leetcode-tree-108. Convert Sorted Array to Binary Search Tree

题目

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

讲一个升序的数组，转换为一个BST(搜索二叉树)

• 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

思路

• 通过中序遍历得到的二叉搜索树就是一个升序的数组（左-根-右）
• 反过来思考，中间点肯定就是二叉树的根节点

所以获取中间值nums[mid]为根节点root，root.left又是[0,mid]的中间值
同理root.right是[mid,nums.lenght]的中间值
然后采用递归即可得到

解法

var sortedArrayToBST = function(nums){
    if(!nums.length) return null
    var mid = Math.floor(nums.length/2)
    var root = new TreeNode(nums[mid])

    root.left = sortedArrayToBST(nums.slice(0,mid))
    root.right = sortedArrayToBST(nums.slice(mid+1))
    return node
}

按照上面例子就是
1 queue = [3]
2 node = 3, level = [3], queue = []
3 node.left = 9, node.right = 20, queue = [9,20]

下一轮循环
1 queue = [9,20]
2 node = 9,level = [9],queue = [20]
3 node = 20,level = [9,20], queue = []
4 node.left = 15, node.right = 7,queue = [17,7]

再一次下一轮。。。