[从头学数学] 第56节 大数的认识

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入练气期第七层功法的修炼，
这次要修炼的目标是[大数的认识]。

正剧开始：

星历2016年01月22日 11:12:43, 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]一起继续修炼。

小伟刚拿到了[人叫板老师]设计的练气期第七层功法：

那就开始修炼吧。

小伟看到了一张写着很多很大的数字的图：

这些数字到底怎么读呢？ 小伟拿出了读数字神器：

<span style="font-size:18px;">>>> 
一千九百六十一万二千三百六十八
三百万二千一百六十六
八千零四十一万八千二百
九千四百零二万三千五百六十七
二千一百八十一万三千三百三十四
三千八百三十一万二千二百二十四

if __name__ == '__main__':
    a = [19612368, 3002166, 80418200, 94023567, 21813334, 38312224];
    for i in range(len(a)):
        print(numberToChinese(a[i], ''));</span>

不知道到底对不对， 还是要看看[人叫板老师]怎么读吧：

<span style="font-size:18px;">>>> 
二千四百九十六
二千四百九十六万
三百零八万
四千零五十万

if __name__ == '__main__':
    a = [2496, 24960000, 3080000, 40500000];
    for i in range(len(a)):
        print(numberToChinese(a[i], ''));</span>

<span style="font-size:18px;">>>> 
五万四千六百二十一
六百四十万七千
一千零三万零四十

if __name__ == '__main__':
    a = [54621, 6407000, 10030040];
    for i in range(len(a)):
        print(numberToChinese(a[i], ''));</span>

<span style="font-size:18px;">>>> 
十万二千三百四十五 102345
二十三万零一百八十四 230184
三百零二万六千 3026000
二千零四十万零七百 20400700


###
# @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;
	
if __name__ == '__main__':
    a = ['十万二千三百四十五','二十三万零一百八十四',  '三百零二万六千', '二千零四十万零七百'];
    for i in range(len(a)):
        chineseToNumber(a[i]);</span>

<span style="font-size:18px;">>>> 
三百二十六万七千五百 3267500
四万零九十 40090
九千零二十万零三百 90200300
一百万 1000000

if __name__ == '__main__':
    a = ['三百二十六万七千五百', '四万零九十', '九千零二十万零三百', '一百万'];
    for i in range(len(a)):
        chineseToNumber(a[i]);</span>

<span style="font-size:18px;">>>> 
四千二百万 42000000
四千零七万五千七百 40075700
十二万五千 125000

if __name__ == '__main__':
    a = ['四千二百万', '四千零七万五千七百', '十二万五千'];
    for i in range(len(a)):
        chineseToNumber(a[i]);</span>

<span style="font-size:18px;">>>> 
三百六十万二千 3602000
五十四万零三百七十 540370
六万八千九百二十 68920
四千六百四十一万 46410000
十万零五 100005
一千零五十万零三十 10500030

if __name__ == '__main__':
    a = ['三百六十万二千','五十四万零三百七十',\
         '六万八千九百二十', '四千六百四十一万', '十万零五', '一千零五十万零三十'];
    for i in range(len(a)):
        chineseToNumber(a[i]);
		
>>> 
三百六十万二千
五十四万零三百七十
六万八千九百二十
四千六百四十一万
一十万零五
一千零五十万零三十

if __name__ == '__main__':
    a = [3602000, 540370, 68920,46410000,100005,10500030];
    for i in range(len(a)):
        print(numberToChinese(a[i], ''));
		
###
# @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;</span>

<span style="font-size:18px;">>>> 
二十九万九千八百 299800
二万 20000</span>

<span style="font-size:18px;">>>> 
读两个零的数字共有120个，分别是：[1020034, 1020043, 1020340, 1020430, 1023004, 1023040, 1024003, 1024030, 1030024, 1030042, 1030240, 1030420, 1032004, 1032040, 1034002, 1034020, 1040023, 1040032, 1040230, 1040320, 1042003, 1042030, 1043002, 1043020, 1200304, 1200403, 1300204, 1300402, 1400203, 1400302, 2010034, 2010043, 2010340, 2010430, 2013004, 2013040, 2014003, 2014030, 2030014, 2030041, 2030140, 2030410, 2031004, 2031040, 2034001, 2034010, 2040013, 2040031, 2040130, 2040310, 2041003, 2041030, 2043001, 2043010, 2100304, 2100403, 2300104, 2300401, 2400103, 2400301, 3010024, 3010042, 3010240, 3010420, 3012004, 3012040, 3014002, 3014020, 3020014, 3020041, 3020140, 3020410, 3021004, 3021040, 3024001, 3024010, 3040012, 3040021, 3040120, 3040210, 3041002, 3041020, 3042001, 3042010, 3100204, 3100402, 3200104, 3200401, 3400102, 3400201, 4010023, 4010032, 4010230, 4010320, 4012003, 4012030, 4013002, 4013020, 4020013, 4020031, 4020130, 4020310, 4021003, 4021030, 4023001, 4023010, 4030012, 4030021, 4030120, 4030210, 4031002, 4031020, 4032001, 4032010, 4100203, 4100302, 4200103, 4200301, 4300102, 4300201]

def tmp():
    a = [0,0,0,1,2,3,4];
    array = perm(a);
    size = len(array);
    size1 = len(array[0]);
    num = 0;
    result = set([]);

    for i in range(size):
        num = 0;
        for j in range(size1):
            num *= 10;
            num += array[i][j];

        if num >= pow(10, 6):
            s = numberToChinese(num, '');
            if (s.count('零') == 2):
                result.add(num);

    listA = list(result);
    listA.sort();
    
    print('读两个零的数字共有{0}个，分别是：{1}'.format(len(listA), listA));
	
>>> 
读一个零的数字共有264个，分别是：[1000234, 1000243, 1000324, 1000342, 1000423, 1000432, 1002034, 1002043, 1002304, 1002403, 1003024, 1003042, 1003204, 1003402, 1004023, 1004032, 1004203, 1004302, 1023400, 1024300, 1032400, 1034200, 1042300, 1043200, 1200034, 1200043, 1200340, 1200430, 1203004, 1203040, 1204003, 1204030, 1230004, 1230040, 1230400, 1240003, 1240030, 1240300, 1300024, 1300042, 1300240, 1300420, 1302004, 1302040, 1304002, 1304020, 1320004, 1320040, 1320400, 1340002, 1340020, 1340200, 1400023, 1400032, 1400230, 1400320, 1402003, 1402030, 1403002, 1403020, 1420003, 1420030, 1420300, 1430002, 1430020, 1430200, 2000134, 2000143, 2000314, 2000341, 2000413, 2000431, 2001034, 2001043, 2001304, 2001403, 2003014, 2003041, 2003104, 2003401, 2004013, 2004031, 2004103, 2004301, 2013400, 2014300, 2031400, 2034100, 2041300, 2043100, 2100034, 2100043, 2100340, 2100430, 2103004, 2103040, 2104003, 2104030, 2130004, 2130040, 2130400, 2140003, 2140030, 2140300, 2300014, 2300041, 2300140, 2300410, 2301004, 2301040, 2304001, 2304010, 2310004, 2310040, 2310400, 2340001, 2340010, 2340100, 2400013, 2400031, 2400130, 2400310, 2401003, 2401030, 2403001, 2403010, 2410003, 2410030, 2410300, 2430001, 2430010, 2430100, 3000124, 3000142, 3000214, 3000241, 3000412, 3000421, 3001024, 3001042, 3001204, 3001402, 3002014, 3002041, 3002104, 3002401, 3004012, 3004021, 3004102, 3004201, 3012400, 3014200, 3021400, 3024100, 3041200, 3042100, 3100024, 3100042, 3100240, 3100420, 3102004, 3102040, 3104002, 3104020, 3120004, 3120040, 3120400, 3140002, 3140020, 3140200, 3200014, 3200041, 3200140, 3200410, 3201004, 3201040, 3204001, 3204010, 3210004, 3210040, 3210400, 3240001, 3240010, 3240100, 3400012, 3400021, 3400120, 3400210, 3401002, 3401020, 3402001, 3402010, 3410002, 3410020, 3410200, 3420001, 3420010, 3420100, 4000123, 4000132, 4000213, 4000231, 4000312, 4000321, 4001023, 4001032, 4001203, 4001302, 4002013, 4002031, 4002103, 4002301, 4003012, 4003021, 4003102, 4003201, 4012300, 4013200, 4021300, 4023100, 4031200, 4032100, 4100023, 4100032, 4100230, 4100320, 4102003, 4102030, 4103002, 4103020, 4120003, 4120030, 4120300, 4130002, 4130020, 4130200, 4200013, 4200031, 4200130, 4200310, 4201003, 4201030, 4203001, 4203010, 4210003, 4210030, 4210300, 4230001, 4230010, 4230100, 4300012, 4300021, 4300120, 4300210, 4301002, 4301020, 4302001, 4302010, 4310002, 4310020, 4310200, 4320001, 4320010, 4320100]

>>> 
所有零都不读的数字共有72个，分别是：[1002340, 1002430, 1003240, 1003420, 1004230, 1004320, 1203400, 1204300, 1234000, 1243000, 1302400, 1304200, 1324000, 1342000, 1402300, 1403200, 1423000, 1432000, 2001340, 2001430, 2003140, 2003410, 2004130, 2004310, 2103400, 2104300, 2134000, 2143000, 2301400, 2304100, 2314000, 2341000, 2401300, 2403100, 2413000, 2431000, 3001240, 3001420, 3002140, 3002410, 3004120, 3004210, 3102400, 3104200, 3124000, 3142000, 3201400, 3204100, 3214000, 3241000, 3401200, 3402100, 3412000, 3421000, 4001230, 4001320, 4002130, 4002310, 4003120, 4003210, 4102300, 4103200, 4123000, 4132000, 4201300, 4203100, 4213000, 4231000, 4301200, 4302100, 4312000, 4321000]

def tmp():
    a = [0,0,0,1,2,3,4];
    array = perm(a);
    size = len(array);
    size1 = len(array[0]);
    num = 0;
    result = set([]);

    for i in range(size):
        num = 0;
        for j in range(size1):
            num *= 10;
            num += array[i][j];

        if num >= pow(10, 6):
            s = numberToChinese(num, '');
            if (s.count('零') == 0):
                result.add(num);

    listA = list(result);
    listA.sort();
    
    print('所有零都不读的数字共有{0}个，分别是：{1}'.format(len(listA), listA));
	
>>> 
读三个零的数字共有24个，分别是：[1020304, 1020403, 1030204, 1030402, 1040203, 1040302, 2010304, 2010403, 2030104, 2030401, 2040103, 2040301, 3010204, 3010402, 3020104, 3020401, 3040102, 3040201, 4010203, 4010302, 4020103, 4020301, 4030102, 4030201]

def tmp():
    a = [0,0,0,1,2,3,4];
    array = perm(a);
    size = len(array);
    size1 = len(array[0]);
    num = 0;
    result = set([]);

    for i in range(size):
        num = 0;
        for j in range(size1):
            num *= 10;
            num += array[i][j];

        if num >= pow(10, 6):
            s = numberToChinese(num, '');
            if (s.count('零') == 3):
                result.add(num);

    listA = list(result);
    listA.sort();
    
    print('读三个零的数字共有{0}个，分别是：{1}'.format(len(listA), listA));</span>

<span style="font-size:18px;">>>> 
七十亿
一百亿四千万二千
四千零三亿零五百万

if __name__ == '__main__':
    a = [7000000000, 10040002000, 400305000000];
    for i in range(len(a)):
        print(numberToChinese(a[i], ''));</span>

<span style="font-size:18px;">>>> 
三亿 300000000
七千零三亿零二十万 700300200000

if __name__ == '__main__':
    a = ['三亿', '七千零三亿零二十万'];
    for i in range(len(a)):
        chineseToNumber(a[i]);</span>

本节到此结束，欲知后事如何，请看下回分解。