Leetcode 311: Sparse Matrix Multiplication

Posted 2020-10-18 Keep walking

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:

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

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


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

 1 public class Solution {
 2     public int[,] Multiply(int[,] A, int[,] B) {
 3         int rows = A.GetLength(0), cols = A.GetLength(1), colsB = B.GetLength(1);
 4                 
 5         var result = new int[rows, colsB];
 6         
 7         // since it‘s a sparse matrix, we only want to know rows/cols with a non-zero element
 8         var nonZeroRows = new bool[rows];
 9         var nonZeroCols = new bool[colsB];
10         
11         for (int i = 0; i < rows; i++)
12         {
13             for (int j = 0; j < cols; j++)
14             {
15                 if (A[i, j] != 0)
16                 {
17                     nonZeroRows[i] = true;
18                     continue;
19                 }
20             }
21         }
22         
23         // A‘s cols = B‘s rows
24         for (int j = 0; j < colsB; j++)
25         {
26             for (int i = 0; i < cols; i++)
27             {
28                 if (B[i, j] != 0)
29                 {
30                     nonZeroCols[j] = true;
31                     continue;
32                 }
33             }
34         }
35         
36         for (int i = 0; i < rows; i++)
37         {
38             for (int j = 0; j < colsB; j++)
39             {
40                 if (nonZeroRows[i] && nonZeroCols[j])
41                 {
42                     for (int c = 0; c < cols; c++)
43                     {
44                         result[i, j] += A[i, c] * B[c, j];
45                     }
46                 }
47             }
48         }
49         
50         return result;
51     }
52 }
53 
54 // brute force, timeout
55 public class Solution1 {
56     public int[,] Multiply(int[,] A, int[,] B) {
57         int rows = A.GetLength(0), cols = A.GetLength(1), colsB = B.GetLength(1);
58         
59         var result = new int[rows, colsB];
60         
61         for (int i = 0; i < rows; i++)
62         {
63             for (int j = 0; j < colsB; j++)
64             {
65                 for (int c = 0; c < cols; c++)
66                 {
67                     result[i, j] += A[i, c] * B[c, j];
68                 }
69             }
70         }
71         
72         return result;
73     }
74 }