543. Diameter of Binary Tree

Leetcode 链接

题目

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.

题意解析

找出二叉树中任意两个点之间的最远距离。

解决方案

• 将情况分为三种：（1）这两个点的连线经过了 root 根节点 （2）这两个点都在 root 的左子树 （3）这两个点都在 root 的右子树

Go 代码

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */

var levelRecord map[*TreeNode]int

func diameterOfBinaryTree(root *TreeNode) int {
    levelRecord = make(map[*TreeNode]int)
    getLevel(root) // NOTE: we only check the all nodes' level once
    return helper(root)
}

func helper(root *TreeNode) int {
    if root == nil || (root.Left == nil && root.Right == nil) {
        return 0
    }

    withoutRoot := max(helper(root.Left), helper(root.Right))
    withRoot := levelRecord[root.Left] + levelRecord[root.Right]

    return max(withoutRoot, withRoot)
}

func getLevel(root *TreeNode) int {
    res := 0
    if root != nil {
        res = max(getLevel(root.Left), getLevel(root.Right)) + 1
    }

    levelRecord[root] = res
    return res
}

func max(a, b int) int {
    if a > b {
        return a
    }

    return b
}