Lecture 175:-FW To Find Diameter

Sure! To find the diameter of a binary tree, you can implement a function that calculates the longest path (number of edges) between any two nodes in the tree. The diameter of a binary tree is the length of the longest path between any two nodes, which may or may not pass through the root.

Here's a Python implementation of finding the diameter of a binary tree:

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class TreeNode: def __init__(self, data): self.data = data self.left = None self.right = None def diameter_of_binary_tree(root): if root is None: return 0 # Calculate the height of the left and right subtrees left_height = height_of_binary_tree(root.left) right_height = height_of_binary_tree(root.right) # Calculate the diameter considering three cases: # 1. Diameter passes through the root (left_height + right_height + 1) # 2. Diameter lies entirely in the left subtree # 3. Diameter lies entirely in the right subtree return max(left_height + right_height + 1, diameter_of_binary_tree(root.left), diameter_of_binary_tree(root.right)) def height_of_binary_tree(node): if node is None: return 0 left_height = height_of_binary_tree(node.left) right_height = height_of_binary_tree(node.right) return max(left_height, right_height) + 1 # Example usage root = TreeNode(1) root.left = TreeNode(2) root.right = TreeNode(3) root.left.left = TreeNode(4) root.left.right = TreeNode(5) diameter = diameter_of_binary_tree(root) print("Diameter of the binary tree:", diameter)

In this example, we have defined a TreeNode class to represent individual nodes of the binary tree. The diameter_of_binary_tree function calculates the diameter of the binary tree using a recursive approach. It calculates the height of the left and right subtrees using the height_of_binary_tree function and considers three cases to calculate the diameter:

The diameter passes through the root node.

The diameter lies entirely in the left subtree.

The diameter lies entirely in the right subtree.

The maximum of these three cases gives the final diameter of the binary tree.

Keep in mind that this implementation has a time complexity of O(N^2), where N is the number of nodes in the binary tree, due to repeated calculations of heights. This can be optimized to O(N) using a bottom-up approach to calculate heights while simultaneously calculating the diameter.