#177 Convert Sorted Array to Binary Search Tree With Minimal Height

题目描述：

Given a sorted (increasing order) array, Convert it to create a binary tree with minimal height.

 Notice

There may exist multiple valid solutions, return any of them.

Have you met this question in a real interview? 

Yes

Example

Given [1,2,3,4,5,6,7], return

     4   /   \  2     6 / \    / \1   3  5   7

题目思路：

对于bst来说，最矮的bst应该是以A中的中位数作为root的一个bst，它的左子树为中位数之前的那些数组成的bst，右子树为中位数之后的那些数组成的bst。这样就是一个recursion的算法。

Mycode（AC = 135ms）：

/** * Definition of TreeNode: * class TreeNode { * public: *     int val; *     TreeNode *left, *right; *     TreeNode(int val) { *         this->val = val; *         this->left = this->right = NULL; *     } * } */class Solution {public:    /**     * @param A: A sorted (increasing order) array     * @return: A tree node     */    TreeNode *sortedArrayToBST(vector<int> &A) {        // write your code here        return sortedArrayToBST(A, 0, A.size() - 1);    }        TreeNode *sortedArrayToBST(vector<int> &A, int start, int end) {        if (start > end) {            return NULL;        }        else if (start == end) {            return new TreeNode(A[start]);        }        else {            int mid = (start + end) / 2;            TreeNode *root = new TreeNode(A[mid]);                        root->left = sortedArrayToBST(A, start, mid - 1);            root->right = sortedArrayToBST(A, mid + 1, end);                        return root;        }    }};