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.

Method1 DFS (n time, 1 space)

• This question is similiar to https://www.gitbook.com/book/bfmc/algorithm/edit\#/edit/master/big-motherfucking-g/binary-tree-maximum-path-sum.md?\_k=4sxwf7
• We also maintain a global "diameter" value and do dfs.
• For each node, add up the value of the diameter of its left and right subtree, compare it with the global diameter value.

• At the end of the dfs function, return 1+max(left, right) to allow its parent callstack to compute its own diameter value.

• class Solution(object):
    def diameterOfBinaryTree(self, root):
        self.best = 0
        self.dfs(root)
        return self.best
    def dfs(self, root):
        if not root:
            return 0
        left = self.dfs(root.left)
        right = self.dfs(root.right)
        self.best = max(self.best, left + right)
        return 1 + max(left, right)