LeetCode题解：Unique Binary Search Trees

Unique Binary Search Trees

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

思路：

典型的动态规划题目。

BST(n) = Sum(i, 1, n, BST(i - 1) * BST(n - i))

其中(i, 1, n)表示i的取值范围从1到n。

题解：

class Solution {public:    vector<int> history;        Solution()    {        history.push_back(1);        history.push_back(1);        history.push_back(2);    }        int numTrees(int n)     {        while(history.size() <= n)        {            int last = history.size();            int accumu = 0;            for(int i = 1 ;i <= last; ++i)                accumu += history[i - 1] * history[last - i];            history.push_back(accumu);        }                return history[n];    }};