<< problem 98 - Anagramic squares Arranged probability - problem 100 >>

Problem 99: Largest exponential

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.

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.

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 #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 <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;

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.

Interactive test

You can submit your own input to my program and it will be instantly processed at my server:

Input data (separated by spaces or newlines):

This is equivalent to
echo "" | ./99

Output:

(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

March 1, 2017 submitted solution

Hackerrank

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 never an option.

projecteuler.net/thread=99 - 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-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)

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:

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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.
 << problem 98 - Anagramic squares Arranged probability - problem 100 >>
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