<< problem 111 - Primes with runs Non-bouncy numbers - problem 113 >>

# Problem 112: Bouncy numbers

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%.

# 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".

# 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.

# 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):
Note: Enter p and q such that p/q is your percentage, e.g. 90 100 => 90%

This is equivalent to
echo "1 90 100" | ./112

Output:

(please click 'Go !')

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)

# Benchmark

The correct solution to the original Project Euler problem was found in 0.02 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 11, 2017 submitted solution

# Hackerrank

My code solved 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 never an option.

projecteuler.net/thread=112 - 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-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)

# 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 already 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:

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The 133 solved problems had an average difficulty of 16.9% at Project Euler and I scored 11,174 points (out of 12300) at Hackerrank's Project Euler+.
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