Unique Binary Search Tree@leetcode

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Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

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

» Solve this problem

此题刚开始看上去无从下手，但是稍作分析就会发现，比较简单。简单在于它不用我们输出所有的 BST，而仅仅是给出有多少个就可以了。这样我们可以一个一个当作root看子树的个数。这时候就是recursion and dp了。这个时候又注意到，当结点i当root时，所有小于i的，会在左子树，所有大于i的，会在右子树。就是个简单的递归了。




更简单的逻辑．