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# 108. Convert Sorted Array to Binary Search Tree

## 題目 :

Given an integer array nums where the elements are sorted in ascending order, convert it to a height-balanced binary search tree.

A height-balanced binary tree is a binary tree in which the depth of the two subtrees of every node never differs by more than one.

### Example :

Note

Example 1:

Input: nums = [-10,-3,0,5,9] Output: [0,-3,9,-10,null,5] Explanation: [0,-10,5,null,-3,null,9] is also accepted:

Example 2:

Input: nums = [1,3] Output: [3,1] Explanation: [1,3] and [3,1] are both a height-balanced BSTs.

#### 解題思路 :

• 這題需要我們將遞增序列的數列轉換成height-balacend的BST，題目定義為每一個node所連接的左右subtree之間深度不能差超過1
• 其實呢這題考察我們對BST的熟悉度跟Recursive的熟練度
• 若要左右高度相仿的subtree，那該root必須是該遞增序列的中位數才能使得左右subtree node數平均分布，然後每一個node都遵守與root一樣的準則寫出recursive code

### Recursive解法

• time complexity: O(n) , space complexity: O(1)

Runtime: 0 ms, faster than 100.00% of Go online submissions for Convert Sorted Array to Binary Search Tree.

 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 `````` ``````/** * Definition for a binary tree node. * type TreeNode struct { * Val int * Left *TreeNode * Right *TreeNode * } */ func sortedArrayToBST(nums []int) *TreeNode { if len(nums) == 0{ return nil } left := 0 right := len(nums)-1 mid := (right + left)/2 node := &TreeNode{ Val: nums[mid], Left: sortedArrayToBST(nums[left:mid]), Right: sortedArrayToBST(nums[mid+1:right+1]), } return node } ``````