版权声明:假装有个原创声明……虽然少许博文不属于完全原创,但也是自己辛辛苦苦总结的,转载请注明出处,感谢! https://blog.csdn.net/m0_37454852/article/details/86593071
1034 有理数四则运算 (20 分)
本题要求编写程序,计算 2 个有理数的和、差、积、商。
输入格式:
输入在一行中按照 a1/b1 a2/b2 的格式给出两个分数形式的有理数,其中分子和分母全是整型范围内的整数,负号只可能出现在分子前,分母不为 0。
输出格式:
分别在 4 行中按照 有理数1 运算符 有理数2 = 结果 的格式顺序输出 2 个有理数的和、差、积、商。注意输出的每个有理数必须是该有理数的最简形式 k a/b,其中 k 是整数部分,a/b 是最简分数部分;若为负数,则须加括号;若除法分母为 0,则输出 Inf。题目保证正确的输出中没有超过整型范围的整数。
输入样例 1:
2/3 -4/2
输出样例 1:
2/3 + (-2) = (-1 1/3)
2/3 - (-2) = 2 2/3
2/3 * (-2) = (-1 1/3)
2/3 / (-2) = (-1/3)
输入样例 2:
5/3 0/6
输出样例 2:
1 2/3 + 0 = 1 2/3
1 2/3 - 0 = 1 2/3
1 2/3 * 0 = 0
1 2/3 / 0 = Inf
using namespace std;
#include<algorithm>
#include<iostream>
#include<cstdio>
typedef struct Fraction//分数结构体
{
long long int up, down;//分子分母
}Fraction;
Fraction A, B;
long long int gcd(long long int a, long long int b)//求最大公约数
{
if(!b) return a;
return gcd(b, a%b);
}
Fraction reduction(Fraction X)//化简
{
if(X.down < 0) X.up = -X.up, X.down = -X.down;
if(!X.up) X.down = 1;
else
{
long long int d = gcd(abs(X.up), abs(X.down));
X.up /= d, X.down /= d;
}
return X;
}
void print_X(Fraction X)//打印某有理数
{
X = reduction(X);
if(!X.up) printf("0");
else if(X.down == 1)
{
if(X.up < 0) printf("(%lld)", X.up);
else printf("%lld", X.up);
}
else if(abs(X.up) > X.down)//假分数
{
if(X.up < 0)
{
printf("(%lld %lld/%lld)", X.up/X.down, abs(X.up%X.down), X.down);
}
else
{
printf("%lld %lld/%lld", X.up/X.down, X.up%X.down, X.down);
}
}
else
{
if(X.up < 0) printf("(%lld/%lld)", X.up, X.down);
else printf("%lld/%lld", X.up, X.down);
}
}
void print(Fraction A, char ch, Fraction B)//打印有理数1 运算符 有理数2 =
{
print_X(A);
printf(" %c ", ch);
print_X(B);
printf(" = ");
}
void print_result(Fraction R)//打印运算结果和回车
{
print_X(R);
printf("\n");
}
Fraction ADD(Fraction A, Fraction B)//加减乘除
{
Fraction result;
result.down = A.down*B.down;
result.up = A.up*B.down + A.down*B.up;
return result;
}
Fraction MINUS(Fraction A, Fraction B)
{
Fraction result;
result.down = A.down*B.down;
result.up = A.up*B.down - A.down*B.up;
return result;
}
Fraction MULTIPLY(Fraction A, Fraction B)
{
Fraction result;
result.down = A.down*B.down;
result.up = A.up*B.up;
return result;
}
Fraction DIVIDE(Fraction A, Fraction B)
{
Fraction result;
result.down = A.down*B.up;
result.up = A.up*B.down;
return result;
}
int main()
{
scanf("%lld/%lld %lld/%lld", &A.up, &A.down, &B.up, &B.down);
print(A, '+', B);
print_result(ADD(A, B));
print(A, '-', B);
print_result(MINUS(A, B));
print(A, '*', B);
print_result(MULTIPLY(A, B));
print(A, '/', B);
if(!reduction(B).up) printf("Inf\n");//除数为0单独考虑
else print_result(DIVIDE(A, B));
return 0;
}