# Perfect Binary Tree

#### In this tutorial, you will learn about the perfect binary tree. Also, you will find working examples for checking a perfect binary tree in C.

A perfect binary tree is a type of binary tree in which every internal node has exactly two child nodes and all the leaf nodes are at the same level.

All the internal nodes have a degree of 2.

Recursively, a perfect binary tree can be defined as:

- If a single node has no children, it is a perfect binary tree of height
`h = 0`

, - If a node has
`h > 0`

, it is a perfect binary tree if both of its subtrees are of height`h - 1`

and are non-overlapping.

## C Examples

The following code is for checking whether a tree is a perfect binary tree.

```
// Checking if a binary tree is a perfect binary tree in C
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
struct node {
int data;
struct node *left;
struct node *right;
};
// Creating a new node
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);
}
// Calculate the depth
int depth(struct node *node){
int d = 0;
while (node != NULL) {
d++;
node = node->left;
}
return d;
}
// Check if the tree is perfect
bool is_perfect(struct node *root, int d, int level){
// Check if the tree is empty
if (root == NULL)
return true;
// Check the presence of children
if (root->left == NULL && root->right == NULL)
return (d == level + 1);
if (root->left == NULL || root->right == NULL)
return false;
return is_perfect(root->left, d, level + 1) &&
is_perfect(root->right, d, level + 1);
}
// Wrapper function
bool is_Perfect(struct node *root){
int d = depth(root);
return is_perfect(root, d, 0);
}
int main(){
struct node *root = NULL;
root = newnode(1);
root->left = newnode(2);
root->right = newnode(3);
root->left->left = newnode(4);
root->left->right = newnode(5);
root->right->left = newnode(6);
if (is_Perfect(root))
printf("The tree is a perfect binary treen");
else
printf("The tree is not a perfect binary treen");
}
```

## Perfect Binary Tree Theorems

- A perfect binary tree of height h has
`2`

node.^{h + 1}– 1 - A perfect binary tree with n nodes has height
`log(n + 1) – 1 = Θ(ln(n))`

. - A perfect binary tree of height h has
`2`

leaf nodes.^{h} - The average depth of a node in a perfect binary tree is
`Θ(ln(n))`

.

# Python Example for Beginners

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There are two sides to machine learning:

**Practical Machine Learning:**This is about querying databases, cleaning data, writing scripts to transform data and gluing algorithm and libraries together and writing custom code to squeeze reliable answers from data to satisfy difficult and ill defined questions. It’s the mess of reality.**Theoretical Machine Learning**: This is about math and abstraction and idealized scenarios and limits and beauty and informing what is possible. It is a whole lot neater and cleaner and removed from the mess of reality.

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