Unique Binary Search Tree II

Question

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

Example Given n = 3, your program should return all 5unique BST's shown below.

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

Thoughts

对这个数字序列，遍历所有可以做root的，并且对左右所有可以做child的也遍历

Solution

class Solution:
    # @paramn n: An integer
    # @return: A list of root
    def generateTrees(self, n):
        # write your code here
        return self.generate(1, n)

    def generate(self, start, end):
        result = []
        if start > end:
            result.append(None)
            return result

        for i in range(start, end+1):
            left = self.generate(start, i - 1)
            right = self.generate(i+1, end)

            for l in left:
                for r in right:
                    root = TreeNode(i)
                    root.left = l
                    root.right = r
                    result.append(root)
        return result