Prime Ring Problem (UVA 524, HDU 1016, UVALive 5270, ZOJ 1457, SCU 1545, Regionals 1996 >> Asia - Shanghai)

///     Raihan Ruhin
///     CSE, Jahangirnagar University.
///     Dhaka-Bangladesh.
///     id: raihanruhin (topcoder / codeforces / codechef / uva), 3235 (lightoj)
///     mail: raihanruhin@ (yahoo / gmail / facebook)
///     blog: ruhinraihan.blogspot.com

#include<bits/stdc++.h>
using namespace std;

#define SET(a) memset(a,-1,sizeof(a))
#define CLR(a) memset(a,0,sizeof(a))
#define PI acos(-1.0)

#define MOD 1000000007
#define MX 100010

int ring[20], n;
bool isPrime[33], taken[20];

void print()
{
    cout<<ring[1];
    for(int i=2;i<=n;i++)
        cout<<" "<<ring[i];
    cout<<"\n";
return;
}

void backTrack(int tot, int lst) //(total taken already, last taken number)
{
    if(tot==n)
    {
        if(isPrime[lst+1])
            print();
        return;
    }

    for(int i=2;i<=n;i++)
        if(!taken[i])
            if(isPrime[lst+i])
            {
                taken[i]=1;
                ring[tot+1]=i;
                backTrack(tot+1, i);
                taken[i]=0;
            }
return;
}

int main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);
    int kk=1, tc, m;
    string s;
    isPrime[2]=isPrime[3]=isPrime[5]=isPrime[7]=isPrime[11]=isPrime[13]=isPrime[17]=isPrime[19]=isPrime[23]=isPrime[29]=isPrime[31]=1;
    while(cin>>n)
    {
        CLR(taken);
        CLR(ring);
        ring[1]=taken[1]=1;//first circle fixed
        if(kk>1) cout<<"\n";
        cout<<"Case "<<kk++<<":\n";
        backTrack(1, 1); //first circle taken
    }
return 0;
}