Kertoma

#include <iostream>
#include <array>
#include <cmath>
#include <algorithm>

#define PI 3.14159265358979323846

// Length of factorial
// Improved approximation (x2)

uint32_t StirlingAprox(double n)
{
    return (uint32_t) floor(floor((log(2.0 * PI * n)/2.0 + n * (log(n)-1.0))/log(10.0)) + 1);
}

int main()
{
    std::array<uint32_t, 10> frequency = {};
    uint32_t length = 0;

    for(auto& i : frequency)
    {
        std::cin >> i;
        length += i;
    }

    // Check special cases that share the same factorial length
    std::array<uint32_t, 10> factorialSpecial = {0, 0, 1, 0, 0, 0, 0, 0, 0, 0};
    if(frequency == factorialSpecial)
    {
        std::cout << "2\n";
        return 0;
    }
    factorialSpecial = {0, 0, 0, 0, 0, 0, 1, 0, 0, 0};
    if(frequency == factorialSpecial)
    {
        std::cout << "3\n";
        return 0;
    }
    factorialSpecial = {0, 0, 1, 0, 1, 0, 0, 0, 0, 0};
    if(frequency == factorialSpecial)
    {
        std::cout << "4\n";
        return 0;
    }
    factorialSpecial = {1, 1, 1, 0, 0, 0, 0, 0, 0, 0};
    if(frequency == factorialSpecial)
    {
        std::cout << "5\n";
        return 0;
    }
    factorialSpecial = {1, 0, 0, 0, 0, 1, 0, 1, 0, 0};
    if(frequency == factorialSpecial)
    {
        std::cout << "6\n";
        return 0;
    }
    factorialSpecial = {2, 0, 0, 0, 1, 1, 0, 0, 0, 0};
    if(frequency == factorialSpecial)
    {
        std::cout << "7\n";
        return 0;
    }
    // Use Stirling’s approximation to get a table of values during compile time and check if there is a hit
    // Have to check until 10^5

    // Overkill :)
    std::array<uint32_t, 200000> lengths = {};
    for(int i = 0; i < 200000; i++) // 100000 != 10000
        lengths[i] = StirlingAprox(i + 1);

    auto loc = std::find(lengths.begin(), lengths.end(), length);
    if (loc != std::end(lengths))
    {
        std::cout << std::distance(lengths.begin(), loc) + 1 << "\n";
    }
    else
    {
        // Stirling’s approximation doesn't work anymore :C
        std::cout << "-1\n";
    }

}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 1, 2, 3

Verdict: ACCEPTED

Test 6

Group: 1, 2, 3

Verdict: ACCEPTED

Test 7

Group: 2, 3

Verdict: ACCEPTED

Test 8

Group: 2, 3

Verdict: ACCEPTED

Test 9

Group: 2, 3

Verdict: ACCEPTED

Test 10

Group: 2, 3

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: ACCEPTED

Test 15

Group: 3

Verdict: ACCEPTED

Test 16

Group: 3

Verdict: ACCEPTED