<< 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.

# 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.

# Interactive test

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

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

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:

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.

red problems are solved but exceed the time limit of one minute or the memory limit of 256 MByte.

*Please click on a problem's number to open my solution to that problem:*

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I scored 12,983 points (out of 15100 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+.

Look at my progress and performance pages to get more details.

My username at Project Euler is

**stephanbrumme**while it's stbrumme at Hackerrank.

# 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 >> |