Q108. Convert Sorted Array to Binary Search Tree

直达：https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/description/

Given an array where elements are sorted in ascending order, convert it to a height balanced BST.

For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees ofeverynode never differ by more than 1.

Example:

Given the sorted array: [-10,-3,0,5,9],

One possible answer is: [0,-3,9,-10,null,5], which represents the following height balanced BST:

      0
     / \
   -3   9
   /   /

分析

在有序数组中，去中间元素作为根节点，左侧序列迭代的构建新的子树作为根节点的左子树，右侧部分作为右子树。递归进行直到序列为空。

C++代码

/**
 * 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* sortedArrayToBST(vector<int>& nums) {
        return helper(nums, 0, nums.size()-1);
    }
private:
    TreeNode* helper(vector<int>& nums, int left, int right){
        if(left > right) return NULL;
        int mid = (right-left)/2+left;
        TreeNode* root = new TreeNode(nums[mid]);
        root->left = helper(nums, left, mid-1);
        root->right = helper(nums, mid+1, right);
        return root;
    }
};