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95. Unique Binary Search Trees II

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

Constraints:

• 0 <= n <= 8

Solutions (Python)

1. Recursion

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def generateTrees(self, n: int) -> List[TreeNode]:
        def helper(m: int, n: int) -> List[TreeNode]:
            if m > n:
                return [None]

            ret = []

            for val in range(m, n + 1):
                for left in helper(m, val - 1):
                    for right in helper(val + 1, n):
                        ret.append(TreeNode(val, left, right))

            return ret

        return helper(1, n) if n > 0 else []