/*
VIM: let b:lcppflags="-std=c++14 -O2 -pthread -I."
VIM: let b:wcppflags="/O2 /EHsc /DWIN32"
VIM-: let b:cppflags=g:Iboost.g:Itbb
VIM-: let b:ldflags=g:Lboost.g:Ltbb
VIM-: let b:ldlibpath=g:Bboost.g:Btbb
VIM-: let b:argv=""
*/
#include <iostream>
#include <exception>
#include <chrono>
#include <cmath>

/*
 * Given a positive integer which fits in a 32 bit signed integer, find if it
 * can be expressed as A^P where P > 1 and A > 0. A and P both should be
 * integers.
 */

bool isPower(int X) {

    if ( X == 1 ){
        return true;
    }

    double log_X = std::log(X);
    long long end = log_X / std::log(2) +1;
    for ( int i = 2; i <= end; ++i ) {
        double A = std::exp(log_X/double(i));
        double rA = std::round(A);
        std::cout << "--> A=" << A << " r(" << rA <<  ") I=" << i << " diff=" << std::fabs(A-rA) << std::endl;
        if ( std::fabs(A-rA) < 0.00001 ) {
            int int_A = rA;
            std::cout << "Testing --> A=" << A << " r("<<int_A <<  ") I=" << i << std::endl;
            long long test = 1;
            for ( int j = 0; j < i; ++j ) {
                test *= int_A;
            }
            if ( test == X ) {
                std::cout << "X=" << X << " A=" << int_A << " I=" << i << std::endl;
                return true;
            }
        }
    }
    std::cout << "X=" << X << " no power found." << std::endl;
    return false;
}


int main ( void )
{try{
    auto begin = std::chrono::high_resolution_clock::now();

    isPower(1);
    isPower(4);
    isPower(3);
    isPower(27);
    isPower(1024000000);
    isPower(1024*1024*1024);

    //......

    auto end = std::chrono::high_resolution_clock::now();
    std::chrono::duration<double> seconds = end - begin;
    std::cout << "Time: " << seconds.count() << std::endl;
    return 0;
}
catch ( const std::exception& e )
{
    std::cerr << std::endl
            << "std::exception(\"" << e.what() << "\")." << std::endl;
    return 2;
}
catch ( ... )
{
    std::cerr  << std::endl
            << "unknown exception." << std::endl;
    return 1;
}}