suanfa/public/c/ch2/juzhen/juzhennew.c

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

#define SIZE 4 // 矩阵的大小

// 检查一个数是否是2的幂次方
bool isPowerOfTwo(int num) {
    return (num & (num - 1)) == 0;
}

// 矩阵加法
void add(int* a, int* b, int* c, int length) {
    for (int i = 0; i < length * length; i++) {
        c[i] = a[i] + b[i];
    }
}

// 获取结果矩阵
void getResult(int* a, int* b, int* result) {
    int p1 = a[0] * (b[1] - b[3]);
    int p2 = (a[0] + a[1]) * b[3];
    int p3 = (a[2] + a[3]) * b[0];
    int p4 = a[3] * (b[2] - b[0]);
    int p5 = (a[0] + a[3]) * (b[0] + b[3]);
    int p6 = (a[1] - a[3]) * (b[2] + b[3]);
    int p7 = (a[0] - a[2]) * (b[0] + b[1]);

    result[0] = p5 + p4 - p2 + p6;
    result[1] = p1 + p2;
    result[2] = p3 + p4;
    result[3] = p5 + p1 - p3 - p7;
}

// Strassen 矩阵乘法
void sMM(int* a, int* b, int* result, int length) {
    if (length == 2) {
        getResult(a, b, result);
    } else {
        int tlength = length / 2;
        int* aa = (int*)malloc(tlength * tlength * sizeof(int));
        int* ab = (int*)malloc(tlength * tlength * sizeof(int));
        int* ac = (int*)malloc(tlength * tlength * sizeof(int));
        int* ad = (int*)malloc(tlength * tlength * sizeof(int));
        int* ba = (int*)malloc(tlength * tlength * sizeof(int));
        int* bb = (int*)malloc(tlength * tlength * sizeof(int));
        int* bc = (int*)malloc(tlength * tlength * sizeof(int));
        int* bd = (int*)malloc(tlength * tlength * sizeof(int));
        int* t1 = (int*)malloc(tlength * tlength * sizeof(int));
        int* t2 = (int*)malloc(tlength * tlength * sizeof(int));
        int* t3 = (int*)malloc(tlength * tlength * sizeof(int));
        int* t4 = (int*)malloc(tlength * tlength * sizeof(int));
        int* temp = (int*)malloc(length * length * sizeof(int));

        for (int i = 0; i < length; i++) {
            for (int j = 0; j < length; j++) {
                if (i < tlength) {
                    if (j < tlength) {
                        aa[i * tlength + j] = a[i * length + j];
                        ba[i * tlength + j] = b[i * length + j];
                    } else {
                        ab[i * tlength + (j - tlength)] = a[i * length + j];
                        bb[i * tlength + (j - tlength)] = b[i * length + j];
                    }
                } else {
                    if (j < tlength) {
                        ac[(i - tlength) * tlength + j] = a[i * length + j];
                        bc[(i - tlength) * tlength + j] = b[i * length + j];
                    } else {
                        ad[(i - tlength) * tlength + (j - tlength)] = a[i * length + j];
                        bd[(i - tlength) * tlength + (j - tlength)] = b[i * length + j];
                    }
                }
            }
        }

        int* t1_ = (int*)malloc(tlength * tlength * sizeof(int));
        int* t2_ = (int*)malloc(tlength * tlength * sizeof(int));
        int* t3_ = (int*)malloc(tlength * tlength * sizeof(int));
        int* t4_ = (int*)malloc(tlength * tlength * sizeof(int));
        
        sMM(aa, ba, t1_, tlength);
        sMM(ab, bc, t2_, tlength);
        add(t1_, t2_, t1_, tlength);
        
        sMM(aa, bb, t2_, tlength);
        sMM(ab, bd, t3_, tlength);
        add(t2_, t3_, t2_, tlength);
        
        sMM(ac, ba, t3_, tlength);
        sMM(ad, bc, t4_, tlength);
        add(t3_, t4_, t3_, tlength);
        
        sMM(ac, bb, t4_, tlength);
        sMM(ad, bd, t1_, tlength);
        add(t4_, t1_, t4_, tlength);
        
        for (int i = 0; i < length; i++) {
            for (int j = 0; j < length; j++) {
                if (i < tlength) {
                    if (j < tlength)
                        result[i * length + j] = t1[i * tlength + j];
                    else
                        result[i * length + j] = t2[i * tlength + (j - tlength)];
                } else {
                    if (j < tlength)
                        result[i * length + j] = t3[(i - tlength) * tlength + j];
                    else
                        result[i * length + j] = t4[(i - tlength) * tlength + (j - tlength)];
                }
            }
        }

        free(aa);
        free(ab);
        free(ac);
        free(ad);
        free(ba);
        free(bb);
        free(bc);
        free(bd);
        free(t1_);
        free(t2_);
        free(t3_);
        free(t4_);
        free(temp);
    }
}

int main() {
    int a[SIZE * SIZE] = { 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4 };
    int b[SIZE * SIZE] = { 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4 };
    int c[SIZE * SIZE];
    
    sMM(a, b, c, SIZE);
    
    for (int i = 0; i < SIZE * SIZE; i++) {
        printf("%d ", c[i]);
        if ((i + 1) % SIZE == 0) // 换行
            printf("\n");
    }
    
    printf("%d\n", isPowerOfTwo(1));
    printf("%d\n", isPowerOfTwo(2));
    printf("%d\n", isPowerOfTwo(4));
    printf("%d\n", isPowerOfTwo(6));
    printf("%d\n", isPowerOfTwo(443));

    return 0;
}