<< problem 16 - Power digit sum | Maximum path sum I - problem 18 >> |

# Problem 17: Number letter counts

(see projecteuler.net/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.

# Algorithm

My program converts a number into its "written" representation because of the Hackerrank requirements (see below).

A simple loop from 1 to 1000 creates a ton of string and computes the sums their lengths.

The function `convert`

immediately returns the name of numbers in [0;19].

For all other numbers it calls itself recursively:

e.g. when the parameter `x`

is in [20;99] then its higher digit is converted directly into a word, its lower is found by a recursive call

My code is a bit bloated because of spelling differences between Project Euler and Hackerrank.

I had to be a bit careful not to call the function `convert`

recursively with parameter zero.

## Alternative Approaches

The original problem can be solved by just counting the letter without actually "building" the names, too.

## Modifications by HackerRank

The Hackerrank problem is quite different: you have to convert a number into its name.

Their spelling rules vary, too.

*Note:* Unlike most of my other programs, `#define ORIGINAL`

is not active in the source code listing due to interactive tests.

## Note

Rules for finding the English names of numbers have far less exceptions than the German rules ...

# My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too.

The code contains `#ifdef`

s to switch between the original problem and the Hackerrank version.

Enable `#ifdef ORIGINAL`

to produce the result for the original problem (default setting for most problems).

#include <iostream>
#include <string>
// customize code for original problem
//#define ORIGINAL

// convert a number into its written representation

std::string convert(unsigned long long x)
{
#ifdef ORIGINAL
const std::string Gap = " And "; // British
const std::string ConnectTensAndOnes = "-";
#else
const std::string Gap = " ";
const std::string ConnectTensAndOnes = " ";
#endif
// none-composite names
switch">switch(x)
{
case 0: return "Zero";
case 1: return "One";
case 2: return "Two";
case 3: return "Three";
case 4: return "Four";
case 5: return "Five";
case 6: return "Six";
case 7: return "Seven";
case 8: return "Eight";
case 9: return "Nine";
case 10: return "Ten";
case 11: return "Eleven";
case 12: return "Twelve";
case 13: return "Thirteen";
case 14: return "Fourteen";
case 15: return "Fifteen";
case 16: return "Sixteen";
case 17: return "Seventeen";
case 18: return "Eighteen";
case 19: return "Nineteen";
default: break;
}
// two-digit composite names
if (x >= 20 && x < 100)
{
auto ones = x % 10;
auto tens = x / 10;
auto strOnes = (ones != 0) ? ConnectTensAndOnes + convert(ones) : "";
switch (tens)
{
case 2: return "Twenty" + strOnes;
case 3: return "Thirty" + strOnes;
case 4: return "Forty" + strOnes; // <= often misspelt/misspelled ;)
case 5: return "Fifty" + strOnes;
case 6: return "Sixty" + strOnes;
case 7: return "Seventy" + strOnes;
case 8: return "Eighty" + strOnes;
case 9: return "Ninety" + strOnes;
default: break; // never reached
}
}
// three-digit composite names
if (x >= 100 && x < 1000)
{
auto onesAndTens = x % 100;
auto hundreds = x / 100;
auto strOnesAndTens = (onesAndTens != 0) ? Gap + convert(onesAndTens) : "";
return convert(hundreds) + " Hundred" + strOnesAndTens;
}
// four to six digits
if (x >= 1000 && x < 1000000)
{
auto low = x % 1000; // variable names got too long, I went for a generic one ...
auto high = x / 1000;
auto strLow = (low != 0) ? Gap + convert(low) : "";
return convert(high) + " Thousand" + strLow;
}
// seven to nine digits
if (x >= 1000000 && x < 1000000000)
{
auto low = x % 1000000;
auto high = x / 1000000;
auto strLow = (low != 0) ? Gap + convert(low) : "";
return convert(high) + " Million" + strLow;
}
// ten to twelve digits
if (x >= 1000000000 && x < 1000000000000ULL) // careful: must be a 64 bit constant, add "LL"
{
auto low = x % 1000000000;
auto high = x / 1000000000;
auto strLow = (low != 0) ? Gap + convert(low) : "";
return convert(high) + " Billion" + strLow;
}
// thirteen to fifteen digits
if (x >= 1000000000000ULL && x < 1000000000000000ULL)
{
auto low = x % 1000000000000ULL;
auto high = x / 1000000000000ULL;
auto strLow = (low != 0) ? Gap + convert(low) : "";
return convert(high) + " Trillion" + strLow;
}
// not reached
return "?";
}
int main()
{
#ifdef ORIGINAL
// count number of letters
unsigned int sum = 0;
for (unsigned int i = 1; i <= 1000; i++)
{
auto name = convert(i);
for (auto c : name)
if (std::isalpha(c)) // discard spaces/hyphens/etc.
sum++;
}
std::cout << sum << std::endl;
#else
// just print several names according to input
unsigned int tests;
std::cin >> tests;
while (tests--)
{
unsigned long long x;
std::cin >> x;
std::cout << convert(x) << std::endl;
}
#endif
return 0;
}

This solution contains 11 empty lines, 13 comments and 8 preprocessor commands.

# Interactive test

You can submit your own input to my program and it will be instantly processed at my server:

This live test is based on the Hackerrank problem.

This is equivalent to`echo "1 17" | ./17`

Output:

*(this interactive test is still under development, computations will be aborted after one second)*

# Benchmark

The correct solution to the original Project Euler problem was found in **less than 0.01** seconds on a Intel® Core™ i7-2600K CPU @ 3.40GHz.

(compiled for x86_64 / Linux, GCC flags: `-O3 -march=native -fno-exceptions -fno-rtti -std=c++11 -DORIGINAL`

)

See here for a comparison of all solutions.

**Note:** interactive tests run on a weaker (=slower) computer. Some interactive tests are compiled without `-DORIGINAL`

.

# Changelog

February 24, 2017 submitted solution

April 3, 2017 added comments

# Hackerrank

see https://www.hackerrank.com/contests/projecteuler/challenges/euler017

My code solved **6** out of **6** test cases (score: **100%**)

# Difficulty

Project Euler ranks this problem at **5%** (out of 100%).

Hackerrank describes this problem as **easy**.

*Note:*

Hackerrank has strict execution time limits (typically 2 seconds for C++ code) and often a much wider input range than the original problem.

In my opinion, Hackerrank's modified problems are usually a lot harder to solve. As a rule thumb: brute-force is never an option.

# Links

projecteuler.net/thread=17 - **the** best forum on the subject (*note:* you have to submit the correct solution first)

Code in various languages:

Python: www.mathblog.dk/project-euler-17-letters-in-the-numbers-1-1000/ (written by Kristian Edlund)

Haskell: github.com/nayuki/Project-Euler-solutions/blob/master/haskell/p017.hs (written by Nayuki)

Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p017.java (written by Nayuki)

Mathematica: github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p017.mathematica (written by Nayuki)

C: github.com/eagletmt/project-euler-c/blob/master/10-19/problem17.c (written by eagletmt)

Go: github.com/frrad/project-euler/blob/master/golang/Problem017.go (written by Frederick Robinson)

Javascript: github.com/dsernst/ProjectEuler/blob/master/17 Number letter counts.js (written by David Ernst)

Scala: github.com/samskivert/euler-scala/blob/master/Euler017.scala (written by Michael Bayne)

# Heatmap

green problems solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too.

yellow problems score less than 100% at Hackerrank (but still solve the original problem).

gray problems are already solved but I haven't published my solution yet.

blue problems are already solved and there wasn't a Hackerrank version of it (at the time I solved it) or I didn't care about it because it differed too much.

*Please click on a problem's number to open my solution to that problem:*

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |

26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 |

76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | 125 |

126 | 127 | 128 | 129 | 130 | 131 | 132 | 133 | 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 | 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 |

151 | 152 | 153 | 154 | 155 | 156 | 157 | 158 | 159 | 160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 | 172 | 173 | 174 | 175 |

176 | 177 | 178 | 179 | 180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 190 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | 200 |

<< problem 16 - Power digit sum | Maximum path sum I - problem 18 >> |