Project Euler Problem 17 (C++和Python代码实现和解析)

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本文探讨了将1到1000的整数转换为其英文单词表示，并计算总字母数量的问题。通过分析不同数值范围的单词构成规律，设计了C++与Python代码实现方案，有效地解决了问题。

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Problem 17 : Number letter counts

If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.

If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?

NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of “and” when writing out numbers is in compliance with British usage.

1. 数的字母计数

如果从1到5的数是用单词写出来：one, two, three, four, five，那么总共使用的字母为 3 + 3 + 5 + 4 + 4 = 19。

如果从1到1000的所有数（含1000）用单词写出来，用到多少个字母呢？

注意：不要计算空格或连字符。例如，342 (three hundred and forty-two) 包含23个字母，115 (one hundred and fifteen) 包含20个字母。在写出数时，要使用“and”以符合英国用法。

2. 求解分析

首先，我们要知道1到1000个数用英语单词写出来的所有类型：
“one”, “two”, “three”, “four”, “five”, “six”, “seven”,“eight”, “nine”, “ten”, “eleven”, “twelve”, “thirteen”, “fourteen”,“fifteen”,“sixteen”, “seventeen”, “eighteen”, “nineteen”, “twenty”,“thirty”, “forty”, “fifty”, “sixty”, “seventy”, “eighty”, “ninety”,“hundred”, “thousand”, “and”

另外，要搞清楚每个数用单词写出的方法，主要是使用"and"。

然后，每种单词的字母个数可以在先算出来，保存在一个数组里，最后组合以下就算出最后的字母的个数。

3. C++ 代码实现

类PE0017的类图如下：
在这里插入图片描述

全局变量numberString 是字符串数组，保存所有32种关键字字符串。
成员变量m_digits[]用于保存每个数的数字，最多四个。成员变量m_lettersArray[]用来保存32种类型的字符数。
成员函数 getDigitsOfNumber(int number) 把数number的取每一位，结果保存在成员变量数组m_digits里。
成员函数 getUnitValue() 返回个位数的数字。
成员函数 getDecadeValue() 返回十位数的数字。
成员函数 getHundredValue() 返回百位数的数字。
构造函数PE0017() 遍历所有全局字符串数组 numberString，给成员变量m_lettersArray赋初值。
成员函数 getLettersSumOfNumber(int number) 计算一个数number的字符个数。
成员函数 getSumOfLetters(int max_number) 统计从1到max_number的所有数的字母个数。

C++ 代码

#include <iostream>
#include <vector>
#include <string>
#include <cassert>

using namespace std;

const int max_types = 32;
string numberString[max_types]={"", "one", "two", "three", "four", "five",
"six", "seven","eight", "nine", "ten", "eleven", "twelve", "thirteen", 
"fourteen","fifteen","sixteen", "seventeen", "eighteen", "nineteen", 
"twenty","thirty", "forty", "fifty", "sixty", "seventy", "eighty", 
"ninety","hundred", "thousand", "and"};

/*
#define C_blank 0  // blank
#define C_1     1  // one
#define C_2     2  // two
#define C_3     3  // three
#define C_4     4  // four
#define C_5     5  // five
#define C_6     6  // six
#define C_7     7  // seven
#define C_8     8  // eight
#define C_9     9  // nine

#define C_10    10  // ten
#define C_11    11  // eleven
#define C_12    12  // twelve
#define C_13    13  // thirteen
#define C_14    14  // fourteen
#define C_15    15  // fifteen
#define C_16    16  // sixteen
#define C_17    17  // seventeen
#define C_18    18  // eighteen
#define C_19    19  // nineteen

#define C_20    20  // twenty
#define C_30    21  // thirty 
#define C_40    22  // forty
#define C_50    23  // fifty
#define C_60    24  // sixty
#define C_70    25  // seventy
#define C_80    26  // eighty
#define C_90    27  // ninety
#define C_100   28  // hundred
#define C_1000  29  // thousand 
#define C_and   30  // and

#define C_MAX   C_and
*/

class PE0017
{
private:
    static const int max_digits = 4;
    static const int C_1    = 1;
    static const int C_19   = 19;
    static const int C_100  = 28;
    static const int C_1000 = 29;
    static const int C_and  = 30;

    int m_digits[max_digits];
    int m_lettersArray[max_types];

    void getDigitsOfNumber(int number);
    int getUnitValue()    { return m_digits[0]; }
    int getDecadeValue()  { return m_digits[1]; }
    int getHundredValue() { return m_digits[2]; }
    
public:
    PE0017();
    int getLettersSumOfNumber(int number);
    int getSumOfLetters(int max_number);
};

PE0017::PE0017()
{
    for (int i=0; i<max_types; i++)
    {
        m_lettersArray[i] = numberString[i].size();
    }
}

void PE0017::getDigitsOfNumber(int number)
{
    memset(m_digits, 0, sizeof(m_digits));

    int i = 0;
    while(number > 0)
    {
        m_digits[i++] = number%10;
        number /= 10;
    }
}

int PE0017::getLettersSumOfNumber(int number)
{
    getDigitsOfNumber(number);

    int unitDigit    = getUnitValue();
    int decadeDigit  = getDecadeValue();
    int hundredDigit = getHundredValue();    

    int sumOfLetters = 0;

    if (1000 == number)
    {
        sumOfLetters += m_lettersArray[C_1000] + m_lettersArray[C_1];
    }
    else
    {
        if (hundredDigit > 0) 
        {
            sumOfLetters += m_lettersArray[hundredDigit]+m_lettersArray[C_100];
            if (decadeDigit+unitDigit > 0)
            {
                sumOfLetters += m_lettersArray[C_and]; 
            }
        }

        if (decadeDigit > 1) 
        {
            sumOfLetters += m_lettersArray[decadeDigit+C_19-1];
        }
        else if (decadeDigit == 1)
        {
            sumOfLetters += m_lettersArray[10+unitDigit];
        }

        if (unitDigit > 0 && decadeDigit != 1) 
        {
            sumOfLetters += m_lettersArray[unitDigit];
        }
    }

    return  sumOfLetters;  
}

int PE0017::getSumOfLetters(int max_number)
{
    int sumOfLetters = 0;

    for(int i=1; i<=max_number; i++)
    {
        sumOfLetters += getLettersSumOfNumber(i);
    }
    return sumOfLetters;
}

int main()
{
    PE0017 pe0017;

    assert(20 == pe0017.getLettersSumOfNumber(115));

    int sumOfLetters = pe0017.getSumOfLetters(1000);
    
    cout << "The letters "<<sumOfLetters<<" are used for all the numbers "<<endl;
    cout << "from 1 to 1000 (one thousand) inclusive in words." << endl; 

    return 0;
}

4. Python 代码实现

Python和C++采用一样的实现方法。虽然方法没有什么巧妙，但还是很实用和易懂的。

Python 代码

def getDigits(number):
    digits = [0]*4
    numOfDigits = 0
    while number >= 1:                           
        digits[numOfDigits] = number%10
        number      /= 10
        numOfDigits += 1
    return digits
        
def getLettersSumOfNumber(number):
    """
    C_blank = 0   # blank
    C_1 =     1   # one
    C_2 =     2   # two
    C_3 =     3   # three
    C_4 =     4   # four
    C_5 =     5   # five
    C_6 =     6   # six
    C_7 =     7   # seven
    C_8 =     8   # eight
    C_9 =     9   # nine
    C_10 =    10  # ten
    C_11 =    11  # eleven
    C_12 =    12  # twelve
    C_13 =    13  # thirteen
    C_14 =    14  # fourteen
    C_15 =    15  # fifteen
    C_16 =    16  # sixteen
    C_17 =    17  # seventeen
    C_18 =    18  # eighteen
    C_19 =    19  # nineteen
    C_20 =    20  # twenty
    C_30 =    21  # thirty 
    C_40 =    22  # forty
    C_50 =    23  # fifty
    C_60 =    24  # sixty
    C_70 =    25  # seventy
    C_80 =    26  # eighty
    C_90 =    27  # ninety
    C_100 =   28  # hundred
    C_1000 =  29  # thousand 
    C_and  =  30  # and
    """
    numberString = ["", "one", "two", "three", "four", "five",
        "six", "seven","eight", "nine", "ten", "eleven", "twelve", "thirteen", 
        "fourteen","fifteen","sixteen", "seventeen", "eighteen", "nineteen", 
        "twenty","thirty", "forty", "fifty", "sixty", "seventy", "eighty", 
        "ninety","hundred", "thousand", "and"]
    
    letters_list = [ len(item) for item in numberString ]
    
    digits = getDigits(number)

    unitDigit    = int(digits[0])
    decadeDigit  = int(digits[1])
    hundredDigit = int(digits[2])

    sumOfLetters = 0

    C_1, C_19, C_100, C_1000, C_and = 1, 19, 28, 29, 30

    if 1000 == number:
        sumOfLetters += letters_list[C_1000] + letters_list[C_1]
    else:
        if hundredDigit > 0:
            sumOfLetters += letters_list[hundredDigit]+letters_list[C_100]
            if decadeDigit+unitDigit > 0:
                sumOfLetters += letters_list[C_and]

        if decadeDigit > 1: 
            sumOfLetters += letters_list[decadeDigit+C_19-1]
        elif decadeDigit == 1:
            sumOfLetters += letters_list[10+unitDigit]

        if unitDigit > 0 and decadeDigit != 1:
            sumOfLetters += letters_list[unitDigit]

    return  sumOfLetters

def getSumOfLetters(max_number):
    sumOfLetters = 0;
    for i in range (1, max_number+1):
        sumOfLetters += getLettersSumOfNumber(i)
    return sumOfLetters
    
def main():
    assert 20 == getLettersSumOfNumber(115)
    assert 23 == getLettersSumOfNumber(342)
    print("The letters", getSumOfLetters(1000), "are used for all the numbers ")
    print("from 1 to 1000 (one thousand) inclusive in words.") 

if  __name__ == '__main__':
    main()