Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?
Example:
Input: 3 Output: 5 Explanation: 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
class Solution_96_1 { public: int numTrees(int n) { vector<int> f(n + 1, 0); f[0] = 1; f[1] = 1; for (int i = 2; i <= n; ++i) { for (int k = 1; k <= i; ++k) f[i] += f[k - 1] * f[i - k]; } return f[n]; } };