LeetCode 题解（97）: Binary Tree Maximum Path Sum

题目：

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

Return 6.

题解：

此题不需要求产生最大值的路径，而只需要求最大值，故而不难。用递归的Post Order Tranverse即可。注意Java和Python都是按值传递int，故而需要用class封装。

c++版：

class Solution {public:int maxPathSum(TreeNode* root) {int globalM = INT_MIN;find(root, globalM);return globalM;}int find(TreeNode* root, int& globalM) {if (root == NULL) {return 0;}int left = find(root->left, globalM);int right = find(root->right, globalM);int localML = left + root->val;int localMR = right + root->val;int localM = localML;if (localMR > localM)localM = localMR;if (root->val > localM)localM = root->val;if (localM > globalM)globalM = localM;localML + localMR - root->val > globalM ? globalM = localML + localMR - root->val : globalM = globalM;return localM;}};

Java版：

/** * Definition for a binary tree node. * public class TreeNode { *     int val; *     TreeNode left; *     TreeNode right; *     TreeNode(int x) { val = x; } * } */ class Result {    int result;    Result(int x){result = x;}} public class Solution {    public int maxPathSum(TreeNode root) {        Result global = new Result(Integer.MIN_VALUE);        find(root, global);        return global.result;    }        int find(TreeNode root, Result global) {        if(root == null)            return 0;        int left = find(root.left, global);        int right = find(root.right, global);        int leftM = left + root.val;        int rightM = right + root.val;        int local = leftM;        if(rightM > local)            local = rightM;        if(root.val > local)            local = root.val;        if(local > global.result)            global.result = local;        global.result = left + right + root.val > global.result ? left + right + root.val : global.result;        return local;    }}

Python版：

# Definition for a binary tree node.# class TreeNode:#     def __init__(self, x):#         self.val = x#         self.left = None#         self.right = Noneimport sysclass Result:    def __init__(self, x):        self.result = xclass Solution:    # @param {TreeNode} root    # @return {integer}    def maxPathSum(self, root):        globalM = Result(-sys.maxint)        self.find(root, globalM)        return globalM.result            def find(self, root, globalM):        if root == None:            return 0        left = self.find(root.left, globalM)        right = self.find(root.right, globalM)        local = left + root.val        if right + root.val > local:            local = right + root.val        if root.val > local:            local = root.val        if local > globalM.result:            globalM.result = local        if left + right + root.val > globalM.result:            globalM.result = left + right + root.val        return local