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.

tiles

How many ways can a row measuring fifty units in length be tiled?

NOTE: This is related to Problem 116.

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

My code

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

The code contains #ifdefs 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.

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 5" | ./117

Output:

(please click 'Go !')

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)

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

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 never 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:

Python: 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)

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
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
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 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 !