Data Structures and Algorithms (Some Questions for You - Answer to Question 9) - Tirthankar Pal - MBA from IIT Kharagpur, GATE, GMAT, IIT Written Test, Interview were a part of MBA Entrance, B.S. in Computer Science from NIELIT

 In a complete binary tree of depth d (complete including last level), give an expression to find the number of leaf nodes in the binary tree.

A node is a leaf node if both left and right child nodes of it are NULL. 
Here is an algorithm to get the leaf node count.

getLeafCount(node)
1) If node is NULL then return 0.
2) Else If left and right child nodes are NULL return 1.
3) Else recursively calculate leaf count of the tree using below formula.
    Leaf count of a tree = Leaf count of left subtree + 
                                 Leaf count of right subtree

Leaf count for the above tree is 3.

// C implementation to find leaf count of a given Binary tree #include <stdio.h> #include <stdlib.h>    /* A binary tree node has data, pointer to left child     and a pointer to right child */ struct node  {     int data;     struct node* left;     struct node* right; };    /* Function to get the count of leaf nodes in a binary tree*/ unsigned int getLeafCount(struct node* node) {   if(node == NULL)            return 0;   if(node->left == NULL && node->right==NULL)           return 1;               else      return getLeafCount(node->left)+            getLeafCount(node->right);       }    /* Helper function that allocates a new node with the    given data and NULL left and right pointers. */ struct node* newNode(int data)  {   struct node* node = (struct node*)                        malloc(sizeof(struct node));   node->data = data;   node->left = NULL;   node->right = NULL;        return(node); }    /*Driver program to test above functions*/   int main() {   /*create a tree*/     struct node *root = newNode(1);   root->left        = newNode(2);   root->right       = newNode(3);   root->left->left  = newNode(4);   root->left->right = newNode(5);            /*get leaf count of the above created tree*/   printf("Leaf count of the tree is %d", getLeafCount(root));        getchar();   return 0; }

Output: 

The leaf count of binary tree is : 3

Time & Space Complexities: Since this program is similar to traversal of tree, time and space complexities will be same as Tree traversal 

Tirthankar Pal

MBA from IIT Kharagpur with GATE, GMAT, IIT Kharagpur Written Test, and Interview
2 year PGDM (E-Business) from Welingkar, Mumbai
4 years of Bachelor of Science (Hons) in Computer Science from the National Institute of Electronics and Information Technology
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10 years of Experience in Software Development out of that 6 years 8 months in Wipro
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