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我一直在尝试解决 Euler 17 并且遇到了一些麻烦。该问题的定义是：

如果数字 1 到 5 用单词写出：一、二、三、四、五，那么总共使用了 3 + 3 + 5 + 4 + 4 = 19 个字母。

如果用文字写出从 1 到 1000（一千）的所有数字，将使用多少个字母？

注意：不要计算空格或连字符。例如，342（三百四十二）包含 23 个字母，而 115（一百一十五）包含 20 个字母。在写出数字时使用“and”符合英国的用法。

我是用 Python 写的，代码看了三四遍还是看不出问题出在哪里。它很长（我刚开始学习python，以前从未编码过），但我基本上只是定义了不同的函数，它们采用不同的位数并计算每个字母的数量。我最终得到 21254，看起来实际答案是 21124，所以我正好相差 130。任何帮助将不胜感激。

# create dict mapping numbers to their
# lengths in English

maps = {}
maps[0] = 0
maps[1] = 3
maps[2] = 3
maps[3] = 5
maps[4] = 4
maps[5] = 4
maps[6] = 3
maps[7] = 5
maps[8] = 5
maps[9] = 4
maps[10] = 3
maps[11] = 6
maps['and'] = 3
maps['teen'] = 4
maps[20] = 6
maps[30] = 6
maps[40] = 5
maps[50] = 5
maps[60] = 6
maps[70] = 7
maps[80] = 6
maps[90] = 6
maps[100] = 7
maps[1000] = 8

# create a list of numbers 1-1000
def int_to_list(number):
    s = str(number)
    c = []
    for digit in s:
        a = int(digit)
        c.append(a)
    return c  # turn a number into a list of its digits
def list_to_int(numList):
    s = map(str, numList)
    s = ''.join(s)
    s = int(s)
    return s


L = []
for i in range(1,1001,1):
    L.append(i)

def one_digit(n):
    q = maps[n]
    return q
def eleven(n):
    q = maps[11]
    return q
def teen(n):
    digits = int_to_list(n) 
    q = maps[digits[1]] + maps['teen']
    return q
def two_digit(n):
    digits = int_to_list(n)
    first = digits[0]
    first = first*10
    second = digits[1]
    q = maps[first] + one_digit(second)
    return q
def three_digit(n):
    digits = int_to_list(n)
    first = digits[0]
    second = digits[1]
    third = digits[2]

    # first digit length
    f = maps[first]+maps[100]

    if second == 1 and third == 1:
        s = maps['and'] + maps[11]
    elif second == 1 and third != 1:
        s = digits[1:]
        s = list_to_int(s)
        s = maps['and'] + teen(s)
    elif second == 0 and third == 0:
        s = maps[0]
    elif second == 0 and third != 0:
        s = maps['and'] + maps[third]
    else:
        s = digits[1:]
        s = list_to_int(s)
        s = maps['and'] + two_digit(s)

    q = f + s
    return q
def thousand(n):
    q = maps[1000]
    return q

# generate a list of all the lengths of numbers

lengths = []


for i in L:
    if i < 11:
        n = one_digit(i)
        lengths.append(n)
    elif i == 11:
        n = eleven(i)
        lengths.append(n)
    elif i > 11 and i < 20:
        n = teen(i)
        lengths.append(n)
    elif i > 20 and i < 100:
        n = two_digit(i)
        lengths.append(n)
    elif i >= 100 and i < 1000:
        n = three_digit(i)
        lengths.append(n)
    elif i == 1000:
        n = thousand(i)
        lengths.append(n)
    else:
        pass

# since "eighteen" has eight letters (not 9), subtract 10
sum = sum(lengths) - 10
print "Your number is: ", sum
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1 回答 1

9

解释差异

您的代码充满了错误：

  1. 这是错误的：

    maps[60] = 6

    对错误的贡献：+100（因为它影响 60 到 69、160 到 169、...、960 到 969）。

  2. 有几个少年误会了：

    >>> teen(12)
7
>>> teen(13)
9
>>> teen(15)
8
>>> teen(18)
9

    对错误的贡献：+40（因为它影响 12、13、...、112、113、...、918）

  3. 以及任意数量的 x10 形式：

    >>> three_digit(110)
17

    对错误的贡献：9（因为 110、210、... 910）

  4. 数字 20 不计入（您考虑i < 20但i > 20不考虑i == 20）。

    对误差的贡献：-6

  5. 数字 1000 用英语写成“一千”，但是：

    >>> thousand(1000)
8

    对误差的贡献：-3

  6. 最后减去 10 以弥补其中一个错误。

    对误差的贡献：-10

总误差：100 + 40 + 9 - 6 - 3 - 10 = 130。

你怎么能避免这些错误

通过尝试直接处理字母计数，您很难检查自己的工作。“一百一十”又有多少个字母？是17还是16？如果您采用了这样的策略，那么测试您的工作会容易得多：

unit_names = """zero one two three four five six seven eight nine ten
                eleven twelve thirteen fourteen fifteen sixteen seventeen
                eighteen nineteen""".split()
tens_names = """zero ten twenty thirty forty fifty sixty seventy eighty
                ninety""".split()

def english(n):
    "Return the English name for n, from 0 to 999999."
    if n >= 1000:
        thous = english(n // 1000) + " thousand"
        n = n % 1000
        if n == 0:
            return thous
        elif n < 100:
            return thous + " and " + english(n)
        else:
            return thous + ", " + english(n)
    elif n >= 100:
        huns = unit_names[n // 100] + " hundred"
        n = n % 100
        if n == 0:
            return huns
        else:
            return huns + " and " + english(n)
    elif n >= 20:
        tens = tens_names[n // 10]
        n = n % 10
        if n == 0:
            return tens
        else:
            return tens + "-" + english(n)
    else:
        return unit_names[n]

def letter_count(s):
    "Return the number of letters in the string s."
    import re
    return len(re.findall(r'[a-zA-Z]', s))

def euler17():
    return sum(letter_count(english(i)) for i in range(1, 1001))

使用这种方法可以更轻松地检查您的结果：

>>> english(967)
'nine hundred and sixty-seven'
于 2012-09-28T20:57:05.520 回答