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