SparseMatrixMultiplication.java

package array;

/**
 * Created by gouthamvidyapradhan on 03/12/2017.
 *
 * 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 |

 Solution: Skip the rows and columns which you already know would result in zero after multiplication.
 */
public class SparseMatrixMultiplication {

    /**
     * Main method
     * @param args
     * @throws Exception
     */
    public static void main(String[] args) throws Exception{
        int[][] A = {{1,0,0,1}};
        int[][] B = {{7,0,0}, {0,0,0}, {0,0,1}, {0,0,1}};
        int[][] C = new SparseMatrixMultiplication().multiply(A, B);
    }

    public int[][] multiply(int[][] A, int[][] B) {
        boolean[] AH = new boolean[A.length]; // Metadata for matrix A
        boolean[] BH = new boolean[B[0].length]; // Metadata for matrix A
        for(int i = 0; i < A.length; i ++){
            for(int j = 0; j < A[0].length; j ++){
                if(A[i][j] != 0){
                    AH[i] = true;
                    break;
                }
            }
        }

        for(int i = 0; i < B[0].length; i ++){
            for(int j = 0; j < B.length; j ++){
                if(B[j][i] != 0){
                    BH[i] = true;
                    break;
                }
            }
        }

        int[][] C = new int[A.length][B[0].length];
        for(int i = 0; i < C.length; i ++){
            if(AH[i]){
                for(int j = 0; j < C[0].length; j++){
                    if(BH[j]){
                        int sum = 0;
                        for(int k = 0; k < A[0].length; k++){
                            sum += A[i][k] * B[k][j];
                        }
                        C[i][j] = sum;
                    }
                }
            }
        }
        return C;
    }
}