Determine the count of Leaf nodes in an N-ary tree

Given the value of ‘N’ and ‘I’. Here, $I$ represents the number of internal nodes present in an N-ary tree and every node of the N-ary can either have $N$ childs or zero child. The task is to determine the number of Leaf nodes in n-ary tree.

Examples:

Input : N = 3, I = 5
Output : Leaf nodes = 11

Input : N = 10, I = 10
Output : leaf nodes = 91

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Formula:

where,
I = Number of Internal nodes.
L = Leaf Nodes.
and, N = Number of children each node can have.

Derivation: The tree is an N-ary tree. Assume it has T total nodes, which is the sum of internal nodes (I) and leaf nodes (L). A tree with T total nodes will have (T – 1) edges or branches.

In other words, since the tree is an N-ary tree, each internal node will have N branches contributing a total of N*I internal branches. Therefore we have the following relations from the above explanations,

N * I = T – 1
L + I = T

From the above two equations, we can say that L = (N – 1) * I + 1.

Below is the implementation of the above approach:

C++

// CPP program to find number 
// of leaf nodes 
  
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to calculate 
// leaf nodes in n-ary tree 
int calcNodes(int N, int I) 
{ 
    int result = 0; 
  
    result = I * (N - 1) + 1; 
  
    return result; 
} 
  
// Driver code 
int main() 
{ 
    int N = 5, I = 2; 
  
    cout << "Leaf nodes = " << calcNodes(N, I); 
  
    return 0; 
} 

Java

// Java program to find number  
// of leaf nodes  
  
class GfG  
{ 
  
// Function to calculate  
// leaf nodes in n-ary tree  
static int calcNodes(int N, int I)  
{  
    int result = 0;  
  
    result = I * (N - 1) + 1;  
  
    return result;  
}  
  
// Driver code  
public static void main(String[] args)  
{  
    int N = 5, I = 2;  
  
    System.out.println("Leaf nodes = " +  
                        calcNodes(N, I));  
} 
}  
  
// This code is contributed by Prerna Saini 

Python3

# Python3 program to find number  
# of leaf nodes  
  
# Function to calculate  
# leaf nodes in n-ary tree  
def calcNodes(N, I): 
    result = 0
  
    result = I * (N - 1) + 1
  
    return result  
  
# Driver Code  
if __name__ == '__main__': 
    N = 5
    I = 2
  
    print("Leaf nodes = ",  
           calcNodes(N, I)) 
  
# This code is contributed  
# by SHUBHAMSINGH10 

C#

// C# program to find number  
// of leaf nodes  
using System; 
  
class GFG  
{ 
  
// Function to calculate  
// leaf nodes in n-ary tree  
static int calcNodes(int N, int I)  
{  
    int result = 0;  
  
    result = I * (N - 1) + 1;  
  
    return result;  
}  
  
// Driver code  
public static void Main()  
{  
    int N = 5, I = 2;  
  
    Console.Write("Leaf nodes = " +  
                  calcNodes(N, I));  
} 
}  
  
// This code is contributed 
// by Akanksha Rai 

PHP

<?php 
// PHP program to find number 
// of leaf nodes 
  
// Function to calculate 
// leaf nodes in n-ary tree 
function calcNodes($N, $I) 
{ 
    $result = 0; 
  
    $result = $I * ($N - 1) + 1; 
  
    return $result; 
} 
  
// Driver code 
$N = 5; $I = 2; 
  
echo "Leaf nodes = " .  
      calcNodes($N, $I); 
  
// This code is contributed 
// by Akanksha Rai 
?> 

Output:

Leaf nodes = 9

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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