<< 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.

# 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 solved **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.

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