[Project Euler] Problem 17

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.

 

我们先来看看数字有什么规律吧

0：null           10：ten            20：twenty            ......           100：one hundred

1：one          11：eleven        21：twenty-one      ......           101：one hundred and one

2：two          12：twelve        22：twenty-two      ......           102：one hundred and two

.........

 

1000 one thousand

 

可以看出当十位是1时，要单独考虑。

当十位数不是1时，是在十位数的基础上加上各位数的长度

当有百位数时，百位由百位上的数加上hundred and

为整百时，会少一个and

 

 

所以编程如下

#include < iostream >
using namespace std;

int main(){
int letters = 0 ;
const int Unit[ 10 ] = { 0 , 3 , 3 , 5 , 4 , 4 , 3 , 5 , 5 , 4 };
const int Tens[ 10 ] = { 0 , 0 , 6 , 6 , 5 , 5 , 5 , 7 , 6 , 6 };
const int Tensone[ 10 ] = { 3 , 6 , 6 , 8 , 8 , 7 , 7 , 9 , 8 , 8 };
for ( int i = 1 ;i < 1000 ;i ++ ){
if (i / 10 % 10 == 1 ){
letters = letters + Tensone[i % 10 ];
} else {
letters = letters + Unit[i % 10 ];
letters += Tens[i / 10 % 10 ];
}
if (i / 100 > 0 ){
if (i % 100 == 0 ){
letters += Unit[i / 100 ] + 7 ;
} else {
letters += Unit[i / 100 ] + 10 ;
}
}
}
letters += 11 ;
cout << letters << endl;
return 0 ;
}

 

这道题就是要考虑完所有特殊情况