<< problem 123 - Prime square remainders Palindromic sums - problem 125 >>

The radical of n, rad(n), is the product of the distinct prime factors of n.
For example, 504 = 23 * 32 * 7, so rad(504) = 2 * 3 * 7 = 42.

If we calculate rad(n) for 1 <= n <= 10, then sort them on rad(n), and sorting on n if the radical values are equal, we get:

Unsorted Sorted
11 111
22 222
33 423
42 824
55 335
66 936
77 557
82 668
93 779
1010 101010

Let E(k) be the kth element in the sorted n column; for example, E(4) = 8 and E(6) = 9.

If rad(n) is sorted for 1 <= n <= 100000, find E(10000).

# My Algorithm

Similar to a prime sieve I find all multiples of each prime.
There is one struct Radical for every number n, its product starts with 1 and is multiplied by a prime factors of n.
A simple comparison operator<() will be used to sort all radicals.

A full sort isn't needed - there is the nice nth_element algorithm in C++'s STL which ensures that a single element is at the correct position -
without a strict guarantee that other elements are perfectly sorted, too. This partial sort is often much faster than a full sort.

## Modifications by HackerRank

I don't properly re-use radicals for consecutive test cases and can't handle huge search spaces. I couldn't care less ...

# Interactive test

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

Number of test cases (1-5):

Input data (separated by spaces or newlines):
Note: Enter the total number of radicals and the sorted position k to get E(k)

This is equivalent to
echo "2 10 4 10 6" | ./124

Output:

Note: the original problem's input 100000 10000 cannot be entered
because just copying results is a soft skill reserved for idiots.

(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, too. Or just jump to my GitHub repository.

       #include <iostream>
#include <vector>
#include <algorithm>

{
// current number
unsigned int n;
// product of all prime factors
unsigned int product;

// compare two object, prefer lower product (and lower n if products are equal)
{
if (product != other.product)
return product < other.product;
return n < other.n;
}
};

// all relevant redicals

// return a certain radical (1-based index)
unsigned int getNth(unsigned int index)
{
index--; // 1-based instead of 0-based
// partial sort
}

int main()
{
unsigned int tests;
std::cin >> tests;
while (tests--)
{
unsigned int limit = 100000;
std::cin >> limit;

for (unsigned int i = 0; i <= limit; i++)
{
current.n = i;
current.product = 1;
}

// some big value to push zero to the back

// compute radicals using a "sieve"
{
// process only primes
if (current.product != 1)
continue;

// adjust all of their multiples
for (unsigned int j = current.n; j <= limit; j += current.n)
}

// get n-th element
unsigned int pos = 10000;
std::cin >> pos;
std::cout << getNth(pos) << std::endl;
}
return 0;
}


This solution contains 10 empty lines, 13 comments and 3 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

May 19, 2017 submitted solution

# Hackerrank

My code solves 4 out of 10 test cases (score: 30%)

I failed 4 test cases due to wrong answers and 2 because of timeouts

# Difficulty

Project Euler ranks this problem at 25% (out of 100%).

Hackerrank describes this problem as advanced.

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.

# 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 [new] the flashing problem is the one I solved most recently

I stopped working on Project Euler problems around the time they released 617.
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The 310 solved problems (that's level 12) had an average difficulty of 32.6% at Project Euler and
I scored 13526 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.

 << problem 123 - Prime square remainders Palindromic sums - problem 125 >>
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