分治法 java_Java实现用传统分治法解决矩阵相乘问题

好的，下面是用传统分治法解决矩阵相乘问题的Java实现：

public class MatrixMultiplication {

    public static int[][] multiply(int[][] A, int[][] B) {
        int n = A.length;
        int[][] C = new int[n][n];
        if (n == 1) {
            C[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];

            // Divide A matrix into 4 sub-matrices
            divideMatrix(A, A11, 0 , 0);
            divideMatrix(A, A12, 0 , n/2);
            divideMatrix(A, A21, n/2, 0);
            divideMatrix(A, A22, n/2, n/2);
            // Divide B matrix into 4 sub-matrices
            divideMatrix(B, B11, 0 , 0);
            divideMatrix(B, B12, 0 , n/2);
            divideMatrix(B, B21, n/2, 0);
            divideMatrix(B, B22, n/2, n/2);

            // Recursively multiply sub-matrices
            int[][] C11 = addMatrix(multiply(A11,B11), multiply(A12,B21));
            int[][] C12 = addMatrix(multiply(A11,B12), multiply(A12,B22));
            int[][] C21 = addMatrix(multiply(A21,B11), multiply(A22,B21));
            int[][] C22 = addMatrix(multiply(A21,B12), multiply(A22,B22));

            // Combine sub-matrices into the result matrix
            combineMatrix(C11, C, 0 , 0);
            combineMatrix(C12, C, 0 , n/2);
            combineMatrix(C21, C, n/2, 0);
            combineMatrix(C22, C, n/2, n/2);
        }
        return C;
    }

    // Divide matrix into sub-matrices
    public static void divideMatrix(int[][] P, int[][] C, int iB, int jB) {
        for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++) {
            for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++) {
                C[i1][j1] = P[i2][j2];
            }
        }
    }

    // Combine sub-matrices into the result matrix
    public static void combineMatrix(int[][] C, int[][] P, int iB, int jB) {
        for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++) {
            for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++) {
                P[i2][j2] = C[i1][j1];
            }
        }
    }

    // Add two matrices
    public static int[][] addMatrix(int[][] A, int[][] B) {
        int n = A.length;
        int[][] C = new int[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = A[i][j] + B[i][j];
            }
        }
        return C;
    }

    public static void main(String[] args) {
        int[][] A = {{1, 2}, {3, 4}};
        int[][] B = {{5, 6}, {7, 8}};
        int[][] C = multiply(A, B);
        for (int i = 0; i < C.length; i++) {
            for (int j = 0; j < C.length; j++) {
                System.out.print(C[i][j] + " ");
            }
            System.out.println();
        }
    }
}

这个程序将两个n×n的矩阵相乘，其中n是2的幂。如果n等于1，则直接计算乘积。否则，将每个矩阵分成四个n/2×n/2的子矩阵，并递归地计算子矩阵的乘积。最后，将四个子矩阵的乘积组合成结果矩阵。