    arr[1].append(2)
    arr[1].append(3)
    arr[1].append(6)
    arr[2].append(4)
    arr[2].append(1)
    arr[2].append(5)
    arr[3].append(1)
    arr[4].append(2)
    arr[5].append(2)
    arr[6].append(1)
  
    print("Diameter of n-ary tree is " +
          str(findDiameter(arr, n)))
 
# This code is contributed by rutvik_56

C#

// C# Program to find Diameter of n-ary tree
using System;
using System.Collections.Generic;
 
class GFG
{
     
// Here 10000 is maximum number of nodes 
// in given tree.
static int []diameter = new int[10001];
 
// The Function to do bfs traversal.
// It uses iterative approach to do bfs
// bfsUtil()
static int bfs(int init, 
               List<List<int>>arr, int n)
{
    // Initializing queue
    Queue<int> q = new Queue<int>();
    q.Enqueue(init);
 
    int []visited = new int[n + 1];
    for (int i = 0; i <= n; i++) 
    {
        visited[i] = 0;
        diameter[i] = 0;
    }
 
    // Pushing each node in queue
    q.Enqueue(init);
 
    // Mark the traversed node visited
    visited[init] = 1;
    while (q.Count > 0) 
    {
        int u = q.Peek();
        q.Dequeue();
        for (int i = 0; 
                 i < arr[u].Count; i++) 
        {
            if (visited[arr[u][i]] == 0)
            {
                visited[arr[u][i]] = 1;
 
                // Considering weight of edges equal to 1
                diameter[arr[u][i]] += diameter[u] + 1;
                q.Enqueue(arr[u][i]);
            }
        }
    }
    int iN = 0;
    for(int i = 0; i <= n; i++)
    {
        if(diameter[i] > diameter[iN])
        iN = i;
    }
     
    // return index of max value in diameter
    return iN;
}
 
static int findDiameter(List<List<int>> arr, int n)
{
    int init = bfs(1, arr, n);
    int val = bfs(init, arr, n);
    return diameter[val];
}
 
// Driver Code
public static void Main(String []args)
{
    // Input number of nodes
    int n = 6;
 
    List<List<int>> arr = new
    List<List<int>>();
     
    for(int i = 0; i < n + 1; i++)
    {
        arr.Add(new List<int>());
    }
 
    // Input nodes in adjacency list
    arr[1].Add(2);
    arr[1].Add(3);
    arr[1].Add(6);
    arr[2].Add(4);
    arr[2].Add(1);
    arr[2].Add(5);
    arr[3].Add(1);
    arr[4].Add(2);
    arr[5].Add(2);
    arr[6].Add(1);
 
    Console.Write("Diameter of n-ary tree is {0}\n",
                              findDiameter(arr, n));
}
}
 
// This code is contributed by PrinciRaj1992

Javascript

<script>
 
    // JavaScript Program to find Diameter of n-ary tree
     
    // Here 10000 is maximum number of nodes in
    // given tree.
    let diameter = new Array(10001);
 
    // The Function to do bfs traversal.
    // It uses iterative approach to do bfs
    // bfsUtil()
    function bfs(init, arr, n)
    {
        // Initializing queue
        let q = [];
        q.push(init);
 
        let visited = new Array(n + 1);
        for (let i = 0; i <= n; i++)
        {
            visited[i] = 0;
            diameter[i] = 0;
        }
 
        // Pushing each node in queue
        q.push(init);
 
        // Mark the traversed node visited
        visited[init] = 1;
        while (q.length > 0)
        {
            let u = q[0];
            q.shift();
            for (let i = 0;
                     i < arr[u].length; i++)
            {
                if (visited[arr[u][i]] == 0)
                {
                    visited[arr[u][i]] = 1;
 
                    // Considering weight of edges equal to 1
                    diameter[arr[u][i]] += diameter[u] + 1;
                    q.push(arr[u][i]);
                }
            }
        }
        let In = 0;
        for(let i = 0; i <= n; i++)
        {
            if(diameter[i] > diameter[In])
            In = i;
        }
 
        // return index of max value in diameter
        return In;
    }
 
    function findDiameter(arr, n)
    {
        let init = bfs(1, arr, n);
        let val = bfs(init, arr, n);
        return diameter[val];
    }
     
    // Input number of nodes
    let n = 6;
  
    let arr = [];
      
    for(let i = 0; i < n + 1; i++)
    {
        arr.push([]);
    }
  
    // Input nodes in adjacency list
    arr[1].push(2);
    arr[1].push(3);
    arr[1].push(6);
    arr[2].push(4);
    arr[2].push(1);
    arr[2].push(5);
    arr[3].push(1);
    arr[4].push(2);
    arr[5].push(2);
    arr[6].push(1);
  
    document.write("Diameter of n-ary tree is " + 
    findDiameter(arr, n) + "</br>");
 
</script>

Output

Diameter of n-ary tree is 3

Time complexity: O(n^2)
Auxiliary Space: O(10001)