108. Convert Sorted Array to Binary Search Tree

• Difficulty: Easy

• Topics: Tree, Depth-first Search

• Similar Questions:

  • Convert Sorted List to Binary Search Tree

Problem:

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 of every node 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
   /   /
 -10  5

Solutions:

/**
 * 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) {
        int n = nums.size();
        return helper(nums, 0, n - 1);
    }

    TreeNode* helper(vector<int>& nums, int left, int right) {
        if (left > right)   return NULL;
        if (left == right)  return new TreeNode(nums[left]);

        int mid = left + (right - left)/2;
        TreeNode* root = new TreeNode(nums[mid]);
        root->left = helper(nums, left, mid - 1);
        root->right = helper(nums, mid + 1, right);
        return root;
    }
};