乙级(Basic Level) 1024 有理数四则运算

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

Python:
def gcd(a,b):
    m = max(a,b)
    n = min(a,b)
    while(n!=0):
        r = m%n
        m = n
        n = r
    #print(m)
    return m

a = input().split()
a[0] = a[0].split('/')
a[1] = a[1].split('/')
a[0] = [int(i) for i in a[0]]
a[1] = [int(i) for i in a[1]]
b = gcd(abs(a[0][0]),abs(a[0][1]))
a[0][0],a[0][1] = int(a[0][0]/b),int(a[0][1]/b)
b = gcd(abs(a[1][0]),abs(a[1][1]))
a[1][0],a[1][1] = int(a[1][0]/b),int(a[1][1]/b)
b = [0,0,0,0,0,0]
c = [0,0,0]
b[0] = int(a[0][0]/a[0][1])
b[1] = a[0][0]%a[0][1]
b[2] = a[0][1]
b[3] = int(a[1][0]/a[1][1])
b[4] = a[1][0]%a[1][1]
b[5] = a[1][1]
for i in ['+','-','*','/']:
    if b[0] or b[1]:
        if b[0]<0:
            print('(',end='')
        if b[0]:
            print(b[0],end='')
        if b[0] and b[1]:
            print(' ',end='')
        if b[1]:
            print(str(b[1])+'/'+str(b[2]),end='')
        if b[0]<0:
            print(')',end='')
        print('',i,end=' ')
    else:
        print('0',i,end=' ')
    if b[3] or b[4]:
        if b[3]<0:
            print('(',end='')
        if b[3]:
            print(b[3],end='')
        if b[3] and b[4]:
            print(' ',end='')
        if b[4]:
            print(str(b[4])+'/'+str(b[5]),end='')
        if b[3]<0:
            print(')',end='')
        print(' ',end='')
        print('=',end=' ')
    else:
        print('0','=',end=' ')
    if i=='+':
        left = False
        num = a[0][0]*a[1][1] + a[0][1]*a[1][0]
        if num<0:
            num = abs(num)
            print('(-',end='')
            left = True
        if num==0:
            print('0')
        else:
            num2 = a[0][1]*a[1][1]
            num3 = gcd(num%num2,num2)
            if int(num/num2)!=0:
                print(int(num/num2),end='')
                if num%num2!=0:
                    print(' ',end='')
            if num%num2!=0:
                print(str(int(num%num2/num3))+'/'+str(int(num2/num3)),end='')
            if left:
                print(')',end='')
            print()
    elif i=='-':
        left = False
        num = a[0][0]*a[1][1] - a[0][1]*a[1][0]
        if num<0:
            num = abs(num)
            print('(-',end='')
            left = True
        if num==0:
            print(0)
        else:
            num2 = a[0][1]*a[1][1]
            num3 = gcd(num%num2,num2)
            if int(num/num2)!=0:
                print(int(num/num2),end='')
                if num%num2!=0:
                    print(' ',end='')
            if num%num2!=0:
                print(str(int(num%num2/num3))+'/'+str(int(num2/num3)),end='')
            if left:
                print(')',end='')
            print()
    elif i=='*':
        left = False
        num = a[0][0] * a[1][0]
        if num<0:
            num = abs(num)
            print('(-',end='')
            left = True
        if num==0:
            print(0)
        else:
            num2 = a[0][1] * a[1][1]
            num3 = gcd(num,num2)
            if int(num/num2)!=0:
                print(int(num/num2),end='')
                if num%num2!=0:
                    print(' ',end='')
            if num%num2 != 0:
                print(str(int(num%num2/num3))+'/'+str(int(num2/num3)),end='')
            if left:
                print(')',end='')
            print()
    elif i=='/':
        left = False
        num = a[0][0]*a[1][1]
        num2 = a[0][1]*a[1][0]
        if num2==0:
            print('Inf')
            break
        elif (num<0 and num2>0) or (num>0 and num2<0):
            print('(-',end='')
            left = True
        num = abs(num)
        num2 = abs(num2)
        if num==0:
            print(0)
        else:
            num3 = gcd(num,num2)
            if int(num/num2)!=0:
                print(int(num/num2),end='')
                if num%num2!=0:
                    print(' ',end='')
            if num%num2!=0:
                print(str(int(num%num2/num3))+'/'+str(int(num2/num3)),end='')
            if left:
                print(')',end='')
            print()