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Decode the Coding Interview in C#: Real-World Examples

Sparse Matrix Multiplication

Explore how to multiply two sparse matrices by leveraging dictionaries to store only non-zero elements. Understand the conversion process, multiplication logic, and how this approach reduces computational overhead. This lesson helps you implement sparse matrix multiplication with improved time and space efficiency.

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Description

We have two sparse matrices, A and B.

“A sparse matrix is one in which most of the elements are zero.”

You need to multiply the two matrices and return the output matrix. You can assume that A’s column number is equal to B’s row number.

Constraints

The following are some constraints:

  • 1 <= A.length, B.length <= 100
  • 1 <= A[i].length, B[i].length <= 100
  • -100 <= A[i][j], B[i][j] <= 100

Let’s review this scenario using the example below:

Coding exercise

C#
using System;
using System.Collections.Generic;
using System.Linq;
class Solution {
    public static int[][] multiply(int[][] A, int[][] B){
        // Your code goes here;
        return new int[][]{};
    }
}
Sparse Matrix Multiplication

Solution

We have two sparse matrices, meaning most of the matrices’ elements are zero. We can represent the input matrices as Dictionaries, and only save the non-zero elements and their ...