<< problem 116 - Red, green or blue tiles | Pandigital prime sets - problem 118 >> |
Problem 117: Red, green, and blue tiles
(see projecteuler.net/problem=117)
Using a combination of black square tiles and oblong tiles chosen from: red tiles measuring two units, green tiles measuring three units, and blue tiles measuring four units, it is possible to tile a row measuring five units in length in exactly fifteen different ways.
How many ways can a row measuring fifty units in length be tiled?
NOTE: This is related to Problem 116.
My Algorithm
... almost the same as problem 115 !
Actually the code is even shorter - the for
-loop in count
runs from 1 to 4 (1 = black, 2 = red, 3 = green, 4 = blue).
There are no "gaps" between tiles because I treat black tiles the same way like any other tile.
These numbers are also called "Generalized Fibonacci numbers", and the special case for this problem is called Tetranacci numbers.
Modifications by HackerRank
As always, Hackerrank's input is ridiculously high and my poor C++ data types can't handle such numbers.
[TODO] find closed formula
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 5" | ./117
Output:
Note: the original problem's input 50
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)
My code
… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too.
The code contains #ifdef
s 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>
#include <vector>
#define ORIGINAL
// memoized solutions
const long long Unknown = -1;
std::vector<long long> solutions;
// find result for row with a certain length
unsigned long long count(unsigned long long space)
{
// finished ?
if (space == 0)
return 1;
// already know the answer ?
if (solutions[space] != Unknown)
return solutions[space];
// insert red blocks at the current position with all possible spaces
unsigned long long result = 0;
for (unsigned long long block = 1; block <= 4 && block <= space; block++)
{
// how much is left after inserting ?
auto next = space - block;
// count all combinations
result += count(next);
}
// memoize result
solutions[space] = result;
return result;
}
int main()
{
unsigned int tests;
std::cin >> tests;
while (tests--)
{
// what number should be exceeded ?
unsigned long long limit = 50;
std::cin >> limit;
// cached results
solutions.clear();
solutions.resize(limit+1, Unknown);
auto result = count(limit);
#ifndef ORIGINAL
result %= 1000000007; // Hackerrank asks for "small" results
#endif
std::cout << result << std::endl;
}
return 0;
}
This solution contains 12 empty lines, 10 comments and 5 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
May 18, 2017 submitted solution
May 18, 2017 added comments
Hackerrank
see https://www.hackerrank.com/contests/projecteuler/challenges/euler117
My code solves 1 out of 6 test cases (score: 0%)
I failed 0 test cases due to wrong answers and 5 because of timeouts
Difficulty
Project Euler ranks this problem at 35% (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=117 - the best forum on the subject (note: you have to submit the correct solution first)
Code in various languages:
C# www.mathblog.dk/project-euler-118-sets-prime-elements/ (written by Kristian Edlund)
Java github.com/nayuki/Project-Euler-solutions/blob/master/java/p118.java (written by Nayuki)
Scala github.com/samskivert/euler-scala/blob/master/Euler118.scala (written by Michael Bayne)
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 | |
the flashing problem is the one I solved most recently |
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I scored 13,486 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 116 - Red, green or blue tiles | Pandigital prime sets - problem 118 >> |