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I need to write a recursive method that multiplies 2 square matrices (size n-by-n). It needs to run in theta(N^3) time but it's not Strassen's algorithm. I've written a method but I am getting a stack overflow. 

Matrix A is       Matrix B is
1 2 1 0           3 2 3 0
2 3 2 0           2 1 2 0
1 2 1 0           3 2 3 0

The two matrices are both int[][]. here is the code I have written:

public int[][] ncubed(int [][]A, int [][]B){
    int w = A.length;
    int [][] C = new int[w][w];
    if (w==1){ 
        C[0][0] = A[0][0] * B[0][0];
    }
    else{
    int [][]A1 = partition(1,A);
    int [][]A2 = partition(2,A);
    int [][]A3 = partition(3,A);
    int [][]A4 = partition(4,A);
    int [][]B1 = partition(1,B);
    int [][]B2 = partition(2,B);
    int [][]B3 = partition(3,B);
    int [][]B4 = partition(4,B);
    int [][]C1 = partition(1,C);
    int [][]C2 = partition(2,C);
    int [][]C3 = partition(3,C);
    int [][]C4 = partition(4,C);

    C1 = add(ncubed(A1,B1),ncubed(A2,B3));
    C2 = add(ncubed(A1,B2),ncubed(A2,B4));
    C3 = add(ncubed(A3,B1),ncubed(A4,B3));
    C4 = add(ncubed(A3,B2),ncubed(A4,B4));

    join(C1, C, 0 , 0);
    join(C2, C, w/2 , 0);
    join(C3, C, 0, w/2);
    join(C4, C, w/2, w/2);

    }
    return C;
}

public int [][] partition(int quadrant, int[][] array){
    int n = array.length;
    int[][] Q = new int[array.length][array.length];
    if(quadrant>4 || quadrant<1) return null;
    switch(quadrant){
    case(1): 
        for(int i = 0; i<(n/2); i++){
            for(int j = 0; j<(n/2); j++){
                Q[i][j] = array[i][j];
            }
        }
        break;
    case(2):
        for(int i = n/2; i<n; i++){
            for(int j = 0; j<(n/2); j++){
                Q[i][j] = array[i][j];
            }
        }
        break;
    case(3):
        for(int i = 0; i<(n/2); i++){
            for(int j = (n/2); j<n; j++){
                Q[i][j] = array[i][j];
            }
        }
        break;
    case(4):
        for(int i = (n/2); i<n; i++){
            for(int j = (n/2); j<n; j++){
                Q[i][j] = array[i][j];
            }
        }
        break;
    }
    return Q;
}

The methods add and join work fine because I've tested them so it's not in that part. I just can't figure out my problem in the actual ncubed method(the matrix multiply method). If anyone is able to help me understand something I'm doing incorrectly or show me another way to do this with the specifications stated at the top, that would be awesome. Thanks for any help.

Don Roby
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EthanSchatz
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    This has got to be one of the least naturally recursive problems I've seen. The best I can come up with treats the top row of the matrix as a row vector, multiplies, then does a recursive call on the remaining rows, but that might as well be iterative. – David Ehrmann Jun 03 '14 at 01:03
  • Have you implement Strassen? Will you game n cube by not doing the trick? – Mingtao Zhang Jun 03 '14 at 01:47
  • The specifications of what I have to do is do an N cubed method that is NOT strassen. I've already implemented strassen. – EthanSchatz Jun 03 '14 at 01:51

1 Answers1

0

The naive method will give you theta(n^3) time -- have you checked out something simpler?

Failing that, have you looked at these similar questions?

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Patrick Collins
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  • I have to write it recursively. I have looked at that triple for loop and I am not allowed to use that. I also have seen those other 2 questions but they were not exactly answered. The one that shows the picture with the text from the book that you linked to the word "these" is the same method I need to write and the same book. But the person who answered it basically wrote the pseudo-code again, which I understand. And I have tried writing it into code now and that's what I posted above. :/ – EthanSchatz Jun 03 '14 at 01:08