算法56-求树中节点的最大距离

题目：
给定一棵二叉树，找到二叉树中最大距离的两个节点，返回最大距离

分析：

1利用二叉树的递归方法，要左子树和右子树要需要的信息

2 需要的信息为节点的高度和节点的最大上的最大距离

代码：

package main
import (
	"fmt"
	"math"

)
type TreeNode struct {
	Data Data
    // 左子树指针
    left *TreeNode
    // 右子树指针
    right *TreeNode
}

type Data struct{
	Name string
    Age int
    Score float32
}
type Info struct{
	Maxdistence int
	High int
	distence int
}
func process(x *TreeNode)Info{
	if x==nil{
		info:=Info{Maxdistence:0,High:0}
		return info
	}
	leftinfo:=process(x.left)
	rightinfo:=process(x.right)
	var info Info
	//当前节点左子树和右子树高度相加再加一，与下层返回给我的左大距离谁打我就记为当前的最大距离，另外保存我的最大距离
	info.High=int(math.Max(float64(leftinfo.High),float64(rightinfo.High)))+1
	// if info.High>int(math.Max(float64(leftinfo.High),float64(rightinfo.High))){
	tmp:=int(math.Max(float64(leftinfo.Maxdistence),float64(rightinfo.Maxdistence)))

	// }else{	
	info.distence=leftinfo.High+rightinfo.High+1

	info.Maxdistence=int(math.Max(float64(info.distence),float64(tmp)))

	// }
	return info
}

func main(){
    // 根节点
    var student Data
    student.Name = "root"
    student.Age = 10
    student.Score = 90
	var root TreeNode
	root.Data=student

    
    // 一级左子树
	var student1l Data
    student1l.Name = "left1"
    student1l.Age = 20
    student1l.Score = 80
	var left1 TreeNode
	left1.Data=student1l
    root.left = &left1
    
    // 一级右子树
	var student1r Data

    student1r.Name = "right1"
    student1r.Age = 30
    student1r.Score = 70
	var right1 TreeNode
	right1.Data=student1r

    root.right = &right1
    
    // 二级左子树
    var left2 TreeNode
	var student2l Data

    student2l.Name = "left2"
    student2l.Age = 40
    student2l.Score = 60
    left2.Data=student2l
    left1.left = &left2

	// 三级右子树
	var left3 TreeNode
	var student3l Data

    student3l.Name = "left3"
    student3l.Age = 45
    student3l.Score = 65
    left3.Data=student3l
    left1.right = &left3

	//四级右子树
	var left4 TreeNode
	var student4l Data

    student4l.Name = "left4"
    student4l.Age = 46
    student4l.Score = 66
    left4.Data=student4l
    left3.right = &left4

	//五级右子树
	var left5 TreeNode
	var student5l Data

	student5l.Name = "left4"
	student5l.Age = 47
	student5l.Score = 67
	left5.Data=student5l
	left4.right = &left5

	fmt.Println(process(&root))
}

总结：
1 节点的高度是经常会用到的需要子树反馈的主要信息，max（左子树的高度，右子树的高度）+自己这一层的高度1
2 节点的最大距离实际是两个子树的最大距离，和左右子树的高度的和再加上1，这三个值中最大的值