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

1. If the current node is null, return 0 (base case).
2. 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.