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
很繁的一个题目，如果正常的计算要分很多类，用到很多if else,,,因为是分数，没有办法直接进行运算，所以想通分后进行运算，
//注：由于时间原因，代码还未完成，只实现了加法。
#include<iostream>
#include<cmath>
#include<string>
using namespace std;
//返回最大公约数。最小公倍数是a1*a2/最大公倍数
long long gcd(long long t1, long long t2) {
return t2 == 0 ? t1 : gcd(t2, t1 % t2);
};
void print_fs(int z, int fz, int fm);
void calcu(int afz0, int afm, int bfz0, int bfm, char ch);
int main()
{
int afz0, afm, bfz0, bfm;
char ch;
scanf_s("%d/%d %d/%d", &afz0, &afm, &bfz0, &bfm);
int az = afz0 / afm;
int afz = afz0 - az * afm;
int bz = bfz0 / bfm;
int bfz = bfz0 - bz * bfm;
print_fs(az, afz, afm);
cout << " + ";
print_fs(bz, bfz, bfm);
cout << " = ";
calcu(afz0, afm, bfz0, bfm, '+');
return 0;
}
void print_fs(int z, int fz,int fm) {
if (z > 0) {
if (fz > 0)
printf("%d %d/%d", z, fz ,fm);
else
printf("%d", z);
}
if (z < 0) {
if (fz > 0)
printf("(%d %d/%d)", z, fz, fm);
else
printf("(%d)", z);
}
if(z==0) {
if (fz > 0)
printf("%d/%d", fz, fm);
if(fz <0)
printf("(%d/%d)", fz, fm);
if(fz==0)
printf("0");
}
}
void calcu(int afz0, int afm, int bfz0, int bfm,char ch) {
int gfm = afm * bfm / gcd(afm, bfm); //公分母
int afz = afz0 * gfm / afm;
int bfz = bfz0 * gfm / bfm;
switch (ch)
{
case '+': {
int sum_fz = afz + bfz;
int sum_z = sum_fz / gfm;
int sum_fz1 = sum_fz -sum_z*gfm;
print_fs(sum_z, abs(sum_fz1/gcd(sum_fz1,gfm)),abs( gfm/ gcd(sum_fz1, gfm)));
}
default:
break;
}
}
//我一开始在print_fs用if else 还用错了，后来去掉了else
一开始写成
if(a>0)...
if(a<0)...
else...
开始脑子抽了 以为这个else 就是a==0的时候。 实际上else是和最近的if(a<0)配对，等价于if(a>=0)
下午回来后继续做，然后是部分通过。
以为是长度问题，把int改成long long，还是错误。
#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<cmath>
#include<string>
using namespace std;
//返回最大公约数。最小公倍数是a1*a2/最大公倍数
long long gcd(long long t1, long long t2) {
return t2 == 0 ? t1 : gcd(t2, t1 % t2);
};
void print_fs(long long z, long long fz, long long fm);
void calcu(long long afz0, long long afm, long long bfz0, long long bfm, char ch);
void print_calcu_result(long long az, long long afz, long long afm, long long bz, long long bfz, long long bfm, long long afz0, long long bfz0, char yunsuan);
int main()
{
long long afz0, afm, bfz0, bfm;
char ch;
scanf("%lld/%lld %lld/%lld", &afz0, &afm, &bfz0, &bfm);
long long az = afz0 / afm;
long long afz = afz0 - az * afm;
long long bz = bfz0 / bfm;
long long bfz = bfz0 - bz * bfm;
print_calcu_result(az, afz, afm, bz, bfz, bfm, afz0, bfz0, '+');
print_calcu_result(az, afz, afm, bz, bfz, bfm, afz0, bfz0, '-');
print_calcu_result(az, afz, afm, bz, bfz, bfm, afz0, bfz0, '*');
print_calcu_result(az, afz, afm, bz, bfz, bfm, afz0, bfz0, '/');
return 0;
}
void print_fs(long long z, long long fz,long long fm) {
if (z > 0) {
if (fz > 0)
printf("%lld %lld/%lld", z, fz ,fm);
if(fz ==0)
printf("%lld", z);
}
if (z < 0) {
if (fz > 0)
printf("(%lld %lld/%lld)", z, fz, abs(fm));
if(fz==0)
printf("(%lld)", z);
}
if(z==0) {
if (fz > 0 && fm>0)
printf("%lld/%lld", fz, fm);
if (fz > 0 && fm < 0)
printf("(%lld/%lld)", -fz, -fm);
if(fz <0)
printf("(%lld/%lld)", fz, (fm));
if(fz==0)
printf("0");
}
}
void calcu(long long afz0, long long afm, long long bfz0, long long bfm,char ch) {
long long gfm = afm * bfm / gcd(afm, bfm); //公分母
long long afz = afz0 * gfm / afm;
long long bfz = bfz0 * gfm / bfm;
switch (ch)
{
case '-': {
bfz *= -1;
}
case '+': {
long long sum_fz = afz + bfz;
long long sum_z = sum_fz / gfm;
long long sum_fz1 = sum_fz -sum_z*gfm;
print_fs(sum_z, (sum_fz1/gcd(sum_fz1,gfm)),( gfm/ gcd(sum_fz1, gfm)));
break;
}
case '/': {
if (bfz == 0) {
cout << "Inf";
break;
}
else {
long long t = bfz0;
bfz0 = bfm;
bfm = t;
}
}
case '*': {
long long ji_fz = afz0 * bfz0;
gfm = afm * bfm;
long long ji_z = ji_fz / gfm;
long long ji_fz1 = ji_fz - ji_z * gfm;
print_fs(ji_z, (ji_fz1 /(gcd(ji_fz1, gfm)) ),( (gfm /(gcd(ji_fz1, gfm))) ));
break;
}
default:
break;
}
}
void print_calcu_result(long long az,long long afz,long long afm,long long bz,long long bfz,long long bfm,long long afz0,long long bfz0,char yunsuan) {
print_fs(az, afz, afm);
cout << " "<<yunsuan<<" ";
print_fs(bz, bfz, bfm);
cout << " = ";
calcu(afz0, afm, bfz0, bfm, yunsuan);
cout << endl;
}
看着这么长，有有些乱，很难找错。
把分数做成了一个类，看起来结构就很比较清楚了。
然而还是有两处测试没有通过。
#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<cmath>
using namespace std;
int gcd(int t1, int t2) {
return t2 == 0 ? t1 : gcd(t2, t1 % t2);
}
class fenshu {
public:
int zhengshu;
int fenzi;
int zfenzi;
int fenmu;
public:
fenshu() :zhengshu(0), fenzi(0), zfenzi(0), fenmu(0) {}
fenshu(int qzheng, int qfenzi, int qfenmu,int qzfenzi=0) :zhengshu(qzheng), fenzi(qfenzi),
fenmu(qfenmu),zfenzi(qzfenzi) { }
//标准形式
void standard() {
zhengshu += fenzi / fenmu; //整数部分
zfenzi = fenzi - zhengshu * fenmu; //真分子
}
//输出标准形式
void print_fs();
fenshu operator+(fenshu b) {
int gfm = fenmu * b.fenmu / gcd(fenmu, b.fenmu); //公分母
int afz = fenzi * gfm / fenmu;
int bfz = b.fenzi * gfm / b.fenmu;
int sum_fz = afz + bfz;
int sum_z = sum_fz / gfm;
int sum_fz1 = sum_fz - sum_z * gfm;
return fenshu(sum_z, (sum_fz1 / gcd(sum_fz1, gfm)), (gfm / gcd(sum_fz1, gfm)), (sum_fz1 / gcd(sum_fz1, gfm)));
}
fenshu operator-(fenshu b) {
fenshu fub = fenshu(b.zhengshu, b.fenzi*-1, b.fenmu);
return (*this + fub);
}
fenshu operator*(fenshu b) {
int ji_fz = fenzi * b.fenzi;
int gfm = fenmu * b.fenmu;
int ji_z = ji_fz / gfm;
int ji_fz1 = ji_fz - ji_z * gfm;
return fenshu(ji_z, ji_fz1 / gcd(ji_fz1, gfm), gfm / gcd(ji_fz1, gfm), ji_fz1 / gcd(ji_fz1, gfm));
}
fenshu operator/(fenshu b) {
if (b.fenzi == 0) {
cout << "Inf";
return fenshu(1, -1, -1,-1);
}
else {
fenshu t = fenshu(b.zhengshu, b.fenmu, b.fenzi);
return (*this *t);
}
}
};
void fenshu::print_fs() {
if (zhengshu > 0) {
if (zfenzi > 0)
printf("%d %d/%d", zhengshu, zfenzi ,fenmu);
if(zfenzi ==0)
printf("%d", zhengshu);
}
if (zhengshu < 0) {
if (zfenzi > 0)
printf("(%d %d/%d)", zhengshu, zfenzi, abs(fenmu));
if(zfenzi==0)
printf("(%d)", zhengshu);
}
if(zhengshu==0) {
if (zfenzi > 0 && fenmu>0)
printf("%d/%d", zfenzi, fenmu);
if (zfenzi > 0 && fenmu < 0)
printf("(%d/%d)", -zfenzi, -fenmu);
if(zfenzi <0)
printf("(%d/%d)", zfenzi, (fenmu));
if(zfenzi==0)
printf("0");
}
}
int main()
{
fenshu a, b;
char ch;
scanf("%d/%d %d/%d", &a.fenzi, &a.fenmu, &b.fenzi, &b.fenmu);
a.standard();
b.standard();
a.print_fs(); cout << " + "; b.print_fs(); cout << " = "; (a + b).print_fs(); cout << endl;
a.print_fs(); cout << " - "; b.print_fs(); cout << " = "; (a - b).print_fs(); cout << endl;
a.print_fs(); cout << " * "; b.print_fs(); cout << " = "; (a * b).print_fs(); cout << endl;
a.print_fs(); cout << " / "; b.print_fs(); cout << " = "; (a / b).print_fs(); cout << endl;
return 0;
}
又改了两小时，然而还有两处没有通过，但是也找不出原因。
#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<cmath>
using namespace std;
int gcd(int t1, int t2) {
return t2 == 0 ? t1 : gcd(t2, t1 % t2);
}
class fenshu {
public:
int zhengshu;
int fenzi;
int zfenzi;
int fenmu;
public:
fenshu() :zhengshu(0), fenzi(0), zfenzi(0), fenmu(0) {}
fenshu(int qzheng, int qfenzi, int qfenmu,int qzfenzi=0) :zhengshu(qzheng), fenzi(qfenzi),
fenmu(qfenmu),zfenzi(qzfenzi) { }
//标准形式
fenshu standard() {
int gcdfz_fm = gcd(fenmu, fenzi);
if (gcdfz_fm != 0) {
fenzi /= gcdfz_fm;
fenmu /= gcdfz_fm;
}
zhengshu += fenzi / fenmu; //整数部分
zfenzi = fenzi - zhengshu * fenmu; //真分子
return fenshu(zhengshu, fenzi, fenmu, zfenzi);
}
//输出标准形式
void print_fs();
fenshu operator+(fenshu b) {
int r_fenzi = fenzi * b.fenmu + b.fenzi*fenmu;
int r_fenmu = fenmu * b.fenmu;
return fenshu(0,r_fenzi,r_fenmu,0);
}
fenshu operator-(fenshu b) {
b.fenzi *= -1;
return *this + b;
}
fenshu operator*(fenshu b) {
int ji_fz = fenzi * b.fenzi;
int gfm = fenmu * b.fenmu;
return fenshu(0, ji_fz, gfm, 0);
}
fenshu operator/(fenshu b) {
if (b.fenzi == 0) {
cout << "Inf";
return fenshu(1, -1, -1,-1);
}
else {
fenshu t = fenshu(b.zhengshu, b.fenmu, b.fenzi);
return (*this *t);
}
}
};
void fenshu::print_fs() {
if (zhengshu > 0) {
if (zfenzi > 0)
printf("%d %d/%d", zhengshu, zfenzi ,fenmu);
if(zfenzi ==0)
printf("%d", zhengshu);
}
if (zhengshu < 0) {
if (zfenzi > 0)
printf("(%d %d/%d)", zhengshu, zfenzi, fenmu);
if(zfenzi==0)
printf("(%d)", zhengshu);
if (zfenzi < 0)
printf("(%d %d/%d)", zhengshu, abs(zfenzi), fenmu);
}
if(zhengshu==0) {
if (zfenzi > 0 )
printf("%d/%d", zfenzi, fenmu);
if(zfenzi <0)
printf("(%d/%d)", zfenzi, (fenmu));
if(zfenzi==0)
printf("0");
}
}
int main()
{
fenshu a, b;
scanf("%d/%d %d/%d", &a.fenzi, &a.fenmu, &b.fenzi, &b.fenmu);
a.standard();
b.standard();
a.print_fs(); cout << " + "; b.print_fs(); cout << " = "; (a + b).standard().print_fs(); cout << endl;
a.print_fs(); cout << " - "; b.print_fs(); cout << " = "; (a - b).standard().print_fs(); cout << endl;
a.print_fs(); cout << " * "; b.print_fs(); cout << " = "; (a * b).standard().print_fs(); cout << endl;
a.print_fs(); cout << " / "; b.print_fs(); cout << " = "; (a / b).standard().print_fs(); cout << endl;
return 0;
}
