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difference between a binary tree and a complete binary tree?

isuro answered on January 23, 2023 Popularity 9/10 Helpfulness 3/10

answer difference between a binary tree and a complete binary tree?

difference between a binary tree and a complete binary tree?

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A binary tree is a tree data structure in which each node has at most 
two children, which are referred to as the left child and the right child. 
Binary trees can have any shape and size, and the nodes do not have to be 
filled in a specific order.

A complete binary tree, on the other hand, is a binary tree in which all
levels of the tree are fully filled, except possibly the last level, and 
all nodes in the last level are as far left as possible. In other words, 
a complete binary tree is a binary tree in which all the levels are 
completely filled and all the leaf nodes are on the same level.

A simple way to identify a complete binary tree is that it is a binary tree 
that is always balanced. The height of the complete binary tree is O(log n)
where n is the number of nodes in the tree.

To summarize, the main difference between a binary tree and a complete 
binary tree is that while a binary tree can have any shape and structure, 
a complete binary tree is a binary tree that is completely filled and balanced.

Here's an example of a simple binary tree implementation in Python:
class BinaryTreeNode:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

class BinaryTree:
    def __init__(self):
        self.root = None

    def insert(self, data):
        new_node = BinaryTreeNode(data)
        if self.root is None:
            self.root = new_node
        else:
            current = self.root
            while True:
                if data < current.data:
                    if current.left is None:
                        current.left = new_node
                        break
                    else:
                        current = current.left
                else:
                    if current.right is None:
                        current.right = new_node
                        break
                    else:
                        current = current.right

This is a simple implementation of a binary tree where each node has at 
most two children, left and right. The insert method first checks if the
tree is empty and if yes it assigns the new_node as the root, otherwise 
it traverse the tree and find the correct place to insert the new_node by
comparing it's value with the value of the current node.

Here's an example of a simple complete binary tree implementation in Python:
class CompleteBinaryTree:
    def __init__(self):
        self.data = []

    def insert(self, value):
        self.data.append(value)
        current_index = len(self.data) - 1
        self._percolate_up(current_index)

    def _percolate_up(self, current_index):
        if current_index > 0:
            parent_index = (current_index - 1) // 2
            if self.data[parent_index] > self.data[current_index]:
                self.data[parent_index], self.data[current_index] = self.data[current_index], self.data[parent_index]
                self._percolate_up(parent_index)


This implementation of complete binary tree is using an array to store the 
values, where the parent node is stored at index n, and the left child is 
stored at index 2n+1 and right child is stored at index 2n+2 in the array. 
The insert method first append the new value to the end of the array and 
then call the _percolate_up method to reorder the tree so that it stays
complete and balanced.

In a complete binary tree, all levels are fully filled and all the leaf 
nodes are on the same level.

It's important to note that these are simple examples and real-world 
implementation may use different data structure to hold the tree and 
different techniques to insert, delete and search elements.

Popularity 9/10 Helpfulness 3/10 Language python

Source: Grepper

Tags: between binary-tree difference python

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Contributed on Jan 23 2023

isuro

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difference between a binary tree and a complete binary tree?

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