<< 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.

# 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 solved **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 never 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 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:*

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