# Full Binary Tree

#### In this tutorial, you will learn about full binary tree and its different theorems. Also, you will find working examples to check full binary tree in C.

A full Binary tree is a special type of binary tree in which every parent node/internal node has either two or no children.

It is also known as a proper binary tree.

## Full Binary Tree Theorems

``````Let, i = the number of internal nodes
n = be the total number of nodes
l = number of leaves
λ = number of levels
``````
1. The number of leaves is `i + 1`.
2. The total number of nodes is `2i + 1`.
3. The number of internal nodes is (n – 1) / 2.
4. The number of leaves is `(n + 1) / 2`.
5. The total number of nodes is `2l – 1`.
6. The number of internal nodes is `l – 1`.
7. The number of leaves is at most `2λ - 1`.

## C Examples

The following code is for checking if a tree is a full binary tree.

``````// Checking if a binary tree is a full binary tree in C

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>

struct Node {
int item;
struct Node *left, *right;
};

// Creation of new Node
struct Node *createNewNode(char k) {
struct Node *node = (struct Node *)malloc(sizeof(struct Node));
node->item = k;
node->right = node->left = NULL;
return node;
}

bool isFullBinaryTree(struct Node *root) {
// Checking tree emptiness
if (root == NULL)
return true;

// Checking the presence of children
if (root->left == NULL && root->right == NULL)
return true;

if ((root->left) && (root->right))
return (isFullBinaryTree(root->left) && isFullBinaryTree(root->right));

return false;
}

int main() {
struct Node *root = NULL;
root = createNewNode(1);
root->left = createNewNode(2);
root->right = createNewNode(3);

root->left->left = createNewNode(4);
root->left->right = createNewNode(5);
root->left->right->left = createNewNode(6);
root->left->right->right = createNewNode(7);

if (isFullBinaryTree(root))
printf("The tree is a full binary treen");
else
printf("The tree is not a full binary fulln");
}``````

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