有理数的四则运算

链接：http://www.nowcoder.com/pat/6/problem/4060

题目描述

本题要求编写程序，计算2个有理数的和、差、积、商。

输入描述:

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。

输出描述:

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。

输入例子:

5/3 0/6

输出例子:

1 2/3 + 0 = 1 2/3

1 2/3 - 0 = 1 2/3

1 2/3 * 0 = 0

1 2/3 / 0 = Inf

思路：多加几个变量保存输入的有理数，1.用来保存最简形式 2.用来保存计算形式，就是通分过的形式。代码写起来比较复杂，还有输入格式的要求也比较多。

浮点错误：出现了除以0的情况。

  1 #include "iostream"
  2 #include <iomanip>
  3 #include <string.h>
  4 #include <string>
  5 #include <vector>
  6 #include <cmath>
  7 #include <cctype>
  8 #include <algorithm>
  9 using namespace std;
 10  
 11 typedef struct YLS{
 12     int z;
 13     int fz;
 14     int fm;
 15 }YLS;
 16  
 17 void change(YLS &yls)
 18 {
 19     if(yls.fm == 0) return;
 20     if(yls.fz/yls.fm != 0)
 21     {
 22         yls.z += yls.fz/yls.fm;
 23         yls.fz = yls.fz%yls.fm;
 24     }
 25 }
 26 void tongFen(YLS &yls1, YLS &yls2)
 27 {
 28      
 29             int t1, t2;
 30             t1 = yls1.fm;
 31             t2 = yls2.fm;
 32             yls1.fz *= t2;
 33             yls1.fm *= t2;
 34             yls2.fz *= t1;
 35             yls2.fm *= t1;
 36 }
 37 void output1(YLS yls1)
 38 {
 39     int mark = 0;
 40     if(yls1.z<0 || yls1.fz<0 ||yls1.fm<0)
 41     {
 42         mark = 1;
 43         cout <<'(';
 44     }
 45     if(yls1.fz==0 && yls1.z==0)
 46     {
 47         cout <<0;
 48     }
 49     else
 50     {
 51         if(yls1.z == 0)
 52         {
 53             if(yls1.fm < 0)
 54             {
 55                 yls1.fm = -yls1.fm;
 56                 yls1.fz = -yls1.fz;
 57             }
 58             cout <<yls1.fz <<"/" <<yls1.fm;
 59         }
 60         else
 61         {
 62             if(yls1.fz == 0)
 63             {
 64                 cout <<yls1.z;
 65             }
 66             else
 67             {
 68                 if(yls1.fm < 0)
 69                 {
 70                     yls1.fm = -yls1.fm;
 71                     yls1.fz = -yls1.fz;
 72                 }
 73                 if(yls1.fz < 0)
 74                 {
 75                     if(yls1.z > 0)   yls1.z = -yls1.z;
 76                     yls1.fz = - yls1.fz;
 77                 }
 78                 cout <<yls1.z <<" " <<yls1.fz <<"/" <<yls1.fm;
 79             }
 80         }
 81     }
 82     if(mark == 1)   cout <<')';
 83     cout <<" " <<"/" <<" ";
 84     cout <<0;
 85     cout <<" " <<"=" <<" ";
 86     cout <<"Inf";
 87 }
 88 void output(YLS yls1, YLS yls2, char c, YLS yls3)
 89 {
 90     int mark = 0;
 91     if(yls1.z<0 || yls1.fz<0 || yls1.fm<0)
 92     {  
 93         mark = 1;
 94         cout <<'(';
 95     }
 96     if(yls1.fz==0 && yls1.z==0)
 97     {
 98         cout <<0;
 99     }
100     else
101     {
102         if(yls1.z == 0)
103         {
104             if(yls1.fm < 0)
105             {
106                 yls1.fm = -yls1.fm;
107                 yls1.fz = -yls1.fz;
108             }
109             cout <<yls1.fz <<"/" <<yls1.fm;
110         }
111         else
112         {
113             if(yls1.fz == 0)
114             {
115                 cout <<yls1.z;
116             }
117             else
118             {
119                 if(yls1.fm < 0)
120                 {
121                     yls1.fm = -yls1.fm;
122                     yls1.fz = -yls1.fz;
123                 }
124                 if(yls1.fz < 0)
125                 {
126                     if(yls1.z > 0)   yls1.z = -yls1.z;
127                     yls1.fz = - yls1.fz;
128                 }
129                 cout <<yls1.z <<" " <<yls1.fz <<"/" <<yls1.fm;
130             }
131         }
132     }
133     if(mark == 1)   cout <<')';
134     cout <<" " <<c <<" ";
135     mark = 0;
136     if(yls2.z<0 || yls2.fz<0 || yls2.fm<0)
137     {  
138         mark = 1;
139         cout <<'(';
140     }
141     if(yls2.fz==0 && yls2.z==0)
142     {
143         cout <<0;
144     }
145     else
146     {
147         if(yls2.z == 0)
148         {
149             if(yls2.fm < 0)
150             {
151                 yls2.fm = -yls2.fm;
152                 yls2.fz = -yls2.fz;
153             }      
154             cout <<yls2.fz <<"/" <<yls2.fm;
155         }
156         else
157         {
158             if(yls2.fz == 0)
159             {
160                 cout <<yls2.z;
161             }
162             else
163             {
164                 if(yls2.fm < 0)
165                 {
166                     yls2.fm = -yls2.fm;
167                     yls2.fz = -yls2.fz;
168                 }
169                 if(yls2.fz < 0)
170                 {
171                     if(yls2.z > 0)   yls2.z = -yls2.z;
172                     yls2.fz = - yls2.fz;
173                 }
174                 cout <<yls2.z <<" " <<yls2.fz <<"/" <<yls2.fm;
175             }
176         }
177     }
178     if(mark == 1)   cout <<')';
179     cout <<" " <<"=" <<" ";
180     mark = 0;
181     if(yls3.z<0 || yls3.fz<0 || yls3.fm<0)
182     {
183         mark = 1;
184         cout <<'(';
185     }
186     if(yls3.fz==0 && yls3.z==0)
187     {
188         cout <<0;
189     }
190     else
191     {
192         if(yls3.z == 0)
193         {
194             if(yls3.fm < 0)
195             {
196                 yls3.fm = -yls3.fm;
197                 yls3.fz = -yls3.fz;
198             }
199             cout <<yls3.fz <<"/" <<yls3.fm;
200         }
201         else
202         {
203             if(yls3.fz == 0)
204             {
205                 cout <<yls3.z;
206             }
207             else
208             {
209                 if(yls3.fm < 0)
210                 {
211                     yls3.fm = -yls3.fm;
212                     yls3.fz = -yls3.fz;
213                 }
214                 if(yls3.fz < 0)
215                 {
216                     if(yls3.z > 0)   yls3.z = -yls3.z;
217                     yls3.fz = -yls3.fz;
218                 }
219                 cout <<yls3.z <<" " <<yls3.fz <<"/" <<yls3.fm;
220             }
221         }
222     }
223     if(mark == 1)   cout <<')';
224 }
225 int gcd(int x, int y)
226 {
227     if(y != 0)
228     {if(x%y == 0)
229     {
230         return y;
231     }
232     else
233     {
234         return gcd(y, x%y);
235     }}
236 }
237 int main()
238 {
239     YLS yls1, yls2, yls3, yls4;
240     yls1.z = 0;
241     cin >>yls1.fz;
242     getchar();
243     cin >>yls1.fm;
244     yls2.z = 0;
245     cin >>yls2.fz;
246     getchar();
247     cin >>yls2.fm;
248  
249     yls3 = yls1;
250     yls4 = yls2;
251     int gys = 0;
252     if(yls2.fz != 0)
253     {
254         gys = gcd(yls2.fz, yls2.fm);
255     }
256     if(gys != 0)
257     {yls2.fz /= gys;
258     yls2.fm /= gys;}
259     gys = 0;
260     if(yls1.fz != 0)
261     {
262         gys = gcd(yls1.fz, yls1.fm);
263     }
264     if(gys != 0)
265     {yls1.fz /= gys;
266     yls1.fm /= gys;}
267     change(yls1);
268     change(yls2);
269      
270     YLS ylsX,ylsY,ylsZ;
271     ylsX = yls3;
272     ylsY = yls4;
273     tongFen(ylsX, ylsY);
274     ylsZ.z = ylsX.z+ylsY.z;
275     ylsZ.fz = ylsX.fz+ylsY.fz;
276     ylsZ.fm = ylsX.fm;
277     gys = 0;
278     if(ylsZ.fz != 0)
279     {
280         gys = gcd(ylsZ.fz, ylsZ.fm);
281     }
282     if(gys != 0)
283     {ylsZ.fz /= gys;
284     ylsZ.fm /= gys;}
285     change(ylsZ);
286     output(yls1, yls2, '+', ylsZ);
287     cout <<endl;
288  
289     ylsZ.z = ylsX.z-ylsY.z;
290     ylsZ.fz = ylsX.fz-ylsY.fz;
291     ylsZ.fm = ylsX.fm;
292     gys = 0;
293     if(ylsZ.fz != 0)
294     {
295         gys = gcd(ylsZ.fz, ylsZ.fm);
296     }
297     if(gys != 0)
298     {ylsZ.fz /= gys;
299     ylsZ.fm /= gys;}
300     change(ylsZ);
301     output(yls1, yls2, '-', ylsZ);
302     cout <<endl;
303  
304     ylsZ.z = 0;
305     ylsZ.fz = yls3.fz*yls4.fz;
306     ylsZ.fm = yls3.fm*yls4.fm;
307     change(ylsZ);
308     gys = 0;
309     if(ylsZ.fz != 0)
310     {
311         gys = gcd(ylsZ.fz, ylsZ.fm);
312     }
313     if(gys != 0)
314     {ylsZ.fz /= gys;
315     ylsZ.fm /= gys;}
316     output(yls1, yls2, '*', ylsZ);
317     cout <<endl;
318  
319     YLS yls5;
320     yls5.fm = yls4.fz;
321     yls5.fz = yls4.fm;
322     if(yls4.fz == 0)
323     {
324         output1(yls1);
325         cout <<endl;
326     }
327     else
328     {
329         ylsZ.z = 0;
330         ylsZ.fz = yls3.fz*yls5.fz;
331         ylsZ.fm = yls3.fm*yls5.fm;
332         change(ylsZ);
333         gys = 0;
334         if(ylsZ.fz != 0)
335         {
336             gys = gcd(ylsZ.fz, ylsZ.fm);
337         }
338         if(gys != 0)
339         {ylsZ.fz /= gys;
340         ylsZ.fm /= gys;}
341         output(yls1, yls2, '/', ylsZ);
342         cout <<endl;
343     }
344     return 0;
345 }