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In this tutorial, you will learn about a complete binary tree and its various sorts. Additionally, you will discover working instances of a complete binary tree in C, C++, Java, and Python.
A complete binary tree is a binary tree where each level, except possibly the last, is completely filled, and all nodes are as far left as possible.
A complete binary tree is a binary tree where all the levels are completely filled except possibly the lowest one, which is filled from the left.
A complete binary tree is much the same as a full binary tree, however with two significant contrasts
- All the leaf elements should lean towards the left.
- The last leaf element probably won’t have a right sibling for example a complete binary tree doesn’t need to be a full binary tree.
In this article, you will learn-
Full Binary Tree vs Complete Binary Tree
How a Complete Binary Tree is Created?
- Select the first element of the list to be the root node. (no. of elements on level-I: 1)
2. Put the second element as a left child of the root node and the third element as the correct child. (no. of elements on level-II: 2)
3. Put the next two elements as the children of the left node of the subsequent level. Once more, put the next two elements as children of the right node of the subsequent level (no. of elements on level-III: 4) elements).
4. Continue to rehash until you arrive at the last element.
Python, Java and C/C++ Examples
Python
# Checking if a binary tree is a complete binary tree in Python
class Node:
def __init__(self, item):
self.item = item
self.left = None
self.right = None
# Count the number of nodes
def count_nodes(root):
if root is None:
return 0
return (1 + count_nodes(root.left) + count_nodes(root.right))
# Check if the tree is complete binary tree
def is_complete(root, index, numberNodes):
# Check if the tree is empty
if root is None:
return True
if index >= numberNodes:
return False
return (is_complete(root.left, 2 * index + 1, numberNodes)
and is_complete(root.right, 2 * index + 2, numberNodes))
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
root.right.left = Node(6)
node_count = count_nodes(root)
index = 0
if is_complete(root, index, node_count):
print("The tree is a complete binary tree")
else:
print("The tree is not a complete binary tree")
Java
// Checking if a binary tree is a complete binary tree in Java
// Node creation
class Node {
int data;
Node left, right;
Node(int item) {
data = item;
left = right = null;
}
}
class BinaryTree {
Node root;
// Count the number of nodes
int countNumNodes(Node root) {
if (root == null)
return (0);
return (1 + countNumNodes(root.left) + countNumNodes(root.right));
}
// Check for complete binary tree
boolean checkComplete(Node root, int index, int numberNodes) {
// Check if the tree is empty
if (root == null)
return true;
if (index >= numberNodes)
return false;
return (checkComplete(root.left, 2 * index + 1, numberNodes)
&& checkComplete(root.right, 2 * index + 2, numberNodes));
}
public static void main(String args[]) {
BinaryTree tree = new BinaryTree();
tree.root = new Node(1);
tree.root.left = new Node(2);
tree.root.right = new Node(3);
tree.root.left.right = new Node(5);
tree.root.left.left = new Node(4);
tree.root.right.left = new Node(6);
int node_count = tree.countNumNodes(tree.root);
int index = 0;
if (tree.checkComplete(tree.root, index, node_count))
System.out.println("The tree is a complete binary tree");
else
System.out.println("The tree is not a complete binary tree");
}
}
C
// Checking if a binary tree is a complete binary tree in C
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
struct Node {
int key;
struct Node *left, *right;
};
// Node creation
struct Node *newNode(char k) {
struct Node *node = (struct Node *)malloc(sizeof(struct Node));
node->key = k;
node->right = node->left = NULL;
return node;
}
// Count the number of nodes
int countNumNodes(struct Node *root) {
if (root == NULL)
return (0);
return (1 + countNumNodes(root->left) + countNumNodes(root->right));
}
// Check if the tree is a complete binary tree
bool checkComplete(struct Node *root, int index, int numberNodes) {
// Check if the tree is complete
if (root == NULL)
return true;
if (index >= numberNodes)
return false;
return (checkComplete(root->left, 2 * index + 1, numberNodes) && checkComplete(root->right, 2 * index + 2, numberNodes));
}
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);
int node_count = countNumNodes(root);
int index = 0;
if (checkComplete(root, index, node_count))
printf("The tree is a complete binary tree\n");
else
printf("The tree is not a complete binary tree\n");
}
C++
// Checking if a binary tree is a complete binary tree in C++
#include <iostream>
using namespace std;
struct Node {
int key;
struct Node *left, *right;
};
// Create node
struct Node *newNode(char k) {
struct Node *node = (struct Node *)malloc(sizeof(struct Node));
node->key = k;
node->right = node->left = NULL;
return node;
}
// Count the number of nodes
int countNumNodes(struct Node *root) {
if (root == NULL)
return (0);
return (1 + countNumNodes(root->left) + countNumNodes(root->right));
}
// Check if the tree is a complete binary tree
bool checkComplete(struct Node *root, int index, int numberNodes) {
// Check if the tree is empty
if (root == NULL)
return true;
if (index >= numberNodes)
return false;
return (checkComplete(root->left, 2 * index + 1, numberNodes) && checkComplete(root->right, 2 * index + 2, numberNodes));
}
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);
int node_count = countNumNodes(root);
int index = 0;
if (checkComplete(root, index, node_count))
cout << "The tree is a complete binary tree\n";
else
cout << "The tree is not a complete binary tree\n";
}
Relationship between array indexes and tree element
A complete binary tree has an intriguing property that we can use to discover the children and parents of any node.
On the off chance that the index of any element in the array is I, the element in the index 2i+1 will turn into the left child and element in 2i+2 index will turn into the right child. Additionally, the parent of any element at index i is given by the lower bound of (I-1)/2.
Let’s test it out,
Left child of 1 (index 0) = element in (2*0+1) index = element in 1 index = 12 Right child of 1 = element in (2*0+2) index = element in 2 index = 9 Similarly, Left child of 12 (index 1) = element in (2*1+1) index = element in 3 index = 5 Right child of 12 = element in (2*1+2) index = element in 4 index = 6
Let us likewise to affirm that the standards hold for discovering parent of any node
Parent of 9 (position 2) = (2-1)/2 = ½ = 0.5 ~ 0 index = 1 Parent of 12 (position 1) = (1-1)/2 = 0 index = 1
Understanding this mapping of array indexes to tree positions is critical to understanding how the Heap Data Structure functions and how it is used to actualize Heap Sort.
Complete Binary Tree Applications
- Heap-based data structures
- Heap sort
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