<< problem 7 - 10001st prime | Special Pythagorean triplet - problem 9 >> |
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?
My 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).
Interactive test
You can submit your own input to my program and it will be instantly processed at my server:
This is equivalent toecho "1 1000 4 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450" | ./8
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. Or just jump to my GitHub repository.
#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, executeecho "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.
Benchmark
The correct solution to the original Project Euler problem was found in less than 0.01 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
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 rarely 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:
C# www.mathblog.dk/solution-to-problem-8-of-project-euler/ (written by Kristian Edlund)
C github.com/eagletmt/project-euler-c/blob/master/1-9/problem8.c (written by eagletmt)
Java github.com/nayuki/Project-Euler-solutions/blob/master/java/p008.java (written by Nayuki)
Javascript github.com/dsernst/ProjectEuler/blob/master/8 Largest product in a series.js (written by David Ernst)
Go github.com/frrad/project-euler/blob/master/golang/Problem008.go (written by Frederick Robinson)
Mathematica github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p008.mathematica (written by Nayuki)
Haskell github.com/nayuki/Project-Euler-solutions/blob/master/haskell/p008.hs (written by Nayuki)
Scala github.com/samskivert/euler-scala/blob/master/Euler008.scala (written by Michael Bayne)
Perl github.com/gustafe/projecteuler/blob/master/008-Largest-product-in-a-series.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 7 - 10001st prime | Special Pythagorean triplet - problem 9 >> |