c语言编程实现模m同余的剩余类级Z/mZ的加法和乘法运算的完整算法

1. 定义结构体表示剩余类

typedef struct {
    int value; // 剩余类的值
    int mod; // 模数
} ResidueClass;

2. 实现加法运算

ResidueClass add(ResidueClass a, ResidueClass b) {
    if (a.mod != b.mod) {
        printf("Error: different modulus.\n");
        exit(1);
    }
    ResidueClass result;
    result.mod = a.mod;
    result.value = (a.value + b.value) % a.mod;
    return result;
}

3. 实现乘法运算

ResidueClass multiply(ResidueClass a, ResidueClass b) {
    if (a.mod != b.mod) {
        printf("Error: different modulus.\n");
        exit(1);
    }
    ResidueClass result;
    result.mod = a.mod;
    result.value = (a.value * b.value) % a.mod;
    return result;
}

4. 完整代码实现

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

typedef struct {
    int value; // 剩余类的值
    int mod; // 模数
} ResidueClass;

ResidueClass add(ResidueClass a, ResidueClass b) {
    if (a.mod != b.mod) {
        printf("Error: different modulus.\n");
        exit(1);
    }
    ResidueClass result;
    result.mod = a.mod;
    result.value = (a.value + b.value) % a.mod;
    return result;
}

ResidueClass multiply(ResidueClass a, ResidueClass b) {
    if (a.mod != b.mod) {
        printf("Error: different modulus.\n");
        exit(1);
    }
    ResidueClass result;
    result.mod = a.mod;
    result.value = (a.value * b.value) % a.mod;
    return result;
}

int main() {
    ResidueClass a = {2, 5};
    ResidueClass b = {3, 5};
    ResidueClass c = add(a, b);
    ResidueClass d = multiply(a, b);
    printf("a + b = %d (mod %d)\n", c.value, c.mod);
    printf("a * b = %d (mod %d)\n", d.value, d.mod);
    return 0;
}