【PAT乙級】1034 有理數四則運算(20)
阿新 • • 發佈:2019-02-06
本題要求編寫程式,計算2個有理數的和、差、積、商。
輸入格式:
輸入在一行中按照“a1/b1 a2/b2”的格式給出兩個分數形式的有理數,其中分子和分母全是整型範圍內的整數,負號只可能出現在分子前,分母不為0。
輸出格式:
分別在4行中按照“有理數1 運算子 有理數2 = 結果”的格式順序輸出2個有理數的和、差、積、商。注意輸出的每個有理數必須是該有理數的最簡形式“k a/b”,其中k是整數部分,a/b是最簡分數部分;若為負數,則須加括號;若除法分母為0,則輸出“Inf”。題目保證正確的輸出中沒有超過整型範圍的整數。
輸入樣例1:
2/3 -4/2
輸出樣例1:
2/3 + (-2) = (-1 1/3) 2/3 - (-2) = 2 2/3 2/3 * (-2) = (-1 1/3) 2/3 / (-2) = (-1/3)
輸入樣例2:
5/3 0/6
輸出樣例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
思路:首先這道題目應該想著怎麼化簡假分數與真分數,加減乘除操作都可以分子分母進行運算之後得出新的分子分母然後再化簡,帶分數的整數部分好求,那麼就要將剩下的分數化為最簡形式。分子分母同時除以它的最大公約數就可以化為最簡了,程式碼如下:求最小公倍數與最大公約數可以參考這篇文章:https://blog.csdn.net/qq_31828515/article/details/51812154#include <iostream> #include <cmath> using namespace std; struct number { long long int k, fenz, fenm; }; long long int a1, b1, a2, b2; long long int maxgongyueshu(long long int x,long long int y) { long long int z = y; while (x%y != 0) { z = x%y; x = y; y = z; } return z; } void huajian(long long int afenz,long long int afenm) { if (afenm == 0) { cout << "Inf"; return; } if (afenz == 0) { cout << 0; return; } number tmp; long long int maxyue; if (abs(afenz) > abs(afenm)) { tmp.k = afenz / afenm; if (abs(afenz)%abs(afenm) == 0) { tmp.fenz = 0; tmp.fenm = 0; } else { tmp.fenz = abs(afenz) - abs(tmp.k)*abs(afenm); maxyue = maxgongyueshu(abs(tmp.fenz), abs(afenm)); tmp.fenz = tmp.fenz / maxyue; tmp.fenm = abs(afenm) / maxyue; } } else if (abs(afenz) == abs(afenm)) { tmp.k = afenz / afenm; tmp.fenz = 0; tmp.fenm = 0; } else { tmp.k = 0; maxyue = maxgongyueshu(abs(afenz), abs(afenm)); tmp.fenz = afenz / maxyue; tmp.fenm = afenm / maxyue; } ///////////////輸出 if (tmp.k == 0) { if (tmp.fenz * tmp.fenm < 0) cout << "(-" << abs(tmp.fenz) << "/" << abs(tmp.fenm) << ")"; else cout << tmp.fenz << "/" << tmp.fenm; } else { if (tmp.fenz == 0 && tmp.fenm == 0) { if (tmp.k>0) cout << tmp.k; else cout << "(" << tmp.k << ")"; } else { if (tmp.k>0) cout << tmp.k<<" "<<tmp.fenz<<"/"<<tmp.fenm; else cout << "(" << tmp.k << " " << tmp.fenz << "/" << tmp.fenm<<")"; } } } void add() { long long int m,n; m = a1*b2 + a2*b1; n = b1*b2; huajian(a1, b1); cout << " + "; huajian(a2, b2); cout << " = "; huajian(m, n); cout << endl; } void mins() { long long int m, n; m = a1*b2 - a2*b1; n = b1*b2; huajian(a1, b1); cout << " - "; huajian(a2, b2); cout << " = "; huajian(m, n); cout << endl; } void multi() { long long int m, n; m = a1*a2; n = b1*b2; huajian(a1, b1); cout << " * "; huajian(a2, b2); cout << " = "; huajian(m, n); cout << endl; } void div() { long long int m, n; m = a1*b2; n = b1*a2; huajian(a1, b1); cout << " / "; huajian(a2, b2); cout << " = "; huajian(m, n); cout << endl; } int main() { scanf("%lld/%lld", &a1, &b1); scanf("%lld/%lld", &a2, &b2); add(); mins(); multi(); div(); return 0; }