124. Binary Tree Maximum Path Sum

Leetcode 链接

题目

Given a non-empty binary tree, find the maximum path sum.

For this problem, a path is defined as any sequence of nodes from some starting node to any node in the tree along the parent-child connections. The path must contain at least one node and does not need to go through the root.

Example 1:

Input: [1,2,3]

       1
      / \
     2   3

Output: 6
Example 2:

Input: [-10,9,20,null,null,15,7]

   -10
   / \
  9  20
    /  \
   15   7

Output: 42

题意解析

在二叉树中找出一条路径，该路径和最大。注意：该路径可能没有经过根节点，也可能不包含叶子节点。

解决方案

先把问题分为两种情况：（1）该路径包含根节点 （2）该路径不包含根节点,该路径处于根节点的左子树或者右子树中。

• 如下代码中，'initMap' 函数的作用是求出从叶子节点到当前节点的最大的路径和

Go 代码

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

var mm map[*TreeNode]int

func maxPathSum(root *TreeNode) int {
    mm = make(map[*TreeNode]int)
    initMap(root)
    return helper(root)
}

func helper(root *TreeNode) int {
    withoutRoot := 0
    switch {
    case root == nil:
        return 0

    case isLeaf(root):
        return root.Val

    case root.Left == nil:
        withoutRoot = helper(root.Right)

    case root.Right == nil:
        withoutRoot = helper(root.Left)

    default:
        withoutRoot = max(helper(root.Left), helper(root.Right))
    }

    withRoot := root.Val
    if mm[root.Left] > 0 {
        withRoot += mm[root.Left]
    }
    if mm[root.Right] > 0 {
        withRoot += mm[root.Right]
    }

    return max(withRoot, withoutRoot)
}

func initMap(root *TreeNode) (res int) {
    switch {
    case root == nil:
        res = 0

    case isLeaf(root):
        mm[root] = root.Val
        if root.Val < 0 {
            res = 0
        } else {
            res = root.Val
        }

    default:
        mm[root] = max(initMap(root.Left), initMap(root.Right)) + root.Val
        res = mm[root]
    }

    return
}

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

func isLeaf(root *TreeNode) bool {
    return root.Left == nil && root.Right == nil
}