<< 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.

# My 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(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 solves **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 rarely 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 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.

red problems are solved but exceed the time limit of one minute or the memory limit of 256 MByte.

*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 |

201 | 202 | 203 | 204 | 205 | 206 | 207 | 208 | 209 | 210 | 211 | 212 | 213 | 214 | 215 | 216 | 217 | 218 | 219 | 220 | 221 | 222 | 223 | 224 | 225 |

226 | 227 | 228 | 229 | 230 | 231 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239 | 240 | 241 | 242 | 243 | 244 | 245 | 246 | 247 | 248 | 249 | 250 |

251 | 252 | 253 | 254 | 255 | 256 | 257 | 258 | 259 | 260 | 261 | 262 | 263 | 264 | 265 | 266 | 267 | 268 | 269 | 270 | 271 | 272 | 273 | 274 | 275 |

276 | 277 | 278 | 279 | 280 | 281 | 282 | 283 | 284 | 285 | 286 | 287 | 288 | 289 | 290 | 291 | 292 | 293 | 294 | 295 | 296 | 297 | 298 | 299 | 300 |

301 | 302 | 303 | 304 | 305 | 306 | 307 | 308 | 309 | 310 | 311 | 312 | 313 | 314 | 315 | 316 | 317 | 318 | 319 | 320 | 321 | 322 | 323 | 324 | 325 |

326 | 327 | 328 | 329 | 330 | 331 | 332 | 333 | 334 | 335 | 336 | 337 | 338 | 339 | 340 | 341 | 342 | 343 | 344 | 345 | 346 | 347 | 348 | 349 | 350 |

351 | 352 | 353 | 354 | 355 | 356 | 357 | 358 | 359 | 360 | 361 | 362 | 363 | 364 | 365 | 366 | 367 | 368 | 369 | 370 | 371 | 372 | 373 | 374 | 375 |

376 | 377 | 378 | 379 | 380 | 381 | 382 | 383 | 384 | 385 | 386 | 387 | 388 | 389 | 390 | 391 | 392 | 393 | 394 | 395 | 396 | 397 | 398 | 399 | 400 |

401 | 402 | 403 | 404 | 405 | 406 | 407 | 408 | 409 | 410 | 411 | 412 | 413 | 414 | 415 | 416 | 417 | 418 | 419 | 420 | 421 | 422 | 423 | 424 | 425 |

426 | 427 | 428 | 429 | 430 | 431 | 432 | 433 | 434 | 435 | 436 | 437 | 438 | 439 | 440 | 441 | 442 | 443 | 444 | 445 | 446 | 447 | 448 | 449 | 450 |

451 | 452 | 453 | 454 | 455 | 456 | 457 | 458 | 459 | 460 | 461 | 462 | 463 | 464 | 465 | 466 | 467 | 468 | 469 | 470 | 471 | 472 | 473 | 474 | 475 |

476 | 477 | 478 | 479 | 480 | 481 | 482 | 483 | 484 | 485 | 486 | 487 | 488 | 489 | 490 | 491 | 492 | 493 | 494 | 495 | 496 | 497 | 498 | 499 | 500 |

501 | 502 | 503 | 504 | 505 | 506 | 507 | 508 | 509 | 510 | 511 | 512 | 513 | 514 | 515 | 516 | 517 | 518 | 519 | 520 | 521 | 522 | 523 | 524 | 525 |

526 | 527 | 528 | 529 | 530 | 531 | 532 | 533 | 534 | 535 | 536 | 537 | 538 | 539 | 540 | 541 | 542 | 543 | 544 | 545 | 546 | 547 | 548 | 549 | 550 |

I scored 13,183 points (out of 15300 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+.

Look at my progress and performance pages to get more details.

My username at Project Euler is

**stephanbrumme**while it's stbrumme at Hackerrank.

# Copyright

I hope you enjoy my code and learn something - or give me feedback how I can improve my solutions.

All of my solutions can be used for any purpose and I am in no way liable for any damages caused.

You can even remove my name and claim it's yours. But then you shall burn in hell.

The problems and most of the problems' images were created by Project Euler.

Thanks for all their endless effort.

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