Calculate size of a tree
In the field of computer science and data structures, one of the fundamental tasks is to calculate the size of a binary tree. The size of a binary tree is defined as the total number of nodes present in the tree. In this post, we will discuss the problem of calculating the size of a binary tree using a recursive approach. We will provide a detailed explanation of the problem, present the algorithm to solve it.
Problem Statement
The problem we are addressing is to calculate the size of a given binary tree. The size of a binary tree is defined as the total number of nodes present in the tree, including both internal nodes and leaf nodes.
Example
Consider the binary tree provided in the code:
5
/ \
2 4
/ / \
7 6 3
\
3
The size of this binary tree is 7, as it contains 7 nodes.
Idea to Solve
The main idea behind solving this problem is to use recursion. We can calculate the size of a binary tree by recursively calculating the size of its left subtree, its right subtree, and then adding 1 to account for the current node. This is because the size of a binary tree can be calculated as the sum of the sizes of its left and right subtrees, plus 1 for the current node.
Algorithm
 If the current node is null, return 0 (base case).
 Otherwise, return the sum of the following:
 Recursively calculate the size of the left subtree.
 Recursively calculate the size of the right subtree.
 Add 1 for the current node.
Pseudocode
function treeSize(node):
if node is null:
return 0
return treeSize(node.left) + treeSize(node.right) + 1

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Time Complexity
The time complexity of the algorithm is O(n), where n is the number of nodes in the binary tree. This is because each node is visited exactly once in the recursive traversal.
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