<< problem 111 - Primes with runs | Non-bouncy numbers - problem 113 >> |
Problem 112: Bouncy numbers
(see projecteuler.net/problem=112)
Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.
Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.
We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.
Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy.
In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538.
Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.
Find the least number for which the proportion of bouncy numbers is exactly 99%.
My Algorithm
isBouncy
determines whether its parameter is bouncy or not by stepping through its digits.
The rest is just a brute-force search.
Modifications by HackerRank
Any percentage can be entered.
Even though my brute-force search finds the solution to the original problem (99%) in less than 0.1 seconds, it's way too slow for
the potentially huge search space of Hackerrank. Someone indicated that one "answer requires about 90 bits".
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 90 100" | ./112
Output:
Note: the original problem's input 99 100
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++ and can be compiled with G++, Clang++, Visual C++. You can download it, too.
#include <iostream>
// return true if x is a bouncy number
bool isBouncy(unsigned long long x)
{
// figure out whether x is monotonic ascending or descending
// it's bouncy if neither ascending nor descending
bool ascending = true;
bool descending = true;
// initial digit (the right-most digit)
auto previous = x % 10;
x /= 10;
// still digits left ?
while (x > 0)
{
// current digit
auto current = x % 10;
// compare two digits
descending &= previous >= current;
ascending &= previous <= current;
// bouncy ?
if (!ascending && !descending)
return true;
// keep going ...
x /= 10;
previous = current;
}
// not bouncy (either ascending, descending or all digits are equal)
return false;
}
int main()
{
unsigned int tests = 1;
std::cin >> tests;
while (tests--)
{
// original problem: 99%
unsigned long long p = 99;
unsigned long long q = 100;
std::cin >> p >> q;
// brute-force ...
unsigned long long current = 100; // no bouncy numbers below 100
unsigned long long numBouncy = 0;
do
{
// check next number if bouncy
current++;
if (isBouncy(current))
numBouncy++;
} while (numBouncy * q < current * p); // same as numBouncy/current == p/q (=99%)
// print result
std::cout << current << std::endl;
}
return 0;
}
This solution contains 13 empty lines, 14 comments and 1 preprocessor command.
Benchmark
The correct solution to the original Project Euler problem was found in 0.02 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 11, 2017 submitted solution
May 11, 2017 added comments
Hackerrank
see https://www.hackerrank.com/contests/projecteuler/challenges/euler112
My code solves 1 out of 16 test cases (score: 0%)
I failed 0 test cases due to wrong answers and 15 because of timeouts
Difficulty
Project Euler ranks this problem at 15% (out of 100%).
Hackerrank describes this problem as advanced.
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=112 - 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-112-density-bouncy-numbers/ (written by Kristian Edlund)
Java github.com/nayuki/Project-Euler-solutions/blob/master/java/p112.java (written by Nayuki)
Scala github.com/samskivert/euler-scala/blob/master/Euler112.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 111 - Primes with runs | Non-bouncy numbers - problem 113 >> |