# 543. Diameter of Binary Tree
Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.
Example:
Given a binary tree
1
/ \
2 3
/ \
4 5
Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3].
Note: The length of path between two nodes is represented by the number of edges between them.
# Solution
Approach 1: traverse the tree recursively while keeping two parameters: the longest path that pass through the node in the subtree, and the longest path seen everywhere in the subtree.
# Code (Python)
Approach 1:
class Solution:
def diameterOfBinaryTree(self, root: TreeNode) -> int:
if not root:
return 0
return self._diameter(root)[1]
def _diameter(self, root):
if not root.left and not root.right:
return (0, 0) # (longest path passing through the root, longest path in subtree)
if root.left and root.right:
left_local, left_global = self._diameter(root.left)
right_local, right_global = self._diameter(root.right)
return (1 + max(left_local, right_local), max(left_global, right_global, 2 + left_local + right_local))
for child in (root.left, root.right):
if not child:
continue
local_val, global_val = self._diameter(child)
return (1 + local_val, max(global_val, 1 + local_val))
# Code (C++)
Approach 1:
Approach 2: