The diameter of a tree (sometimes called the width) is the number of nodes on the longest path between two end nodes. The diagram below shows two trees each with diameter nine, the leaves that form the ends of the longest path are shaded (note that there is more than one path in each tree of length nine, but no path longer than nine nodes).
The diameter of a tree T is the largest of the following quantities:
- the diameter of T’s left subtree.
- the diameter of T’s right subtree.
- the longest path between leaves that goes through the root of T (this can be computed from the heights of the subtrees of T)
Diameter of the given binary tree is 4
Time Complexity: O(n2)
Optimized implementation: The above implementation can be optimized by calculating the height in the same recursion rather than calling a height() separately. Thanks to Amar for suggesting this optimized version. This optimization reduces time complexity to O(n).
The diameter of given binary tree is : 4
Time Complexity: O(n)
Please write comments if you find any of the above codes/algorithms incorrect, or find other ways to solve the same problem.
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- Finding the lexicographically smallest diameter in a binary tree
- Diameter of an N-ary tree
- Diameter of a tree using DFS
- Diameter of n-ary tree using BFS
- Possible edges of a tree for given diameter, height and vertices
- DP on Trees | Set-3 ( Diameter of N-ary Tree )
- Make a tree with n vertices , d diameter and at most vertex degree k
- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- Maximum sub-tree sum in a Binary Tree such that the sub-tree is also a BST
- Convert a Generic Tree(N-array Tree) to Binary Tree
- Check if a binary tree is subtree of another binary tree | Set 1
- Binary Tree to Binary Search Tree Conversion
- Check if a binary tree is subtree of another binary tree | Set 2
- Convert a Binary Tree to Threaded binary tree | Set 1 (Using Queue)
- Check whether a binary tree is a full binary tree or not
- Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)
- Minimum swap required to convert binary tree to binary search tree
- Check whether a binary tree is a full binary tree or not | Iterative Approach