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265 | #include <stdio.h>
#include <stdlib.h>
#define N 512 //定义矩阵的大小（行数），默认参与运算的矩阵为方阵
void plus(int size, int **A, int **B, int **C) { //计算 A+B->C
int i, j;
for (i = 0; i < size; i++) {
for (j = 0; j < size; j++) {
C[i][j] = A[i][j] + B[i][j];
}
}
}
void minus(int size, int **A, int **B, int **C) { //计算 A-B->C
int i, j;
for (i = 0; i < size; i++) {
for (j = 0; j < size; j++) {
C[i][j] = A[i][j] - B[i][j];
}
}
}
void multiply(int size, int **A, int **B, int **C) { //常规算法计算 A*B->C
int i, j, k;
for (i = 0; i < size; i++) {
for (j = 0; j < size; j++) {
C[i][j] = 0;
for (k = 0; k < size; k++) {
C[i][j] = C[i][j] + A[i][k]*B[k][j];
}
}
}
}
void strassen(int size, int **A, int **B, int **C) { //strassen算法计算 A*B->C
int half = size / 2;
if (size == 2) {
multiply(size, A, B, C); //当矩阵阶数为 2 时，达到递归边界，直接按常规算法计算
}
else {
int **A11, **A12, **A21, **A22; //Divide matrix A into 4 sub-matrices
int **B11, **B12, **B21, **B22; //Divide matrix B into 4 sub-matrices
int **C11, **C12, **C21, **C22; //Divide matrix C into 4 sub-matrices
int **AA, **BB; //AA记录矩阵A的子矩阵运算的中间结果，BB记录矩阵B的子矩阵运算的中间结果
int **P1, **P2, **P3, **P4, **P5, **P6, **P7;
//为上述矩阵开空间
A11 = (int**)malloc(sizeof(int*) * half);
A12 = (int**)malloc(sizeof(int*) * half);
A21 = (int**)malloc(sizeof(int*) * half);
A22 = (int**)malloc(sizeof(int*) * half);
B11 = (int**)malloc(sizeof(int*) * half);
B12 = (int**)malloc(sizeof(int*) * half);
B21 = (int**)malloc(sizeof(int*) * half);
B22 = (int**)malloc(sizeof(int*) * half);
C11 = (int**)malloc(sizeof(int*) * half);
C12 = (int**)malloc(sizeof(int*) * half);
C21 = (int**)malloc(sizeof(int*) * half);
C22 = (int**)malloc(sizeof(int*) * half);
AA = (int**)malloc(sizeof(int*) * half);
BB = (int**)malloc(sizeof(int*) * half);
P1 = (int**)malloc(sizeof(int*) * half);
P2 = (int**)malloc(sizeof(int*) * half);
P3 = (int**)malloc(sizeof(int*) * half);
P4 = (int**)malloc(sizeof(int*) * half);
P5 = (int**)malloc(sizeof(int*) * half);
P6 = (int**)malloc(sizeof(int*) * half);
P7 = (int**)malloc(sizeof(int*) * half);
int i, j;
for (i = 0; i < half; i++) {
A11[i] = (int*)malloc(sizeof(int) * half);
A12[i] = (int*)malloc(sizeof(int) * half);
A21[i] = (int*)malloc(sizeof(int) * half);
A22[i] = (int*)malloc(sizeof(int) * half);
B11[i] = (int*)malloc(sizeof(int) * half);
B12[i] = (int*)malloc(sizeof(int) * half);
B21[i] = (int*)malloc(sizeof(int) * half);
B22[i] = (int*)malloc(sizeof(int) * half);
C11[i] = (int*)malloc(sizeof(int) * half);
C12[i] = (int*)malloc(sizeof(int) * half);
C21[i] = (int*)malloc(sizeof(int) * half);
C22[i] = (int*)malloc(sizeof(int) * half);
AA[i] = (int*)malloc(sizeof(int) * half);
BB[i] = (int*)malloc(sizeof(int) * half);
P1[i] = (int*)malloc(sizeof(int) * half);
P2[i] = (int*)malloc(sizeof(int) * half);
P3[i] = (int*)malloc(sizeof(int) * half);
P4[i] = (int*)malloc(sizeof(int) * half);
P5[i] = (int*)malloc(sizeof(int) * half);
P6[i] = (int*)malloc(sizeof(int) * half);
P7[i] = (int*)malloc(sizeof(int) * half);
}
//将 A， B矩阵填入各自的分块矩阵
for (i = 0; i < half; i++) {
for (j = 0; j < half; j++) {
A11[i][j] = A[i][j];
A12[i][j] = A[i][j + half];
A21[i][j] = A[i + half][j];
A22[i][j] = A[i + half][j + half];
B11[i][j] = B[i][j];
B12[i][j] = B[i][j + half];
B21[i][j] = B[i + half][j];
B22[i][j] = B[i + half][j + half];
}
}
//计算开始
minus(half, B12, B22, BB); //Calculating P1 = A11 * (B12 - B22)
strassen(half, A11, BB, P1);
plus(half, A11, A12, AA); //Calculating P2 = (A11 + A12) * B22
strassen(half, AA, B22, P2);
plus(half, A21, A22, AA); //Calculating P3 = (A21 + A22) * B11
strassen(half, AA, B11, P3);
minus(half, B21, B11, BB); //Calculating P4 = A22 * (B21 - B11)
strassen(half, A22, BB, P4);
plus(half, A11, A22, AA); //Calculating P5 = (A11 + A22) * (B11 + B22)
plus(half, B11, B22, BB);
strassen(half, AA, BB, P5);
minus(half, A12, A22, AA); //Calculating P6 = (A12 - A22) * (B21 + B22)
plus(half, B21, B22, BB);
strassen(half, AA, BB, P6);
minus(half, A11, A21, AA); //Calculating P7 = (A11 - A21) * (B11 + B12)
plus(half, B11, B12, BB);
strassen(half, AA, BB, P7);
plus(half, P5, P4, C11); //Calculating C11 = P5 + P4 - P2 + P6
minus(half, C11, P2, C11);
plus(half, C11, P6, C11);
plus(half, P1, P2, C12); //Calculating C12 = P1 + P2
plus(half, P3, P4, C21); //Calculating C21 = P3 + P4
plus(half, P5, P1, C22); //Calculating C22 = P5 + P1 - P3 - P7
minus(half, C22, P3, C22);
minus(half, C22, P7, C22);
//将矩阵C的四个分块矩阵合并填入C中
for (i = 0; i < half; i++) {
for (j = 0; j < half; j++) {
C[i][j] = C11[i][j];
C[i][j + half] = C12[i][j];
C[i + half][j] = C21[i][j];
C[i + half][j + half] = C22[i][j];
}
}
//释放空间
for (i = 0; i < half; 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(P1[i]);
free(P2[i]);
free(P3[i]);
free(P4[i]);
free(P5[i]);
free(P6[i]);
free(P7[i]);
free(AA[i]);
free(BB[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(P1);
free(P2);
free(P3);
free(P4);
free(P5);
free(P6);
free(P7);
free(AA);
free(BB);
}
}
int main() {
int **A = (int**)malloc(sizeof(int*) * N);
int **B = (int**)malloc(sizeof(int*) * N);
int **C = (int**)malloc(sizeof(int*) * N);
int i, j;
for (i = 0; i < N; i++) {
A[i] = (int*)malloc(sizeof(int) * N);
B[i] = (int*)malloc(sizeof(int) * N);
C[i] = (int*)malloc(sizeof(int) * N);
}
//从文件中读取矩阵A
FILE *fa;
fa = fopen("la.txt", "r");
if (fa == NULL) {
printf("Cannot get matrix A!\n");
exit(0);
}
else {
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
fscanf(fa, "%d", &A[i][j]);
}
}
}
fclose(fa);
//从文件中读取矩阵B
FILE *fb;
fb = fopen("lb.txt", "r");
if (fb == NULL) {
printf("Cannot get matrix B!\n");
exit(0);
}
else {
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
fscanf(fb, "%d", &B[i][j]);
}
}
}
fclose(fb);
strassen(N, A, B, C); //strassen算法计算 A*B->C
//打印结果到屏幕的同时，格式化输出到文件
FILE *fc = fopen("lc.txt", "w");
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
printf("%d ", C[i][j]);
if (j != N - 1) {
fprintf(fc, "%d\t", C[i][j]);
}
else {
fprintf(fc, "%d\n", C[i][j]);
}
}
printf("\n");
}
return 0;
}
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