Problem

Given an integer n, generate all structurally unique BST's (binary search trees) that store values 1 … n.

Example:

Input: 3
Output:
[
  [1,null,3,2],
  [3,2,null,1],
  [3,1,null,null,2],
  [2,1,3],
  [1,null,2,null,3]
]
Explanation:
The above output corresponds to the 5 unique BST's shown below:

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

Solution

/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {number} n
 * @return {TreeNode[]}
 */
var generateTrees = function(n) {
  if (n < 1) return [];
  return generate(1, n);
};

var generate = function (l, r) {
  var nodes = [];
  var node = null;
  var left = [];
  var right = [];
  for (var i = l; i <= r; i++) {
    left = generate(l, i - 1);
    right = generate(i + 1, r);
    for (var j = 0; j < left.length; j++) {
      for (var k = 0; k < right.length; k++) {
        node = new TreeNode(i);
        node.left = left[j];
        node.right = right[k];
        nodes.push(node);
      }
    }
  }
  return nodes.length ? nodes : [null];
};

Explain:

例如：有 5 个节点，选取其中 1 个作为 root，还剩 4 个。则左右可分为 (0, 4), (1, 3), (2, 2), (3, 1), (4, 0) 等几种情况，左右的分配用递归得到即可。

Complexity:

• Time complexity :
• Space complexity :