<< problem 19 - Counting Sundays Amicable numbers - problem 21 >>

# Problem 20: Factorial digit sum

n! means n * (n - 1) * ... * 3 * 2 * 1

For example, 10! = 10 * 9 * ... * 3 * 2 * 1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.

Find the sum of the digits in the number 100!

# Algorithm

Substantial parts are similar to problem 16.
The most obvious difference is that carry may become bigger than 1.

## Modifications by HackerRank

Compared to problem 16, timeouts were no issue and therefore the code is actually more compact.

# My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too.

       #include <iostream>
#include <vector>

// store single digits in an array, lowest digit come first
typedef std::vector<unsigned int> Digits;

// return factorial
Digits factorial(unsigned int maxFactor)
{
// 1! = 1
Digits result = { 1 };

// avoid further memory allocations
result.reserve(2568); // 1000! has 2568 digits

// go through all factors
for (unsigned int factor = 2; factor <= maxFactor; factor++)
{
// multiply each digit with current factor
// might overflow into next digit => carry
unsigned int carry = 0;
for (auto& digit : result)
{
digit = digit * factor + carry;

// overflow ?
if (digit >= 10)
{
carry  = digit / 10;
digit %= 10;
}
else
carry  = 0;
}

while (carry != 0)
{
result.push_back(carry % 10);
carry /= 10;
}
}
return result;
}

int main()
{
unsigned int tests;
std::cin >> tests;
while (tests--)
{
unsigned int number;
std::cin >> number;

// add all digits of the factorial
unsigned int sum = 0;
for (auto i : factorial(number))
sum += i;
std::cout << sum << std::endl;
}
return 0;
}


This solution contains 8 empty lines, 10 comments and 2 preprocessor commands.

# Interactive test

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

Number of test cases (1-5):

Input data (separated by spaces or newlines):

This is equivalent to
echo "1 6" | ./20

Output:

Note: the original problem's input 100 cannot be entered
because just copying results is a soft skill reserved for idiots.

(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

# Hackerrank

My code solved 4 out of 4 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 16: Power digit sum

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=20 - 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-20-sum-digits/ (written by Kristian Edlund)
Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p020.java (written by Nayuki)
Mathematica: github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p020.mathematica (written by Nayuki)
C: github.com/eagletmt/project-euler-c/blob/master/20-29/problem20.c (written by eagletmt)
Go: github.com/frrad/project-euler/blob/master/golang/Problem020.go (written by Frederick Robinson)
Javascript: github.com/dsernst/ProjectEuler/blob/master/20 Factorial digit sum.js (written by David Ernst)
Scala: github.com/samskivert/euler-scala/blob/master/Euler020.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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 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 126 solved problems had an average difficulty of 16.0% at Project Euler and I scored 11,074 points (out of 12500) at Hackerrank's Project Euler+.
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