Problem 8: Largest product in a series

(see projecteuler.net/problem=8)

The four adjacent digits in the 1000-digit number that have the greatest product are 9 * 9 * 8 * 9 = 5832.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product.
What is the value of this product?

Algorithm

Starting at each position where at least 13 digits (variable span) can be found,
a loop goes through those 13 digits and:
1. convert each digit from ASCII to numeric: numeric = ascii - '0'
2. multiply all those converted digits
3. if product is higher than before: keep it

Alternative Approaches

If span is large, then an incremental approach might be useful:
instead of multiplying all digits over and over again, we re-use a large portion of last iteration's product.
Let's pretend our sequences contains just 4 elements:
product_0=x_0*x_1*x_2*x_3
then
product_1=x_1*x_2*x_3*x_4=product_0*x_4/x_0

This reduces O-complexity from O(mn) to O(n).

My code

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

#include <iostream>
#include <string>
 
int main()
{
unsigned int tests;
std::cin >> tests;
while (tests--)
{
// length of string
unsigned int length;
// number of relevant consecutive digits
unsigned int span;
// read number as a string
std::string number;
std::cin >> length >> span >> number;
 
// results can be much bigger than 32 bits ... but 64 bits are enough, though
unsigned long long best = 0;
// loop ends when there are less than "span" digits left
for (int start = 0; start + span < length; start++)
{
unsigned long long current = 1;
// convert digits from ASCII to numbers and multiply
for (unsigned int i = 0; i < span; i++)
current *= number[start + i] - '0';
 
// better than before ?
if (best < current)
best = current;
}
 
std::cout << best << std::endl;
}
return 0;
}

In order to run my code, execute
echo "1 1000 13 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450" | ./euler-0008

(input format usually follows Hackerrank's requirements)

This solution contains 4 empty lines, 7 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 1000 4 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450" | ./8

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 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 23, 2017 submitted solution
March 29, 2017 added comments

Hackerrank

see https://www.hackerrank.com/contests/projecteuler/challenges/euler008

My code solves 10 out of 10 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.

Links

projecteuler.net/thread=8 - the best forum on the subject (note: you have to submit the correct solution first)

Code in various languages:

Python: www.mathblog.dk/solution-to-problem-8-of-project-euler/ (written by Kristian Edlund)
Haskell: github.com/nayuki/Project-Euler-solutions/blob/master/haskell/p008.hs (written by Nayuki)
Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p008.java (written by Nayuki)
Mathematica: github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p008.mathematica (written by Nayuki)
C: github.com/eagletmt/project-euler-c/blob/master/1-9/problem8.c (written by eagletmt)
Go: github.com/frrad/project-euler/blob/master/golang/Problem008.go (written by Frederick Robinson)
Javascript: github.com/dsernst/ProjectEuler/blob/master/8 Largest product in a series.js (written by David Ernst)
Scala: github.com/samskivert/euler-scala/blob/master/Euler008.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.

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The 163 solved problems had an average difficulty of 22.2% at Project Euler and I scored 11,907 points (out of 13200) 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, especially in my coding blog.
some names mentioned on this site may be trademarks of their respective owners.
thanks to the KaTeX team for their great typesetting library !