95. Unique Binary Search Trees II(dfs经典题目)

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

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

class Solution(object):
    def generateTrees(self, n):
        """
        :type n: int
        :rtype: List[TreeNode]
        """
        if n == 0: return []
        return self.generateTreesDFS(1, n)

    def generateTreesDFS(self, left, right):
        if left > right:
            return [None]
        res = []
        for i in range(left, right + 1):
            left_nodes = self.generateTreesDFS(left, i - 1)
            right_nodes = self.generateTreesDFS(i + 1, right)
            for left_node in left_nodes:
                for right_node in right_nodes:
                    root = TreeNode(i)
                    root.left = left_node
                    root.right = right_node
                    res.append(root)
        return res

所有的解就是分别以1,2,3...n做根节点的解的集合.而以i为根节点的解的个数就是左右子树的解的积.
递归求解.