LeetCode-96-Unique Binary Search Trees

算法描述：

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

解题思路：动态规划，f(n) = f(0)*f(n-1) +  f(1)*f(n-2) + f(2)*f(n-3) + f(3)*f(n-4) + f(4)*f(n-5) ...... f(n-1)*f(0)

    int numTrees(int n) {
        vector<int> dp(n+1,0);
        dp[0] =1;
        for(int i = 1; i <= n; i++){
            for(int j=0; j < i; j++){
                dp[i] += dp[j]*dp[i-j-1];
            }
        }
        return dp[n];
    }