LCMGCD.cpp

#include <vector>
#include <map>
#include <functional>
#include <algorithm>
using namespace std;

// BEGIN CUT HERE

#include <iostream>
#include <sstream>
#include <string>
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v);
// END CUT HERE

class LCMGCD{public:
string isPossible( vector <int> x, int t )
{
    int n = (int)x.size();
    vector<int> a(n), b(n);

    for (int i=0; i<n; i++)
    {
        while (x[i]%2==0)
            x[i] /= 2,
            a[i]++;
        while (x[i]%3==0)
            x[i] /= 3,
            b[i]++;
    }
    int ta=0, tb=0;
    while (t%2==0)
        t/=2,
        ta++;
    while (t%3==0)
        t/=3,
        tb++;

    for (int i=0; i<n; i++)
    {
        a[i] = a[i]>ta ? 1 : a[i]<ta ? -1 : 0;
        b[i] = b[i]>tb ? 1 : b[i]<tb ? -1 : 0;
    }

    map<pair<int,int>, int> M;

    vector<pair<int,int>> A;
    for (int i=0; i<n; i++)
    {
        pair<int,int> p = make_pair(a[i], b[i]);
        //if (M[p]>=2)
        if (M[p]>=1)
            continue;
        M[p]++;
        A.push_back(p);
    }

    n = (int)A.size();

    vector<int> memo(1<<n, -1);

    auto ab2p = [](int a, int b){return (a+1)*3 + (b+1);};

    function<int(int)> BT = [&](int s)->int
    {
        if (memo[s]!=-1)
            return memo[s];

        int c = 0;
        int a, b;
        for (int i=0; i<n; i++)
        if (s>>i&1)
            c++,
            a = A[i].first,
            b = A[i].second;
        if (c==1)
        {
            return memo[s] = 1<<ab2p(a, b);
        }

        int ret = 0;

        for (int s1=s; s1>0; s1=(s1-1)&s)
        {
            int s2 = s^s1;
            if (s2>0)
            {
                int r1 = BT(s1);
                int r2 = BT(s2);

                for (int c1=0; c1<9; c1++)
                if (r1>>c1&1)
                for (int c2=0; c2<9; c2++)
                if (r2>>c2&1)
                {
                    int a1 = c1/3-1;
                    int b1 = c1%3-1;
                    int a2 = c2/3-1;
                    int b2 = c2%3-1;

                    ret |= 1<<ab2p(max(a1,a2), max(b1,b2));
                    ret |= 1<<ab2p(min(a1,a2), min(b1,b2));
                }
            }
        }

        return memo[s] = ret;
    };

    return BT((1<<n)-1)>>ab2p(0,0)&1 ? "Possible" : "Impossible";
}};

// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
 { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
 { os << "{ ";
   for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
   os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const string& Expected, const string& Received) {
 bool ok = (Expected == Received);
 if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
 cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END	 verify_case(_, LCMGCD().isPossible(x, t));}
int main(){

CASE(0)
	int x_[] = {2,3};
	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_)); 
	int t = 6; 
	string _ = "Possible"; 
END
CASE(1)
	int x_[] = {4,9};
	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_)); 
	int t = 6; 
	string _ = "Impossible"; 
END
CASE(2)
	int x_[] = {6,12,24,18,36,72,54,108,216};
	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_)); 
	int t = 36; 
	string _ = "Possible"; 
END
CASE(3)
	int x_[] = {6,27,81,729};
	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_)); 
	int t = 6; 
	string _ = "Impossible"; 
END
CASE(4)
	int x_[] = {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_)); 
	int t = 1; 
	string _ = "Possible"; 
END
CASE(5)
	int x_[] = {72,16,16,16,16,16,27,27,27,27,27,27,27,27,27};
	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_)); 
	int t = 72; 
	string _ = "Possible"; 
END
CASE(6)
	int x_[] = {100663296, 544195584, 229582512, 59049};
	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_)); 
	int t = 60466176; 
	string _ = "Possible"; 
END
CASE(7)
	int x_[] = {2,4,8,16,32,64};
	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_)); 
	int t = 256; 
	string _ = "Impossible"; 
END

}
// END CUT HERE