[LeetCode] 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

一般只求结果的数量而不要求所有可能的解就可能用DP来解决了，f[i][j] = sum(f[i][k-1] * f[k+1][j]); i <= k <= j

class Solution {
private:
    int f[1000][1000];
public:
    int getF(int beg, int end)
    {
        if (beg > end)
            return 1;
            
        return f[beg][end];
    }
    
    int numTrees(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        for(int i = 0; i < n; i++)
            f[i][i] = 1;
            
        for(int len = 2; len <= n; len++)
            for(int beg = 0; beg < n; beg++)
            {
                int end = beg + len - 1;
                if (end >= n)
                    break;
                
                f[beg][end] = 0;
                for(int mid = beg; mid <= end; mid++)
                    f[beg][end] += getF(beg, mid - 1) * getF(mid + 1, end);
            }
            
        return f[0][n-1];
    }
};