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PSYCHON.cpp
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PSYCHON.cpp
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// AC, ALGO: Number Theory, Prime Factorization.
// DISCLAIMER: Sieve of Atkins part of the solution was not coded by me & I have cited the source below.
/* Some Helpful Links:
http://thomasinterestingblog.wordpress.com/2011/11/30/generating-primes-with-the-sieve-of-atkin-in-c/
http://en.wikipedia.org/wiki/Sieve_of_Atkin
*/
// For any clarifications, contact me at: [email protected]
#include <cstdio>
#include <cmath>
using namespace std;
#define limit 10000001
int root = ceil(sqrt(limit));
bool sieve[limit];
int primes[(limit/2)+1], insert = 2, z, x, y, n, r, a, i, even, odd, ctr;
int main()
{
//Create the various different variables required
primes[0] = 2, primes[1] = 3 ;
for( z = 0; z < limit; z++ )
sieve[z] = false; //Not all compilers have false as the default boolean value
for( x = 1; x <= root; x++ )
{
for( y = 1; y <= root; y++ )
{
//Main part of Sieve of Atkin
n = ( 4 * x * x ) + ( y * y );
if( n <= limit && ( n % 12 == 1 || n % 12 == 5 ) )
sieve[n] ^= true;
n = ( 3 * x * x ) + ( y * y );
if( n <= limit && n % 12 == 7 )
sieve[n] ^= true;
n = ( 3 * x * x ) - ( y * y );
if( x > y && n <= limit && n % 12 == 11 )
sieve[n] ^= true;
}
}
//Mark all multiples of squares as non-prime
sieve[2] = sieve[3] = true;
for ( r = 5; r <= root; r++ )
{
if ( sieve[r] )
{
for ( i = r * r; i < limit; i += r * r )
sieve[i] = false;
}
}
//Add into prime array
for( a = 5; a < limit; a++ )
{
if( sieve[a] )
{
primes[insert] = a;
insert++;
}
}
int N, M, t;
for( scanf("%d",&t); t--; )
{
scanf("%d",&N);
M = N;
if( M == 1 || sieve[M] )
{
printf("Ordinary Number\n");
continue;
}
i = even = odd = 0;
while( M != 1 )
{
ctr = 0;
while( M % primes[i] == 0 )
{
ctr++;
M /= primes[i];
}
i++;
if( ! ( ctr & 1 ) && ctr )
even++;
else if( ctr & 1 && ctr )
odd++;
if( sieve[M] )
{
odd++;
break;
}
}
puts( odd >= even ? "Ordinary Number" : "Psycho Number" );
}
return 0;
}