<< problem 33 - Digit cancelling fractions | Circular primes - problem 35 >> |

# Problem 34: Digit factorials

(see projecteuler.net/problem=34)

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

*Note:* as 1! = 1 and 2! = 2 are not sums they are not included.

# My Algorithm

This problem is very similar to problem 30.

There is no 8-digit number which can be the sum of the factorials of its digits because 8 * 9! = 2903040 is a 7-digit number.

I precomputed the factorials 0! to 9! instead of writing a short and simple *factorial* function.

Each number is split into its digits (again I begin with the least-significant, "I chop them from the right side")

and then the factorial of these digits is looked up and added.

Nothing spectacular - a very easy problem.

## Modifications by HackerRank

The sums must be divisible by the number, not equal.

# My code

… was written in C++ 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>
int main()
{
// precompute factorials of all possible digits 0!..9!
const unsigned int factorials[] = { 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 };
// no more than 7*9! = 2540160 for the original problem
unsigned int limit;
std::cin >> limit;
// result (differs for Hackerrank modified problem !)
unsigned int result = 0;
for (unsigned int i = 10; i < limit; i++)
{
unsigned int sum = 0;
// split i into its digits
unsigned int x = i;
while (x > 0)
{
// add factorial of the right-most digit
sum += factorials[x % 10];
// remove that digit
x /= 10;
}
#define ORIGINAL
#ifdef ORIGINAL
// equal ?
if (sum == i)
result += i;
#else
// divisible ?
if (sum % i == 0)
result += i;
#endif
}
std::cout << result << std::endl;
return 0;
}

This solution contains 7 empty lines, 8 comments and 5 preprocessor commands.

# Interactive test

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

This is equivalent to`echo 145 | ./34`

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 0.05 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 23, 2017 submitted solution

April 6, 2017 added comments

# Hackerrank

see https://www.hackerrank.com/contests/projecteuler/challenges/euler034

My code solves **5** out of **5** 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.

# Similar problems at Project Euler

Problem 30: Digit fifth powers

*Note:* I'm not even close to solving all problems at Project Euler. Chances are that similar problems do exist and I just haven't looked at them.

# Links

projecteuler.net/thread=34 - **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-34-factorial-digits/ (written by Kristian Edlund)

Haskell: github.com/nayuki/Project-Euler-solutions/blob/master/haskell/p034.hs (written by Nayuki)

Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p034.java (written by Nayuki)

Mathematica: github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p034.mathematica (written by Nayuki)

C: github.com/eagletmt/project-euler-c/blob/master/30-39/problem34.c (written by eagletmt)

Javascript: github.com/dsernst/ProjectEuler/blob/master/34 Digit factorials.js (written by David Ernst)

Scala: github.com/samskivert/euler-scala/blob/master/Euler034.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:*

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I scored 12,983 points (out of 15100 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 33 - Digit cancelling fractions | Circular primes - problem 35 >> |