311. Sparse Matrix Multiplication

Given two sparse matrices A and B, return the result of AB.

You may assume that A's column number is equal to B's row number.

Example:

Input:

A = [
  [ 1, 0, 0],
  [-1, 0, 3]
]

B = [
  [ 7, 0, 0 ],
  [ 0, 0, 0 ],
  [ 0, 0, 1 ]
]

Output:

     |  1 0 0 |   | 7 0 0 |   |  7 0 0 |
AB = | -1 0 3 | x | 0 0 0 | = | -7 0 3 |
                  | 0 0 1 |

vector<vector<int>> multiply(vector<vector<int>>& A, vector<vector<int>>& B) { // time: O(m * k * n); space: O(m * n)
    vector<vector<int> > res(A.size(), vector<int>(B[0].size(), 0));
    for (int i = 0; i < A.size(); ++i) {
        for (int k = 0; k < A[0].size(); ++k) {
            if (A[i][k] != 0) {
                for (int j = 0; j < B[0].size(); ++j) {
                    if (B[k][j] != 0) res[i][j] += A[i][k] * B[k][j];
                }
            }
        }
    }
    return res;
}