Given an integer array with no duplicates. A maximum tree building on this array is defined as follow:

1. The root is the maximum number in the array.
2. The left subtree is the maximum tree constructed from left part subarray divided by the maximum number.
3. The right subtree is the maximum tree constructed from right part subarray divided by the maximum number.

Construct the maximum tree by the given array and output the root node of this tree.

Example 1:

Input: [3,2,1,6,0,5]
Output: return the tree root node representing the following tree:

      6
    /   \
   3     5
    \    / 
     2  0   
       \
        1

Note:

1. The size of the given array will be in the range [1,1000].

解題思路：找出最大值，最大值為root，陣列左側為左子樹，右側為右子樹，依此遞迴。

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* constructMaximumBinaryTree(vector<int>& nums) {
        return helper(0, nums.size() - 1, nums);
    }
    TreeNode* helper(int left, int right, vector<int>& nums) {
        if (left > right)
            return nullptr;
        int maxPos = max(nums, left, right);
        TreeNode* root = new TreeNode(nums[maxPos]);
        root->left = helper(left, maxPos - 1, nums);
        root->right = helper(maxPos + 1, right, nums);
        return root;
    }
    int max(vector<int>& nums, int l, int r) {
        int Pos = l;
        for (int i = l; i <= r; i++) {
            if (nums[Pos] < nums[i]){
                Pos = i;
            }                
        }
        return Pos;        
    }
};