108. Convert Sorted Array to Binary Search Tree

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

Analyze

递归解题, 题目中高度平衡即当前节点的左右子节点的深度不超过 1 要稍微理解下。

  • 当数组为奇数时比如 0, 1, 2, 此时取中间数 1 为根节点, 0 和 2 分别为其左右子节点, 此时满足高度平衡的条件。
  • 当数组为偶数时比如 0, 1, 此时取中间数 1 为根节点, 0 为其左右子节点, 此时满足高度平衡的条件。
/**
 * 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) {
  if (nums.length === 0) return null
  const mid = Math.floor(nums.length / 2)
  const result = new TreeNode(nums[mid])
  const left = nums.slice(0, mid)
  const right = nums.slice(mid + 1, nums.length)
  result.left = sortedArrayToBST(left)
  result.right = sortedArrayToBST(right)
  return result
};

function TreeNode(val) {
  this.val = val;
  this.left = this.right = null;
}