95. Unique Binary Search Trees II

2019-07-28

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:

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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

Code：

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# 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]:
		# trivial case
        if n <= 0:
            return []

		# abstract what magic does and don't try to go down the recursion
		# trying to figure out the solution. just assume magic does its job.
		# assuming magic does what we aspect, the code below should
		# be correct
        def magic(left, right):
            if left > right:
                return [None]
            result = []
            for i in range(left, right + 1):
                for l in magic(left, i - 1):
                    for r in magic(i + 1, right):
                        node = TreeNode(i)
                        node.left = l
                        node.right = r
                        result.append(node)
            return result if result else [None]

        return magic(1, n)
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