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

 /**
  * Definition for binary tree
  * public class TreeNode {
  *     int val;
  *     TreeNode left;
  *     TreeNode right;
  *     TreeNode(int x) { val = x; }
  * }
  */
 public class Solution {
     public class ReturnType {
         int maxSingle;
         int max;
         ReturnType (int maxSingle, int max) {
             this.max = max;
             this.maxSingle = maxSingle;
         }
     }

     public int maxPathSum(TreeNode root) {
         return dfs(root).max;
     }

     public ReturnType dfs(TreeNode root) {
         ReturnType ret = new ReturnType(Integer.MIN_VALUE, Integer.MIN_VALUE);
         if (root == null) {
             return ret;
         }

         ReturnType left = dfs(root.left);
         ReturnType right = dfs(root.right);

         int cross = root.val;

         // if any of the path of left and right is below 0, don't add it.
         cross += Math.max(0, left.maxSingle);
         cross += Math.max(0, right.maxSingle);

         // 注意，这里不可以把Math.max(left.maxSingle, right.maxSingle) 与root.val加起来，
         // 会有可能越界！
         int maxSingle = Math.max(left.maxSingle, right.maxSingle);

         // may left.maxSingle and right.maxSingle are below 0
         maxSingle = Math.max(maxSingle, 0);
         maxSingle += root.val;

         ret.maxSingle = maxSingle;
         ret.max = Math.max(right.max, left.max);
         ret.max = Math.max(ret.max, cross);

         return ret;
     }
 }

GITHUB:

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