Unique Binary Search Trees II

Given an integern, generate all structurally uniqueBST'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

分析

范围内建树min和max

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    def generateTrees(self, n: int) -> List[TreeNode]:     
        if not n:
            return []
        def helper(mn,mx):
            if mn>mx:
                return [None]
            if mn == mx:
                return [TreeNode(mn)]
            res = []
            for i in range(mn,mx+1):                

                for l in helper(mn,i-1):
                    for r in helper(i+1,mx):
                        root = TreeNode(i)
                        root.left,root.right = l,r
                        res.append(root)
            return res

        return helper(1,n)