LeetCode: Binary Tree Maximum Path Sum 解题报告

Binary Tree Maximum Path Sum
Given a binary tree, find the maximum path sum.

The path may start and end at any node in the tree.

For example:
Given the below binary tree,

1
      / \
     2   3

SOLUTION 1:

计算树的最长path有2种情况：

1. 通过根的path.

(1)如果左子树从左树根到任何一个Node的path大于零，可以链到root上

(2)如果右子树从右树根到任何一个Node的path大于零，可以链到root上

2. 不通过根的path. 这个可以取左子树及右子树的path的最大值。

所以创建一个inner class:

记录2个值：

1. 本树的最大path。

2. 本树从根节点出发到任何一个节点的最大path.

注意，当root == null,以上2个值都要置为Integer_MIN_VALUE; 因为没有节点可取的时候，是不存在solution的。以免干扰递归的计算

 1 /**
 2  * Definition for binary tree
 3  * public class TreeNode {
 4  *     int val;
 5  *     TreeNode left;
 6  *     TreeNode right;
 7  *     TreeNode(int x) { val = x; }
 8  * }
 9  */
10 public class Solution {
11     public class ReturnType {
12         int maxSingle;
13         int max;
14         ReturnType (int maxSingle, int max) {
15             this.max = max;
16             this.maxSingle = maxSingle;
17         }
18     }
19
20     public int maxPathSum(TreeNode root) {
21         return dfs(root).max;
22     }
23
24     public ReturnType dfs(TreeNode root) {
25         ReturnType ret = new ReturnType(Integer.MIN_VALUE, Integer.MIN_VALUE);
26         if (root == null) {
27             return ret;
28         }
29
30         ReturnType left = dfs(root.left);
31         ReturnType right = dfs(root.right);
32
33         int cross = root.val;
34
35         // if any of the path of left and right is below 0, don‘t add it.
36         cross += Math.max(0, left.maxSingle);
37         cross += Math.max(0, right.maxSingle);
38
39         // 注意，这里不可以把Math.max(left.maxSingle, right.maxSingle) 与root.val加起来，
40         // 会有可能越界！
41         int maxSingle = Math.max(left.maxSingle, right.maxSingle);
42
43         // may left.maxSingle and right.maxSingle are below 0
44         maxSingle = Math.max(maxSingle, 0);
45         maxSingle += root.val;
46
47         ret.maxSingle = maxSingle;
48         ret.max = Math.max(right.max, left.max);
49         ret.max = Math.max(ret.max, cross);
50
51         return ret;
52     }
53 }

GITHUB:

https://github.com/yuzhangcmu/LeetCode_algorithm/blob/master/tree/MaxPathSum.java