<< 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.
Interactive test
You can submit your own input to my program and it will be instantly processed at my server:
This is equivalent toecho 145 | ./34
Output:
(this interactive test is still under development, computations will be aborted after one second)
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.
Benchmark
The correct solution to the original Project Euler problem was found in 0.05 seconds on an Intel® Core™ i7-2600K CPU @ 3.40GHz.
(compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++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:
C# www.mathblog.dk/project-euler-34-factorial-digits/ (written by Kristian Edlund)
C github.com/eagletmt/project-euler-c/blob/master/30-39/problem34.c (written by eagletmt)
Java github.com/nayuki/Project-Euler-solutions/blob/master/java/p034.java (written by Nayuki)
Javascript github.com/dsernst/ProjectEuler/blob/master/34 Digit factorials.js (written by David Ernst)
Mathematica github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p034.mathematica (written by Nayuki)
Haskell github.com/nayuki/Project-Euler-solutions/blob/master/haskell/p034.hs (written by Nayuki)
Scala github.com/samskivert/euler-scala/blob/master/Euler034.scala (written by Michael Bayne)
Perl github.com/gustafe/projecteuler/blob/master/034-Digit-factorials.pl (written by Gustaf Erikson)
Those links are just an unordered selection of source code I found with a semi-automatic search script on Google/Bing/GitHub/whatever.
You will probably stumble upon better solutions when searching on your own.
Maybe not all linked resources produce the correct result and/or exceed time/memory limits.
Heatmap
Please click on a problem's number to open my solution to that problem:
green | solutions solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too | |
yellow | solutions score less than 100% at Hackerrank (but still solve the original problem easily) | |
gray | problems are already solved but I haven't published my solution yet | |
blue | solutions are relevant for Project Euler only: there wasn't a Hackerrank version of it (at the time I solved it) or it differed too much | |
orange | problems are solved but exceed the time limit of one minute or the memory limit of 256 MByte | |
red | problems are not solved yet but I wrote a simulation to approximate the result or verified at least the given example - usually I sketched a few ideas, too | |
black | problems are solved but access to the solution is blocked for a few days until the next problem is published | |
[new] | the flashing problem is the one I solved most recently |
I stopped working on Project Euler problems around the time they released 617.
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I scored 13526 points (out of 15700 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+.
My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.
Look at my progress and performance pages to get more details.
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 >> |