[从头学数学] 第87节 分数的加法和减法

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入练气期第十层功法的修炼，
这次要修炼的目标是[分数的加法和减法]。

正剧开始：

星历2016年02月14日 13:47:04, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起研究分数的运算

其实对于分数的所有运算，小伟早就有了阿伟制作的神器，有了它，所有的有关分数的题目就是浮云。

<span style="font-size:18px;">###
# @usage   分数运算
# @author  mw
# @date    2016年01月15日  星期五  09:04:31 
# @param
# @return
#
###
def fractionCalc():
    
    # 可以将任意的四则运算表达式用分数进行计算，
    # 而不是将浮点结果简单转化成分数。
    fin = open('input.txt');
    fout= open('output.txt', 'a');
    
    for line in fin.readlines():
        if line[-1] == '\n':
            line = line[:-1];     
            
        if line == '':
            continue;
        elif line.startswith('#'):
            print(line);
            fout.write(line+'\n');
        else:
            try:
                lines = line.split(sep=' ');
                for i in range(len(lines)):
                    if lines[i]=='':
                        continue;
                    #消除空格
                    lines[i] = lines[i].replace(' ', '');
                    expCount = len(lines[i]);
                    expression = '';

                    #分割操作数
                    operands = [];
                    stmp = '';
                    indexBeg = 0;
                    indexEnd = 0;
                    for j in range(expCount):
                        if isOps(lines[i][j]):
                            if stmp != '':
                                operands.append(stmp);
                                stmp = '';
                        else:
                            stmp+=lines[i][j];
                    if stmp != '':
                        operands.append(stmp);
                    
                    print(operands);

                    #操作数修饰
                    operandCount = len(operands);
                    operandString = [];
                    #数字如1/7要转化成Fraction('1/7')这种样式才可以算出正确结果，引号不可以少掉。
                    for j in range(operandCount):
                        stmp = '';
                        stmp = 'Fraction(\''+operands[j]+'\')';
                        operandString.append(stmp);

                    #组装新表达式       
                    typechange = 1;
                    index = 0;
                    expression = '';
                    
                    for j in range(expCount):
                        #操作符直接添加
                        if  isOps(lines[i][j]):
                            expression+=lines[i][j];
                        else:
                            if j > 0 and typechange == 0 and isOps(lines[i][j-1]):
                                typechange = 1;
                            
                            #从操作数序列中选择对应操作数。
                            if typechange == 1:
                                if index > len(operandString):
                                    break;
                                expression += operandString[index];
                                index+=1;
                                typechange = 0;
                     
                    #表达式结果的运算打印
                    s = '{0} = {1} = {2}'.format(lines[i],expression, eval(expression));
                    print(s, end=', ');
                    fout.write(s + ', ');
                print('\n');
                fout.write('\n');
            except:
                #traceback.print_exc();
                ex = '{0} 表达式有误，无法进行计算。'.format(lines[i]);
                print(ex);
                fout.write(ex);
    fout.close();
    fin.close();</span>

小伟刚拿出工具，[人叫板老师]的题海大军就到了：

小伟只需要这样输入：

<span style="font-size:18px;">2/9+5/9
2/7+5/7
5/8+1/8
4+1/4
5/6-1/6
7/10-1/10 
7/9-2/9
1-11/30</span>

就可以得到以下的结果：

<span style="font-size:18px;">2/9+5/9 = Fraction('2')/Fraction('9')+Fraction('5')/Fraction('9') = 7/9, 
2/7+5/7 = Fraction('2')/Fraction('7')+Fraction('5')/Fraction('7') = 1, 
5/8+1/8 = Fraction('5')/Fraction('8')+Fraction('1')/Fraction('8') = 3/4, 
4+1/4 = Fraction('4')+Fraction('1')/Fraction('4') = 17/4, 
5/6-1/6 = Fraction('5')/Fraction('6')-Fraction('1')/Fraction('6') = 2/3, 
7/10-1/10 = Fraction('7')/Fraction('10')-Fraction('1')/Fraction('10') = 3/5, 
7/9-2/9 = Fraction('7')/Fraction('9')-Fraction('2')/Fraction('9') = 5/9, 
1-11/30 = Fraction('1')-Fraction('11')/Fraction('30') = 19/30, </span>

<span style="font-size:18px;">4/15+1/15+7/15 = Fraction('4')/Fraction('15')+Fraction('1')/Fraction('15')+Fraction('7')/Fraction('15') = 4/5, 
</span>

<span style="font-size:18px;">>>> 
1/4 ---> 0.25 

1/4 1/4 ---> 0.5 

1/4 1/2 1/4 ---> 1.0 

1/4 3/4 3/4 1/4 ---> 2.0 

1/4 1 3/2 1 1/4 ---> 4.0 

1/4 5/4 5/2 5/2 5/4 1/4 ---> 8.0 


	def tmp():
    n = 6;
    res = [[1]];
    try:
        for i in range(1, n):
            a = [];
            for j in range(i+1):
                if (j == 0 or j == i):
                    a.append(res[i-1][0]);
                else:
                    a.append(res[i-1][j-1]+res[i-1][j]);
            res.append(a);
    except:
        print('error');

    for i in range(len(res)):
        total = 0;
        for j in range(len(res[i])):
            total += res[i][j];
            res[i][j] = str(Fraction(res[i][j], 4));
            print('{0:^}'.format(res[i][j]), end=' ');
        print('--->', total/4,'\n');
    
    return;</span>

<span style="font-size:18px;">5/6-1/2+1/3
7/8-5/12+1/6
1/2+1/4-1/6
9/4-1/4+1/5
5/6-(1/2+1/3)
7/8-(5/12+1/6)
1/2+(1/4-1/6)
9/4-(1/4+1/5)
2/5+1/3+3/5
1/4+1/3+1/4+2/3
9/7+1/8+3/8+5/7

5/6-1/2+1/3 = Fraction('5')/Fraction('6')-Fraction('1')/Fraction('2')+Fraction('1')/Fraction('3') = 2/3, 
7/8-5/12+1/6 = Fraction('7')/Fraction('8')-Fraction('5')/Fraction('12')+Fraction('1')/Fraction('6') = 5/8, 
1/2+1/4-1/6 = Fraction('1')/Fraction('2')+Fraction('1')/Fraction('4')-Fraction('1')/Fraction('6') = 7/12, 
9/4-1/4+1/5 = Fraction('9')/Fraction('4')-Fraction('1')/Fraction('4')+Fraction('1')/Fraction('5') = 11/5, 
5/6-(1/2+1/3) = Fraction('5')/Fraction('6')-(Fraction('1')/Fraction('2')+Fraction('1')/Fraction('3')) = 0, 
7/8-(5/12+1/6) = Fraction('7')/Fraction('8')-(Fraction('5')/Fraction('12')+Fraction('1')/Fraction('6')) = 7/24, 
1/2+(1/4-1/6) = Fraction('1')/Fraction('2')+(Fraction('1')/Fraction('4')-Fraction('1')/Fraction('6')) = 7/12, 
9/4-(1/4+1/5) = Fraction('9')/Fraction('4')-(Fraction('1')/Fraction('4')+Fraction('1')/Fraction('5')) = 9/5, 
2/5+1/3+3/5 = Fraction('2')/Fraction('5')+Fraction('1')/Fraction('3')+Fraction('3')/Fraction('5') = 4/3, 
1/4+1/3+1/4+2/3 = Fraction('1')/Fraction('4')+Fraction('1')/Fraction('3')+Fraction('1')/Fraction('4')+Fraction('2')/Fraction('3') = 3/2, 
9/7+1/8+3/8+5/7 = Fraction('9')/Fraction('7')+Fraction('1')/Fraction('8')+Fraction('3')/Fraction('8')+Fraction('5')/Fraction('7') = 5/2, </span>

本节到此结束，欲知后事如何，请看下回分解。