Unique Binary Search Trees

Description:

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

Code:

  int numTrees(int n) {
        //f[i][j]表示数字i,i+1,...,j有多少棵不同的树
        int f[MAX][MAX] = {0};
        
        for (int i = 1; i <= n; ++i)
        {//只有一个节点的情况
            f[i][i] = 1;
        }
        
        for (int i = 2; i<=n; ++i)
        {//有2,3,4，....n个元素的情况
            for (int j = 1; j<=n-i+1; ++j )
            {
                int m = j+i-1;
                //计算f[j][m];
                //先考虑两端为根节点的情况
                f[j][m] = f[j][m-1]+f[j+1][m];
                for (int k = j+1; k <= m-1; ++k)//k表示以k为根节点，左边的数据为j...k-1,右边的数据为k+1,..,m
                    f[j][m] += f[j][k-1] * f[k+1][m];
            }
        }
        return f[1][n];
    }