Problem description:

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:

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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 |

Solution:

Matrix multiply:

  • A[i][k]* B[k][j]= C[i][j]
  • C[i][j]= A[i][0]B[0][j]+ A[i][1]B[1][j]+ … +A[i][k]*B[k][j]
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class Solution {
public:
    vector<vector<int>> multiply(vector<vector<int>>& A, vector<vector<int>>& B) {
        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){ //it's sparse matrix, this can reduce redundant calculation
                    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;
    }
};

time complexity: $O(AB)$, $A: A.size()*A[0].size(), B: B.size()*B[0].size()$
space complexity: $O(1)$
reference:
https://goo.gl/yDQCx2