LeetCode Problem : Unique Binary Search Trees

Problem

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) {
    // IMPORTANT: Please reset any member data you declared, as
    // the same Solution instance will be reused for each test case.
    vector<int> M(n + 1);
    M[0] = 1;
    M[1] = 1;
    for(int i = 2; i <= n; ++i){
        int sum = 0;
        for(int j = 1; j <= i; ++j){
            sum += M[j - 1]*M[i - j];
        }
        M[i] = sum;
    }
    return M[n];
}