108.convert-sorted-array-to-binary-search-tree.js

/*
 * @lc app=leetcode id=108 lang=javascript
 *
 * [108] Convert Sorted Array to Binary Search Tree
 *
 * https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/description/
 *
 * algorithms
 * Easy (49.37%)
 * Total Accepted:    255.2K
 * Total Submissions: 507.2K
 * Testcase Example:  '[-10,-3,0,5,9]'
 *
 * 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
 * 
 * 
 */
/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {number[]} nums
 * @return {TreeNode}
 */
var sortedArrayToBST = function(nums) {
    // 由于数组是排序好的，因此一个思路就是将数组分成两半，一半是左子树，另一半是右子树
    // 然后运用“树的递归性质”递归完成操作即可。
    if(nums.length === 0) return null;
    const mid = nums.length >> 1;
    const root = new  TreeNode(nums[mid]);

    root.left = sortedArrayToBST(nums.slice(0, mid));
    root.right = sortedArrayToBST(nums.slice(mid + 1))
    return root;
    // 扩展：  这道题启示我们如果是一个非排序的数组，我们可以先进行排序然后再按上述思路进行。
};