斯特拉森的营业额蛮力

Question

作为一项关于休息的家庭作业，我们的教授要求我们找到斯特拉森的算法效率低于蛮力的地步（具体来说，在我蛮力之前，我应该在这台机器上进行多少次递归？ ）

我是Java，并且真的很难让它恢复到暴力。我有一个跑步课，一个蛮力课，一个叫Strassen的课，还有一个Strassen本身的课。到目前为止，我只会把斯特拉森的课程搞定。我问用户他们想要做多少次递归，然后我把它作为参数传递给Strassen's。这个想法是，当深度＆＃39;深度＆＃39;它变得大于指定的递归数，它调用强力方法来完成。我感到完全迷失了，可能没有正确接近，但我们没有得到非常明确的指示，而且我一直在尝试不同的方法，但无济于事。

public class strassens
{
    private int totalCalls;
    private int runtime;

    public strassens(int recursions, int runtime) 
    {
        totalCalls = recursions;
        this.runtime = runtime;
    }

    public int[][] strassen(int[][] A, int[][] B, int depth)
    {
        int n = A.length;
        if(depth > totalCalls)
        {
            int[][] complete = new int[A.length][B.length];
            complete = bruteForce.brute(n, A, B, runtime);
            return complete;
        }
        int [][] result = new int[n][n];
        if((n%2 != 0 ) && (n != 1))
        {
            int[][] a1, b1, c1;
            int n1 = n+1;
            a1 = new int[n1][n1];
            b1 = new int[n1][n1];
            c1 = new int[n1][n1];
            for(int i=0; i<n; i++)
                for(int j=0; j<n; j++)
                {
                    a1[i][j] = A[i][j];
                    b1[i][j] = B[i][j];
                }
            c1 = strassen(a1, b1, depth++);
            for(int i=0; i<n; i++)
                for(int j=0; j<n; j++)
                    result[i][j] = c1[i][j];
            return result;
        }
        if(n == 1)
        {
            result[0][0] = A[0][0] * B[0][0];
        }
        else
        {
            int [][] A11 = new int[n/2][n/2];
            int [][] A12 = new int[n/2][n/2];
            int [][] A21 = new int[n/2][n/2];
            int [][] A22 = new int[n/2][n/2];
            int [][] B11 = new int[n/2][n/2];
            int [][] B12 = new int[n/2][n/2];
            int [][] B21 = new int[n/2][n/2];
            int [][] B22 = new int[n/2][n/2];
            divideArray(A, A11, 0 , 0);
            divideArray(A, A12, 0 , n/2);
            divideArray(A, A21, n/2, 0);
            divideArray(A, A22, n/2, n/2);
            divideArray(B, B11, 0 , 0);
            divideArray(B, B12, 0 , n/2);
            divideArray(B, B21, n/2, 0);
            divideArray(B, B22, n/2, n/2);
            int [][] P1 = strassen(addMatrices(A11, A22), addMatrices(B11, B22), depth);
            int [][] P2 = strassen(addMatrices(A21, A22), B11, depth);
            int [][] P3 = strassen(A11, subtractMatrices(B12, B22), depth);
            int [][] P4 = strassen(A22, subtractMatrices(B21, B11), depth);
            int [][] P5 = strassen(addMatrices(A11, A12), B22, depth);
            int [][] P6 = strassen(subtractMatrices(A21, A11), addMatrices(B11, B12), depth);
            int [][] P7 = strassen(subtractMatrices(A12, A22), addMatrices(B21, B22), depth);
            int [][] C11 = addMatrices(subtractMatrices(addMatrices(P1, P4), P5), P7);
            int [][] C12 = addMatrices(P3, P5);
            int [][] C21 = addMatrices(P2, P4);
            int [][] C22 = addMatrices(subtractMatrices(addMatrices(P1, P3), P2), P6);
            copySubArray(C11, result, 0 , 0);
            copySubArray(C12, result, 0 , n/2);
            copySubArray(C21, result, n/2, 0);
            copySubArray(C22, result, n/2, n/2);
        }
        return result;
    }

    public int [][] addMatrices(int [][] A, int [][] B)
    {
        int n = A.length;
        int [][] result = new int[n][n];
        for(int i=0; i<n; i++)
            for(int j=0; j<n; j++)
                result[i][j] = A[i][j] + B[i][j];
        return result;
    }

    public int [][] subtractMatrices(int [][] A, int [][] B)
    {
        int n = A.length;
        int [][] result = new int[n][n];
        for(int i=0; i<n; i++)
            for(int j=0; j<n; j++)
                result[i][j] = A[i][j] - B[i][j];
        return result;
    }

    public void divideArray(int[][] parent, int[][] child, int iB, int jB)
    {
        for(int i1 = 0, i2=iB; i1<child.length; i1++, i2++)
            for(int j1 = 0, j2=jB; j1<child.length; j1++, j2++)
            {
                child[i1][j1] = parent[i2][j2];
            }
    }

    public void copySubArray(int[][] child, int[][] parent, int iB, int jB)
    {
        for(int i1 = 0, i2=iB; i1<child.length; i1++, i2++)
            for(int j1 = 0, j2=jB; j1<child.length; j1++, j2++)
            {
                parent[i2][j2] = child[i1][j1];
            }
    }

    public static void printArray(int [][] array)
    {
        int n = array.length;
        System.out.println("Strassens: ");
        for(int i=0; i<n; i++)
        {
            for(int j=0; j<n; j++)
            {
                System.out.print(array[i][j] + " ");
            }
            System.out.println();
        }
    }
}