[从头学数学] 第45节 分数的初步认识

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入练气期第五层功法的修炼，
这次要修炼的目标是[分数的初步认识]。

正剧开始：

星历2016年01月15日 09:00:39, 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。

由于小朋友们在吃着西瓜，小伟判断这是在夏天，应该是暑假吧，那怎么还戴着这种棉帽呢？

<span style="font-size:18px;">def fractionCalc():
    a = Fraction(1, 4);
    print(a);
    b = Fraction(1, 3);
    print(b);
</span>

>>> 
1/4
1/3

<span style="font-size:18px;">>>> 
1/2
1/4
1/6
1/2 > 1/4
1/4 > 1/6

###
# @usage   分数相关的运算
# @author  mw
# @date    2016年01月15日  星期五  09:04:31 
# @param
# @return
#
###
def fractionCalc():
    array = [[1,2],[1,4], [1, 6]];
    fraction = [];
    for i in range(len(array)):
        fraction.append(Fraction(array[i][0], array[i][1]));

    for i in range(len(fraction)):
        print(fraction[i]);

    for i in range(len(fraction)-1):
        a = fraction[i];
        b = fraction[i+1];
        
        if (a > b):
            print('{0} > {1}'.format(a, b));
        elif (a < b):
            print('{0} < {1}'.format(a, b));
        else:
            print('{0} = {1}'.format(a, b));
    return;</span>

小伟给出了解答：

<span style="font-size:18px;">function myDraw() {  
    var config = new PlotConfiguration();  
    config.init();  
    config.setPreference(); 
	//config.setSector(1,1,1,1);
 
    //config.axis2D(0, 0, 180);  
	
	var r = 40;
	var row = 6, col = 13;
	var x = (600-r*(col-1))/2, y = (400-r*(row-1))/2;
	
	for (var i = 0; i < col; i++) {
		for (var j = 0; j < row; j++) {
			shape.strokeRect(x + i*r, y + j*r, r, r);
		}
	}
	
	var array = [1,1,1,2,1,3,1,4];
	
	plot.save()
		.setFillStyle('red');
		
		for (var i = 0; i < array.length / 2; i++) {
			shape.fillRect(x + array[2*i]*r, y + array[2*i+1]*r, r, r);
		}
		
	plot.restore();
		
	x += 2*r;
	array = [1,1,2,1,3,1,4,1];
	
	plot.save()
		.setFillStyle('blue');
		
		for (var i = 0; i < array.length / 2; i++) {
			shape.fillRect(x + array[2*i]*r, y + array[2*i+1]*r, r, r);
		}
		
	plot.restore();
	
	y += 2 * r;
	array = [1,1,1,2,2,1,2,2];
	
	plot.save()
		.setFillStyle('pink');
		
		for (var i = 0; i < array.length / 2; i++) {
			shape.fillRect(x + array[2*i]*r, y + array[2*i+1]*r, r, r);
		}
		
	plot.restore();
	
	x += 3 * r;
	array = [1,2,2,1,2,2,2,3];
	plot.save()
		.setFillStyle('orange');
		
		for (var i = 0; i < array.length / 2; i++) {
			shape.fillRect(x + array[2*i]*r, y + array[2*i+1]*r, r, r);
		}
		
	plot.restore();
	
	x += 2 * r;
	y -= 2 * r;
	array = [1,1,2,1,2,2,2,3];
	plot.save()
		.setFillStyle('purple');
		
		for (var i = 0; i < array.length / 2; i++) {
			shape.fillRect(x + array[2*i]*r, y + array[2*i+1]*r, r, r);
		}
		
	plot.restore();
	
	x+= 3 * r;
	array = [1,1,1,2,2,2,2,3];
	
	plot.save()
		.setFillStyle('cyan');
		
		for (var i = 0; i < array.length / 2; i++) {
			shape.fillRect(x + array[2*i]*r, y + array[2*i+1]*r, r, r);
		}
		
	plot.restore();

}</span>

这是俄罗斯方块啊，阿伟看出来了。

<span style="font-size:18px;">    for i in range(len(fraction)-1):
        a = fraction[i];
        b = fraction[i+1];
        print('{0}+{1}={2}'.format(a, b, a+b));</span>

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

###
# @usage   分数相关的运算
# @author  mw
# @date    2016年01月15日  星期五  09:04:31 
# @param
# @return
#
###
def fractionCalc():
    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:
            lines = line.split(sep=' ');
            for i in range(len(lines)):
                if lines[i]=='':
                    continue;
                
                expression = lines[i];
                ops = [];
                length = len(expression);

                for j in range(length):
                    if expression[j] == '+' or\
                       expression[j] == '-':
                        ops.append(expression[j]);
                    else:
                        pass;

                operands = re.split(r'[+-]{1}', expression);
                operandString = [];
                length = len(operands);
                #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(length):
                    operandString.append('Fraction(\''+operands[j]+'\')');

                expression ='';

                length = len(operandString)-1;

                for j in range(length):
                    expression+=operandString[j]+ops[j];
                expression+=operandString[-1];  

                s = '{0} = {1} = {2}'.format(lines[i],expression, eval(expression));
                print(s, end=', ');
                fout.write(s + ', ');
            print('\n');
            fout.write('\n');
    fout.close();
    fin.close();  </span>

本节到此结束，欲知后事如何，请看下回分解。