<< problem 98 - Anagramic squares | Arranged probability - problem 100 >> |
Problem 99: Largest exponential
(see projecteuler.net/problem=99)
Comparing two numbers written in index form like 2^11 and 3^7 is not difficult, as any calculator would confirm that 2^11 = 2048 < 3^7 = 2187.
However, confirming that 632382^518061 > 519432^525806 would be much more difficult, as both numbers contain over three million digits.
Using base_exp.txt (right click and 'Save Link/Target As...'), a 22K text file containing one thousand lines with a base/exponent pair on each line,
determine which line number has the greatest numerical value.
NOTE: The first two lines in the file represent the numbers in the example given above.
My Algorithm
If a^b < x^y then log{a^b} < log{x^y} which means b * log{a} < y * log{x}.
The logarithm fits easily in a double
.
std::map
is an ascendingly sorted container → its last element has the greatest numerical value.
Modifications by HackerRank
Print the base and exponent of the k-sorted element.
Interactive test
You can submit your own input to my program and it will be instantly processed at my server:
This is equivalent toecho "" | ./99
Output:
(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, as well as the input data, 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 <cmath>
#include <map>
#include <iostream>
#define ORIGINAL
int main()
{
#ifdef ORIGINAL
// read all 1000 pairs, store [logarithm] => [index]
std::map<double, unsigned int> data;
for (unsigned int i = 1; i <= 1000; i++) // first line has index 1 (not 0)
{
unsigned int base, exponent;
char comma; // skip commas in input file
std::cin >> base >> comma >> exponent;
// sort by exponent * log(base)
data[exponent * log(base)] = i;
}
// return index of last input line
std::cout << data.rbegin()->second << std::endl;
return 0;
#else
// how many pairs ?
unsigned int numbers;
std::cin >> numbers;
// read all pairs, store [logarithm] => [base, exponent]
std::map<double, std::pair<unsigned int, unsigned int>> data;
for (unsigned int i = 1; i <= numbers; i++)
{
unsigned int base, exponent;
std::cin >> base >> exponent;
data[exponent * log(base)] = std::make_pair(base, exponent);
}
// which number of the sorted list should be printed ?
unsigned int pos;
std::cin >> pos;
// std::map is sorted, jump to the position
auto i = data.begin();
std::advance(i, pos - 1); // input is 1-based
// get result
auto result = i->second;
auto base = result.first;
auto exponent = result.second;
// and print it
std::cout << base << " " << exponent << std::endl;
return 0;
#endif
}
This solution contains 11 empty lines, 9 comments and 7 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
March 1, 2017 submitted solution
May 6, 2017 added comments
Hackerrank
see https://www.hackerrank.com/contests/projecteuler/challenges/euler099
My code solves 10 out of 10 test cases (score: 100%)
Difficulty
Project Euler ranks this problem at 10% (out of 100%).
Hackerrank describes this problem as medium.
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=99 - 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-99-which-baseexponent-pair-in-the-file-has-the-greatest-numerical-value/ (written by Kristian Edlund)
Java github.com/nayuki/Project-Euler-solutions/blob/master/java/p099.java (written by Nayuki)
Scala github.com/samskivert/euler-scala/blob/master/Euler099.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 98 - Anagramic squares | Arranged probability - problem 100 >> |