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.

求樹的一點到另一點的最大路徑，利用遞歸的方法，ans 在 左子樹，右子樹，root+左+右的最大中產生。

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int ans;
    int maxPathSum(TreeNode *root) {
      ans = INT_MIN;
      travel(root);
      return ans;
    }
    int travel(TreeNode * root){
        if(root == NULL) return 0;
        int sum = root->val;
        int leftsum = travel(root->left);
        int rightsum = travel(root->right);
        if(leftsum > 0) sum += leftsum;
        if(rightsum > 0) sum += rightsum;
        ans = max(ans,sum);
        sum = max(leftsum,rightsum);
        return root->val + (sum > 0 ? sum : 0);
    }
};