Problem 10: Summation of primes

(see projecteuler.net/problem=10)

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.

Algorithm

The prime sieve is more or less unchanged from problem 7.
Then I create a lookup table sums which contains for each prime number p
the sum of all prime numbers <=p.

The test cases may contain numbers which are not prime, too.
Therefore I use upper_bound to find the smallest entry which >=p.
And since we that entry "is one step too far", I go back to the previous entry and print it.

Modifications by HackerRank

My 2-step design was heavily influenced by Hackerrank's large number of test cases:
the "expensive" precomputation is done once and the test cases are computationally very "cheap".

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>
#include <map>
 
int main()
{
// prime numbers beyond this are not relevant for the problem
const unsigned int MaxPrime = 2000000;
 
// precompute all relevant prime numbers
std::vector<unsigned int> primes;
// the only even prime
primes.push_back(2);
// now check all odd numbers for primality
for (unsigned int i = 3; i <= MaxPrime; i += 2)
{
bool isPrime = true;
for (auto p : primes)
{
// no larger prime factor possible ?
if (p*p > i)
break;
 
// no prime number ?
if (i % p == 0)
{
isPrime = false;
break;
}
}
 
// yes, we have a new prime
if (isPrime)
primes.push_back(i);
}
 
// prime numbers were found in ascending order,
// let's add their value and store in a map such that
// [prime number] => [sum of all prime numbers up to the current]
// note: long long is required to avoid overflows
std::map<unsigned int, unsigned long long> sums;
unsigned long long sum = 0;
for (auto p : primes)
{
sum += p;
sums[p] = sum;
}
 
// the test cases are more or less "smart" lookups
unsigned int tests;
std::cin >> tests;
while (tests--)
{
unsigned int x;
std::cin >> x;
 
// find the closest prime number which is bigger than the input
auto i = sums.upper_bound(x);
// go back to the closest prime number which is smaller than the input
i--;
 
// show the sum associated to that prime number
std::cout << i->second << std::endl;
}
return 0;
}

This solution contains 8 empty lines, 15 comments and 3 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 10" | ./10

Output:

(please click 'Go !')

Note: the original problem's input 2000000 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 0.22 seconds on a Intel® Core™ i7-2600K CPU @ 3.40GHz.
Peak memory usage was about 12 MByte.

(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
March 29, 2017 added comments

Hackerrank

see https://www.hackerrank.com/contests/projecteuler/challenges/euler010

My code solves 8 out of 8 test cases (score: 100%)

Difficulty

Project Euler ranks this problem at 5% (out of 100%).

Hackerrank describes this problem as medium.

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 7: 10001st prime

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=10 - the best forum on the subject (note: you have to submit the correct solution first)

Code in various languages:

Python: www.mathblog.dk/sum-of-all-primes-below-2000000-problem-10/ (written by Kristian Edlund)
Haskell: github.com/nayuki/Project-Euler-solutions/blob/master/haskell/p010.hs (written by Nayuki)
Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p010.java (written by Nayuki)
Mathematica: github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p010.mathematica (written by Nayuki)
C: github.com/eagletmt/project-euler-c/blob/master/10-19/problem10.c (written by eagletmt)
Go: github.com/frrad/project-euler/blob/master/golang/Problem010.go (written by Frederick Robinson)
Javascript: github.com/dsernst/ProjectEuler/blob/master/10 Summation of primes.js (written by David Ernst)
Scala: github.com/samskivert/euler-scala/blob/master/Euler010.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.

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
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201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225
226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250
The 160 solved problems had an average difficulty of 21.8% at Project Euler and I scored 11,807 points (out of 13100) at Hackerrank's Project Euler+.
My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.
more about me can be found on my homepage.
some names mentioned on this site may be trademarks of their respective owners.
thanks to the KaTeX team for their great typesetting library !