LeetCode095. 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

---

这应该是一道分治算法的题。

当n=3时，先建一个[1,2,3]的数组，再分别以每个值为root，左边为左子树，右边为右子树。

需要注意的是helper函数里的return [None]而不是return None

class Solution(object):
    def generateTrees(self, n):
        """
        :type n: int
        :rtype: List[TreeNode]
        """
        
        if n==0: return None
        node = [i for i in range(1, n+1)]
        return self.helper(node)
        
    def helper(self, nodelist):
        if not nodelist: return [None]
        res = []

        for i in xrange(len(nodelist)):
            for left in self.helper(nodelist[:i]):
                for right in self.helper(nodelist[i+1:]):
                    node = TreeNode(nodelist[i])
                    node.left = left
                    node.right = right
                    res.append(node)
        return res