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

# Problem 34: Digit factorials

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 #ifdefs 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:

Input data (separated by spaces or newlines):

This is equivalent to
echo 145 | ./34

Output:

(please click 'Go !')

(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

# Hackerrank

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.

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)
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:

 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
The 133 solved problems had an average difficulty of 16.9% at Project Euler and I scored 11,174 points (out of 12300) at Hackerrank's Project Euler+.
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