用C++编写strassen矩阵乘法分治法

以下是使用C语言编写的Strassen矩阵乘法分治法的示例代码：

#include <stdio.h>
#include <stdlib.h>

void matrix_add(int n, int **a, int **b, int **c) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            c[i][j] = a[i][j] + b[i][j];
        }
    }
}

void matrix_sub(int n, int **a, int **b, int **c) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            c[i][j] = a[i][j] - b[i][j];
        }
    }
}

void matrix_multiply_simple(int n, int **a, int **b, int **c) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            c[i][j] = 0;
            for (int k = 0; k < n; k++) {
                c[i][j] += a[i][k] * b[k][j];
            }
        }
    }
}

void matrix_multiply_strassen(int n, int **a, int **b, int **c) {
    if (n <= 64) {  // 使用普通矩阵乘法
        matrix_multiply_simple(n, a, b, c);
        return;
    }

    int **a11 = (int **) malloc(n / 2 * sizeof(int *));
    int **a12 = (int **) malloc(n / 2 * sizeof(int *));
    int **a21 = (int **) malloc(n / 2 * sizeof(int *));
    int **a22 = (int **) malloc(n / 2 * sizeof(int *));
    int **b11 = (int **) malloc(n / 2 * sizeof(int *));
    int **b12 = (int **) malloc(n / 2 * sizeof(int *));
    int **b21 = (int **) malloc(n / 2 * sizeof(int *));
    int **b22 = (int **) malloc(n / 2 * sizeof(int *));
    int **c11 = (int **) malloc(n / 2 * sizeof(int *));
    int **c12 = (int **) malloc(n / 2 * sizeof(int *));
    int **c21 = (int **) malloc(n / 2 * sizeof(int *));
    int **c22 = (int **) malloc(n / 2 * sizeof(int *));
    int **m1 = (int **) malloc(n / 2 * sizeof(int *));
    int **m2 = (int **) malloc(n / 2 * sizeof(int *));
    int **m3 = (int **) malloc(n / 2 * sizeof(int *));
    int **m4 = (int **) malloc(n / 2 * sizeof(int *));
    int **m5 = (int **) malloc(n / 2 * sizeof(int *));
    int **m6 = (int **) malloc(n / 2 * sizeof(int *));
    int **m7 = (int **) malloc(n / 2 * sizeof(int *));

    for (int i = 0; i < n / 2; i++) {
        a11[i] = (int *) malloc(n / 2 * sizeof(int));
        a12[i] = (int *) malloc(n / 2 * sizeof(int));
        a21[i] = (int *) malloc(n / 2 * sizeof(int));
        a22[i] = (int *) malloc(n / 2 * sizeof(int));
        b11[i] = (int *) malloc(n / 2 * sizeof(int));
        b12[i] = (int *) malloc(n / 2 * sizeof(int));
        b21[i] = (int *) malloc(n / 2 * sizeof(int));
        b22[i] = (int *) malloc(n / 2 * sizeof(int));
        c11[i] = (int *) malloc(n / 2 * sizeof(int));
        c12[i] = (int *) malloc(n / 2 * sizeof(int));
        c21[i] = (int *) malloc(n / 2 * sizeof(int));
        c22[i] = (int *) malloc(n / 2 * sizeof(int));
        m1[i] = (int *) malloc(n / 2 * sizeof(int));
        m2[i] = (int *) malloc(n / 2 * sizeof(int));
        m3[i] = (int *) malloc(n / 2 * sizeof(int));
        m4[i] = (int *) malloc(n / 2 * sizeof(int));
        m5[i] = (int *) malloc(n / 2 * sizeof(int));
        m6[i] = (int *) malloc(n / 2 * sizeof(int));
        m7[i] = (int *) malloc(n / 2 * sizeof(int));
    }

    // 将矩阵 a 和 b 拆分成四个子矩阵
    for (int i = 0; i < n / 2; i++) {
        for (int j = 0; j < n / 2; j++) {
            a11[i][j] = a[i][j];
            a12[i][j] = a[i][j + n / 2];
            a21[i][j] = a[i + n / 2][j];
            a22[i][j] = a[i + n / 2][j + n / 2];
            b11[i][j] = b[i][j];
            b12[i][j] = b[i][j + n / 2];
            b21[i][j] = b[i + n / 2][j];
            b22[i][j] = b[i + n / 2][j + n / 2];
        }
    }

    // 计算七个子矩阵的乘积
    matrix_add(n / 2, a11, a22, m1);
    matrix_add(n / 2, b11, b22, m2);
    matrix_multiply_strassen(n / 2, m1, m2, c11);
    matrix_add(n / 2, a21, a22, m1);
    matrix_multiply_strassen(n / 2, m1, b11, c21);
    matrix_sub(n / 2, b12, b22, m1);
    matrix_multiply_strassen(n / 2, a11, m1, c12);
    matrix_sub(n / 2, b21, b11, m1);
    matrix_multiply_strassen(n / 2, a22, m1, c22);
    matrix_add(n / 2, a11, a12, m1);
    matrix_multiply_strassen(n / 2, m1, b22, m2);
    matrix_sub(n / 2, c11, c12, m3);
    matrix_add(n / 2, c21, m2, m4);
    matrix_add(n / 2, c12, m2, m5);
    matrix_sub(n / 2, a21, a11, m1);
    matrix_add(n / 2, b11, b12, m2);
    matrix_multiply_strassen(n / 2, m1, m2, m6);
    matrix_sub(n / 2, c22, m5, m7);

    // 计算结果矩阵
    matrix_add(n / 2, m3, m5, c11);
    matrix_add(n / 2, m4, m6, c12);
    matrix_add(n / 2, m1, m5, c21);
    matrix_add(n / 2, m2, m7, c22);
    for (int i = 0; i < n / 2; i++) {
        for (int j = 0; j < n / 2; j++) {
            c[i][j] = c11[i][j];
            c[i][j + n / 2] = c12[i][j];
            c[i + n / 2][j] = c21[i][j];
            c[i + n / 2][j + n / 2] = c22[i][j];
        }
    }

    // 释放内存
    for (int i = 0; i < n / 2; i++) {
        free(a11[i]);
        free(a12[i]);
        free(a21[i]);
        free(a22[i]);
        free(b11[i]);
        free(b12[i]);
        free(b21[i]);
        free(b22[i]);
        free(c11[i]);
        free(c12[i]);
        free(c21[i]);
        free(c22[i]);
        free(m1[i]);
        free(m2[i]);
        free(m3[i]);
        free(m4[i]);
        free(m5[i]);
        free(m6[i]);
        free(m7[i]);
    }
    free(a11);
    free(a12);
    free(a21);
    free(a22);
    free(b11);
    free(b12);
    free(b21);
    free(b22);
    free(c11);
    free(c12);
    free(c21);
    free(c22);
    free(m1);
    free(m2);
    free(m3);
    free(m4);
    free(m5);
    free(m6);
    free(m7);
}

int main() {
    int n = 4;
    int **a = (int **) malloc(n * sizeof(int *));
    int **b = (int **) malloc(n * sizeof(int *));
    int **c = (int **) malloc(n * sizeof(int *));
    for (int i = 0; i < n; i++) {
        a[i] = (int *) malloc(n * sizeof(int));
        b[i] = (int *) malloc(n * sizeof(int));
        c[i] = (int *) malloc(n * sizeof(int));
    }
    a[0][0] = 1;
    a[0][1] = 2;
    a[0][2] = 3;
    a[0][3] = 4;
    a[1][0] = 5;
    a[1][1] = 6;
    a[1][2] = 7;
    a[1][3] = 8;
    a[2][0] = 9;
    a[2][1] = 10;
    a[2][2] = 11;
    a[2][3] = 12;
    a[3][0] = 13;
    a[3][1] = 14;
    a[3][2] = 15;
    a[3][3] = 16;
    b[0][0] = 17;
    b[0][1] = 18;
    b[0][2] = 19;
    b[0][3] = 20;
    b[1][0] = 21;
    b[1][1] = 22;
    b[1][2] = 23;
    b[1][3] = 24;
    b[2][0] = 25;
    b[2][1] = 26;
    b[2][2] = 27;
    b[2][3] = 28;
    b[3][0] = 29;
    b[3][1] = 30;
    b[3][2] = 31;
    b[3][3] = 32;
    matrix_multiply_strassen(n, a, b, c);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            printf("%d ", c[i][j]);
        }
        printf("\n");
    }
    for (int i = 0; i < n; i++) {
        free(a[i]);
        free(b[i]);
        free(c[i]);
    }
    free(a);
    free(b);
    free(c);
    return 0;
}

在此示例代码中，`matrix_add()`和`matrix_sub()`函数分别实现矩阵加法和减法，`matrix_multiply_simple()`函数实现普通的矩阵乘法，`matrix_multiply_strassen()`函数实现Strassen矩阵乘法分治法。

在`matrix_multiply_strassen()`函数中，当矩阵维度小于等于64时，使用普通矩阵乘法，否则将矩阵拆分成四个子矩阵，分别计算七个子矩阵的乘积，然后计算结果矩阵。

在`main()`函数中，我们初始化两个矩阵`a`和`b`，然后调用`matrix_multiply_strassen()`函数计算它们的乘积。最后，我们输出结果矩阵并释放内存。

注意，此示例代码仅适用于矩阵维度为2的幂次方的情况。如果矩阵维度不是2的幂次方，则需要用0填充矩阵的右下角，使其成为2的幂次方。