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Priority Queue in Data Structure Deque in Data Structure Difference Between Linear And Non Linear Data Structures Queue Operations In Data Structure About Data Structures Data Structures Algorithms Types of Data Structures Big O Notations Introduction to Arrays Introduction to 1D-Arrays Operations on 1D-Arrays Introduction to 2D-Arrays Operations on 2D-Arrays Strings in Data Structures String Operations Application of 2D array Bubble Sort Insertion Sort Sorting Algorithms What is DFS Algorithm What Is Graph Data Structure What is the difference between Tree and Graph What is the difference between DFS and BFS Bucket Sort Dijkstra’s vs Bellman-Ford Algorithm Linear Queue Data Structure in C Stack Using Array Stack Using Linked List Recursion in Fibonacci Stack vs Array What is Skewed Binary Tree Primitive Data Structure in C Dynamic memory allocation of structure in C Application of Stack in Data Structures Binary Tree in Data Structures Heap Data Structure Recursion - Factorial and Fibonacci What is B tree what is B+ tree Huffman tree in Data Structures Insertion Sort vs Bubble Sort Adding one to the number represented an array of digits Bitwise Operators and their Important Tricks Blowfish algorithm Bubble Sort vs Selection Sort Hashing and its Applications Heap Sort vs Merge Sort Insertion Sort vs Selection Sort Merge Conflicts and ways to handle them Difference between Stack and Queue AVL tree in data structure c++ Bubble sort algorithm using Javascript Buffer overflow attack with examples Find out the area between two concentric circles Lowest common ancestor in a binary search tree Number of visible boxes putting one inside another Program to calculate the area of the circumcircle of an equilateral triangle Red-black Tree in Data Structures Strictly binary tree in Data Structures 2-3 Trees and Basic Operations on them Asynchronous advantage actor-critic (A3C) Algorithm Bubble Sort vs Heap Sort Digital Search Tree in Data Structures Minimum Spanning Tree Permutation Sort or Bogo Sort Quick Sort vs Merge Sort Boruvkas algorithm Bubble Sort vs Quick Sort Common Operations on various Data Structures Detect and Remove Loop in a Linked List How to Start Learning DSA Print kth least significant bit number Why is Binary Heap Preferred over BST for Priority Queue Bin Packing Problem Binary Tree Inorder Traversal Burning binary tree Equal Sum What is a Threaded Binary Tree? What is a full Binary Tree? Bubble Sort vs Merge Sort B+ Tree Program in Q language Deletion Operation from A B Tree Deletion Operation of the binary search tree in C++ language Does Overloading Work with Inheritance Balanced Binary Tree Binary tree deletion Binary tree insertion Cocktail Sort Comb Sort FIFO approach Operations of B Tree in C++ Language Recaman’s Sequence Tim Sort Understanding Data Processing Applications of trees in data structures Binary Tree Implementation Using Arrays Convert a Binary Tree into a Binary Search Tree Create a binary search tree Horizontal and Vertical Scaling Invert binary tree LCA of binary tree Linked List Representation of Binary Tree Optimal binary search tree in DSA Serialize and Deserialize a Binary Tree Tree terminology in Data structures Vertical Order Traversal of Binary Tree What is a Height-Balanced Tree in Data Structure Convert binary tree to a doubly linked list Fundamental of Algorithms Introduction and Implementation of Bloom Filter Optimal binary search tree using dynamic programming Right side view of binary tree Symmetric binary tree Trim a binary search tree What is a Sparse Matrix in Data Structure What is a Tree in Terms of a Graph What is the Use of Segment Trees in Data Structure What Should We Learn First Trees or Graphs in Data Structures All About Minimum Cost Spanning Trees in Data Structure Convert Binary Tree into a Threaded Binary Tree Difference between Structured and Object-Oriented Analysis FLEX (Fast Lexical Analyzer Generator) Object-Oriented Analysis and Design Sum of Nodes in a Binary Tree What are the types of Trees in Data Structure What is a 2-3 Tree in Data Structure What is a Spanning Tree in Data Structure What is an AVL Tree in Data Structure Given a Binary Tree, Check if it's balanced

What is a full Binary Tree?

A full binary tree is considered to be a special kind of binary tree in which every single node or leaf node present either contains two children or no children at all. They are all interconnected and fully versed. They are also popularly known as the proper binary tree. They are the ones that keep in check the order and balance of the binary tree. In simpler words, a full binary tree is a tree in which all the nodes are situated at a certain distance from the root node and have two children each.

Theorem for the full binary tree

Suppose we have a binary tree named T which is non-empty then: -

  • Let I be the internal node present in the tree, then L will be the leaf nodes present in the tree, and it will be given by: -
    L = I + 1
  • If the tree T has I number of internal nodes and N stands for the total number of nodes present in that tree, then the formula for the same will be: -
    N = 2I + 1
  • If the tree T consists of N total number of nodes present in the tree, and L is the number of leaf nodes present in the tree, then the formula will be: -
    I = (N-1)/2
  • If the tree T consists of N number of total nodes present in the tree and L stands to be the total amount of leaf nodes present in that tree, then the number of leaf nodes present in the tree is given by: -
    L = (N+1)/2
  •  If the tree T contains L number of leaf nodes and so, to figure out the total amount of leaf nodes, we have to calculate: -
    N = 2L - 1

Algorithm for a full binary tree

Let, i = the number of internal nodes

       n = be the total number of nodes

       l = number of leaves

      λ = number of levels

Implementation

Example 1)

#include <iostream>
using namespace std;


struct Node {
  int key;
  struct Node *lft, *rt;
};


// We will create a new node
struct Node *newNod(char m) {
  struct Node *nod = (struct Node *)malloc(sizeof(struct Node));
  nod->key = m;
  nod->rt = nod->lft = NILL;
  return node;
}


bool isFullBinaryTree(struct Node *rot) {
  
  // Verify if we have any vacant spaces lft.
  if (root == NILL)
    return true;


  // Checking for the presence of children
  if (root->lft == NULL && root->rt == NULL)
    return true;


  if ((root->lft) && (root->rt))
    return (isFullBinaryTree(root->lft) && isFullBinaryTree(root->rt));


  return false;
}


int main() {
  struct Node *root = NULL;
  root = newNode(1);
  root->lft = newNode(2);
  root->rt = newNode(3);
  root->lft->lft = newNode(4);
  root->lft->rt = newNode(5);
  root->lft->rt->lft = newNode(6);
  root->lft->rt->rt = newNode(7);


  if (isFullBinaryTree(root))
    cout << "The tree is a full binary tree\n";
  else
    cout << "The tree is not a full binary tree\n";
}

Output:

WHAT IS A FULL BINARY TREE

Example 2)

// Check whether a C++ program is a full binary tree or not.
#include <bits/stdc++.h>
using namespace std;


/* Creating a tree structure*/
struct Node
{
	int key;
	struct Node *lft, *rt;
};


/* We gain a new function named helper that probably helps us to deposit a new node present in the provided key and the NILL lft and rt pointers.
struct Node *newNod(char m)
{
	struct Node *node = new Nod;
	node->key = m;
	node->rt = node->lft = NILL;
	return node;
}
// This specific function will tell us whether a given tree is a full binary tree or not.
bool isFullTree (struct Node* rot)
{
	// If empty tree
	if (root == NILL)
		return true;


	// If leaf node
	if (root->lft == NULL && root->rt == NULL)
		return true;


	// If both lft and rt are not NULL, and lft & rt subtrees
	// are full
	if ((root->lft) && (root->rt))
		return (isFullTree(root->lft) && isFullTree(root->rt));


	// We reach here when none of the above conditions work
	return false;
}


// Driver Program
int main()
{
	struct Node* root = NULL;
	root = newNode(10);
	root->lft = newNode(20);
	root->rt = newNode(30);


	root->lft->rt = newNode(40);
	root->lft->lft = newNode(50);
	root->rt->lft = newNode(60);
	root->rt->rt = newNode(70);


	root->lft->lft->lft = newNode(80);
	root->lft->lft->rt = newNode(90);
	root->lft->rt->lft = newNode(80);
	root->lft->rt->rt = newNode(90);
	root->rt->lft->lft = newNode(80);
	root->rt->lft->rt = newNode(90);
	root->rt->rt->lft = newNode(80);
	root->rt->rt->rt = newNode(90);


	if (isFullTree(root))
		cout << "The Binary Tree is full\n";
	else
		cout << "The Binary Tree is not full\n";


	return(0);
}

Output:

WHAT IS A FULL BINARY TREE



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