[从头学数学] 第68节 小数的意义和性质

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入练气期第八层功法的修炼，
这次要修炼的目标是[小数的意义和性质]。

正剧开始：

星历2016年02月02日 10:00:05, 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]一起研究小数。

>>> 
零点五八
三点五
四十一点四七

if __name__ == '__main__':
    a = [0.58,3.5,41.47];
    for i in range(len(a)):
        print(floatNumberRead(a[i]));
		
###
# @usage   小数的读法
# @author  mw
# @date    2016年01月21日  星期四  09:53:40 
# @param
# @return
#
###
def floatNumberRead(num):
    #正负号
    if (num < 0):
        sign = '负';
    else:
        sign = '';

    #判断是否小数 
    sOfNum = str(num);
    index = sOfNum.find('.');
    if (index != -1):
        chineseOfNumber=['零','一', '二', '三', '四', '五', '六',\
                     '七', '八', '九'];
        sOfNum = sOfNum[index+1:];
        decimalPart = '点';
        for i in range(len(sOfNum)):
            decimalPart += chineseOfNumber[int(sOfNum[i])];
            
        import math;
        intPart = numberToChinese(math.floor(abs(num)), '');

        return sign+intPart+decimalPart;
    else:
        return sign+numberToChinese(num, '');  
		

>>> 
一点四 写作 1.4
五点八 写作 5.8
零点零九 写作 0.09
零点八八 写作 0.88

###
# @usage   小数的写法
# @author  mw
# @date    2016年02月02日  星期二  09:19:33 
# @param
# @return
#
###
def floatNumberWrite(s):
    #小数点位置
    index = s.find('点');
    #整数部分字符串
    sIntPart = s[:index];
    #小数部分字符串
    sFloatPart = s[index+1:];
    #小数精度位数
    accuracy = len(sFloatPart);
    #print(sIntPart);
    #print(sFloatPart);
    chineseOfNumber=['零','一', '二', '三', '四', '五', '六',\
                     '七', '八', '九'];
    floatPart = 0;
    floatRate = 0.1;
    for i in range(accuracy):
        for j in range(10):
            if chineseOfNumber[j] == sFloatPart[i]:
                floatPart += j * floatRate;
                floatRate*=0.1;
                break;

    intPart = chineseToNumber(sIntPart);
    result = round(intPart + floatPart, accuracy);    
    return result;
	
###
# @usage   数字的中文写法 
# @author  mw
# @date    2016年01月08日  星期五  12:37:26 
# @param
# @return
#
###
def numberToChinese(num, s):
    if (num < 0):
        num = abs(num);
    chineseOfNumber=['零','一', '二', '三', '四', '五', '六',\
                     '七', '八', '九', '十','百','千','万','亿'];
    bit = 0;
    tmp = num;
    if (tmp == 0):
        s = chineseOfNumber[0];
    while (tmp > 0):
        tmp = tmp//10;
        bit+=1;
    tmp = num;
    while (tmp > 0):
        if (tmp < 10):
            s += chineseOfNumber[tmp];
            tmp -= 10;
        elif (tmp < 100):
            s += chineseOfNumber[tmp//10];
            s += '十';
            tmp = tmp%10; 
        elif (tmp < 1000):
            s += chineseOfNumber[tmp//100];
            s += '百';
            tmp = tmp%100;
            if tmp < 10 and tmp > 0:
                s += '零';
        elif (tmp < 10000):
            s += chineseOfNumber[tmp//1000];
            s += '千';
            tmp = tmp%1000;
            if tmp < 100 and tmp > 0:
                s += '零';
        elif (tmp < 100000000):
            s1 = '';
            s += numberToChinese(tmp//10000, s1);
            s += '万';
            tmp =tmp%10000;
            if tmp < 1000 and tmp > 0:
                s += '零';
        elif (tmp >= 100000000):
            s1 = '';
            s += numberToChinese(tmp//100000000, s1);
            s += '亿';
            tmp = tmp%100000000;
            if tmp < 10000000 and tmp > 0:
                s += '零';
        else:
            pass;
    return s;

###
# @usage   数字的中文写法转化为数字
# @author  mw
# @date    2016年01月08日  星期五  09:19:55 
# @param
# @return
#
###

def chineseToNumber(s):
    chineseOfNumber=['零','一', '二', '三', '四', '五', '六',\
                     '七', '八', '九', '十','百','千','万','亿'];
    result = 0;
    #每一组两个数，比如九百，一万，都是由一个值数和一个倍数组成。
    #不可能两个以上的值在一块，但可能两个以上的倍数在一块，比如九九不合法，但四百万合法。
    
    #合法表达为0，不合法为其它值
    illegal = 0;
    #两个长度
    lengthOfStr = len(s);
    lengthOfChs = len(chineseOfNumber);
    #合法性判断
    for i in range(lengthOfStr):
        if illegal == 1:
            break;

        for j in range(lengthOfChs):
            if s[i] == chineseOfNumber[j]:
                break;
            else:
                if j >= lengthOfChs-1:
                    print('含有非中文数字的字符，表达式不合法');
                    illegal = 1;

    for i in range(lengthOfStr-1):
        if illegal == 1:
            break;
        for j in range(10):
            if s[i] == chineseOfNumber[j]:
                if j>0:
                    for k in range(10):
                        if s[i+1] == chineseOfNumber[k]:
                            print('连续两个本数相连而没有倍数，表达式不合法。');
                            illegal = 1;
                            break;
                #当这个数是零时，它后面跟零或倍数都不合法
                else:
                    if s[i+1] == chineseOfNumber[0]:
                        print('连续两个零相连，表达式不合法。');
                        illegal = 1;
                        break;
                    
                    for k in range(10, lengthOfChs):
                        if s[i+1] == chineseOfNumber[k]:
                            print('零后面跟上倍数，表达式不合法。');
                            illegal = 1;
                            break;
                    
    
    for i in range(lengthOfStr-1):
        if illegal == 1:
            if (i > 0):
                print('表达式的倍数排序不符合规范，不合法。');
            break;                    
   
        if s[i] == '十':
            if s[i+1] == '十' or s[i+1] == '百' or s[i+1] == '千':
                illegal = 1;
        elif s[i] == '百':
            if s[i+1] == '十' or s[i+1] == '百' or s[i+1] == '千':
                illegal = 1;
        elif s[i] == '千':
            if s[i+1] == '十' or s[i+1] == '百' or s[i+1] == '千':
                illegal = 1;
        elif s[i] == '万':
            if s[i+1] == '十' or s[i+1] == '百' or s[i+1] == '千':
                illegal = 1;
        elif s[i] == '亿':
            if s[i+1] == '十' or s[i+1] == '百' or s[i+1] == '千' or s[i+1] == '万':
                illegal = 1;
        else:
            pass;

    #合法则计算      
    if illegal!=0:
        print('输入不合法。');
    else:
        value = 0;
        multiple = 1;
        result = 0;
        #超过亿的部分，单独分出来的原因是避免再和万的倍数相乘
        yiPart = 0;
        #超过万的部分
        wanPart = 0;
        for i in range(lengthOfStr):
            if s[i] == '亿':
                result += value+wanPart+yiPart;
                multiple = 100000000;
                value = result;
                result = value*multiple;
                if (i < lengthOfStr-1 and s[i+1] == '亿'):
                    value = 0;
                else:
                    yiPart = result;
                    result = 0;
                multiple = 1;
            elif s[i] == '万':
                result += value+wanPart;
                multiple = 10000;
                value = result;
                result = value*multiple;
                if (i < lengthOfStr-1 and (s[i+1] == '亿' or s[i+1] == '万')):
                    value = 0;
                else:
                    if (result > 100000000):
                        yiPart = result;
                    else:
                        wanPart = result;
                    result = 0;
                multiple = 1;
            elif s[i] == '千':
                multiple = 1000;
                result += value*multiple;
                value = 0;
                multiple = 1;
            elif s[i] == '百':
                multiple = 100;
                result += value*multiple;
                value = 0;
                multiple = 1;
            #十这个数字，即可以作为本数，也可以作为倍数
            elif s[i] == '十':
                if value == 0:
                    value = 10;
                    multiple = 1;
                    result += value*multiple;
                    value = 0;
                else:
                    multiple = 10;
                    result += value*multiple;
                    value = 0;
                    multiple = 1;
            else:
                for j in range(10):
                    if s[i] == chineseOfNumber[j]:
                        value = j;
                        multiple = 1;
                if i >= lengthOfStr-1:
                    result += value * multiple;

        result += wanPart + yiPart;
    #print('{0} {1}'.format(s, result));
    return result;

<span style="font-size:18px;">>>> 
6.5 读作 六点五
0.04 读作 零点零四
6.72 读作 六点七二
0.058 读作 零点零五八
340.09 读作 三百四十点零九
三百点七一 写作 300.71
五点零六 写作 5.06
零点零八九 写作 0.089

def readNumber():
    a = [6.5,0.04,6.72,0.058,340.09];
    for i in range(len(a)):
        print('{0} 读作 {1}'.format(a[i], floatNumberRead(a[i])));

def writeNumber():
    a = ['三百点七一', '五点零六', '零点零八九'];
    for i in range(len(a)):
        print('{0} 写作 {1}'.format(a[i], floatNumberWrite(a[i])));
    

if __name__ == '__main__':
    readNumber();
    writeNumber();</span>

<span style="font-size:18px;">>>> 
29.5 读作 二十九点五
0.84 读作 零点八四
1.2 读作 一点二
1.8 读作 一点八
8844.43 读作 八千八百四十四点四三</span>

<span style="font-size:18px;">>>> 
零点五五七 写作 0.557
四万零七十五点六九 写作 40075.69
十四点八五九 写作 14.859
九十九点七九 写作 99.79</span>

<span style="font-size:18px;">>>> 
0.358, 0.385, 0.538, 0.583, 0.835, 0.853, 符合条件(1)的总共有6个数。
8.035, 8.053, 8.305, 8.503, 符合条件(2)的总共有4个数。
30.58 读作 三十点五八
30.85 读作 三十点八五
50.38 读作 五十点三八
50.83 读作 五十点八三
80.35 读作 八十点三五
80.53 读作 八十点五三
符合条件(3)的总共有6个数。

def tmp():
    a = [3, 0, 5, 8];
    p = perm(a);
    size = len(p);
    set1 = set([]);
    set2 = set([]);
    for i in range(size):
        #最后一位小数不为0
        if (p[i][3] != 0):
            num = p[i][0] + 0.1*p[i][1] + 0.01*p[i][2]+0.001*p[i][3];
            set1.add(round(num,3));

    list1 = list(set1);
    list1.sort();

    count = 0;
    for i in range(len(list1)):
        if (list1[i] < 1):
            print(list1[i], end = ', ');
            count+=1;
    print('符合条件(1)的总共有{0}个数。'.format(count));

    count = 0;
    for i in range(len(list1)):
        if (list1[i] > 8):
            print(list1[i], end = ', ');
            count+=1;
    print('符合条件(2)的总共有{0}个数。'.format(count));

    for i in range(size):
        if (p[i][0] != 0 and p[i][3] != 0):
            num = p[i][0]*10 + p[i][1] + 0.1*p[i][2]+0.01*p[i][3];
            set2.add(round(num,2));

    list2 = list(set2);
    list2.sort();

    count = 0;
    for i in range(len(list2)):
        s = floatNumberRead(list2[i]);
        if (s.find('零') == -1):
            print('{0} 读作 {1}'.format(list2[i], s));
            count+=1;
    print('符合条件(3)的总共有{0}个数。'.format(count));</span>

<span style="font-size:18px;">>>> 
[2.84, 2.88, 2.93, 3.05]

def tmp():
    list1 = list([3.05, 2.84, 2.88, 2.93]);
    list1.sort();
    print(list1);</span>

<span style="font-size:18px;">def tmp():
    list1 = list([3.05, 2.84, 2.88, 2.93]);
    list1.sort();
    print(list1);

    list1.reverse();
    print(list1);</span>

本节到此结束，欲知后事如何，请看下回分解。