e6ccb20270 2014-05-17        kinaba: #include <iostream>
e6ccb20270 2014-05-17        kinaba: #include <sstream>
e6ccb20270 2014-05-17        kinaba: #include <iomanip>
e6ccb20270 2014-05-17        kinaba: #include <vector>
e6ccb20270 2014-05-17        kinaba: #include <string>
e6ccb20270 2014-05-17        kinaba: #include <map>
e6ccb20270 2014-05-17        kinaba: #include <set>
e6ccb20270 2014-05-17        kinaba: #include <algorithm>
e6ccb20270 2014-05-17        kinaba: #include <numeric>
e6ccb20270 2014-05-17        kinaba: #include <iterator>
e6ccb20270 2014-05-17        kinaba: #include <functional>
e6ccb20270 2014-05-17        kinaba: #include <complex>
e6ccb20270 2014-05-17        kinaba: #include <queue>
e6ccb20270 2014-05-17        kinaba: #include <stack>
e6ccb20270 2014-05-17        kinaba: #include <cmath>
e6ccb20270 2014-05-17        kinaba: #include <cassert>
e6ccb20270 2014-05-17        kinaba: #include <tuple>
e6ccb20270 2014-05-17        kinaba: using namespace std;
e6ccb20270 2014-05-17        kinaba: typedef long long LL;
e6ccb20270 2014-05-17        kinaba: typedef complex<double> CMP;
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: class CandidatesSelection { public:
e6ccb20270 2014-05-17        kinaba: 	string possible(vector <string> score, vector <int> result)
e6ccb20270 2014-05-17        kinaba: 	{
e6ccb20270 2014-05-17        kinaba: 		return solve(score, result) ? "Possible" : "Impossible";
e6ccb20270 2014-05-17        kinaba: 	}
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: 	bool solve(vector <string> score, vector <int> result)
e6ccb20270 2014-05-17        kinaba: 	{
e6ccb20270 2014-05-17        kinaba: 		const int N = score.size();
e6ccb20270 2014-05-17        kinaba: 		const int S = score[0].size();
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: 		// po[a][b] : bitmask of skill set that makes a<b.
e6ccb20270 2014-05-17        kinaba: 		vector<vector<LL>> po(N, vector<LL>(N));
e6ccb20270 2014-05-17        kinaba: 		for(int a=0; a<N; ++a)
e6ccb20270 2014-05-17        kinaba: 		for(int b=0; b<N; ++b) if(a!=b)
e6ccb20270 2014-05-17        kinaba: 		{
e6ccb20270 2014-05-17        kinaba: 			LL mask = 0;
e6ccb20270 2014-05-17        kinaba: 			for(int s=0; s<S; ++s)
e6ccb20270 2014-05-17        kinaba: 				if(score[a][s] <= score[b][s])
e6ccb20270 2014-05-17        kinaba: 					mask |= 1LL<<s;
e6ccb20270 2014-05-17        kinaba: 			if(a<b)
e6ccb20270 2014-05-17        kinaba: 				mask |= 1LL<<S;
e6ccb20270 2014-05-17        kinaba: 			po[a][b] = mask;
e6ccb20270 2014-05-17        kinaba: 		}
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: 		vector<vector<int>> now(1, result);
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: 		function<bool(LL,vector<vector<int>>)> rec;
e6ccb20270 2014-05-17        kinaba: 		rec = [&](LL used, vector<vector<int>> obl) {
e6ccb20270 2014-05-17        kinaba: 			LL pos = ~0LL;
e6ccb20270 2014-05-17        kinaba: 			for(auto& oi: obl)
e6ccb20270 2014-05-17        kinaba: 				for(int i=0; i+1<oi.size(); ++i)
e6ccb20270 2014-05-17        kinaba: 					pos &= po[oi[i]][oi[i+1]];
e6ccb20270 2014-05-17        kinaba: 			if(pos & (1LL<<S)) // original order is enough.
e6ccb20270 2014-05-17        kinaba: 				return true;
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: 			bool changed = false;
e6ccb20270 2014-05-17        kinaba: 			for(int s=0; s<S; ++s) if(pos & ~used & (1LL<<s)) {
e6ccb20270 2014-05-17        kinaba: 				vector<vector<int>> next;
e6ccb20270 2014-05-17        kinaba: 				for(auto& oi: obl) {
e6ccb20270 2014-05-17        kinaba: 					vector<int> cur;
e6ccb20270 2014-05-17        kinaba: 					for(int o: oi) {
e6ccb20270 2014-05-17        kinaba: 						if(!cur.empty() && score[cur.back()][s] < score[o][s]) {
e6ccb20270 2014-05-17        kinaba: 							changed = true;
e6ccb20270 2014-05-17        kinaba: 							if(cur.size()>=2)
e6ccb20270 2014-05-17        kinaba: 								next.push_back(cur);
e6ccb20270 2014-05-17        kinaba: 							cur.clear();
e6ccb20270 2014-05-17        kinaba: 						}
e6ccb20270 2014-05-17        kinaba: 						cur.push_back(o);
e6ccb20270 2014-05-17        kinaba: 					}
e6ccb20270 2014-05-17        kinaba: 					if(cur.size()>=2)
e6ccb20270 2014-05-17        kinaba: 						next.push_back(cur);
e6ccb20270 2014-05-17        kinaba: 				}
e6ccb20270 2014-05-17        kinaba: 				obl = std::move(next);
e6ccb20270 2014-05-17        kinaba: 			}
e6ccb20270 2014-05-17        kinaba: 			return changed && rec(used|pos, obl);
e6ccb20270 2014-05-17        kinaba: 		};
e6ccb20270 2014-05-17        kinaba: 		return rec(0, now);
e6ccb20270 2014-05-17        kinaba: 	}
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: };
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: // BEGIN CUT HERE
e6ccb20270 2014-05-17        kinaba: #include <ctime>
e6ccb20270 2014-05-17        kinaba: double start_time; string timer()
e6ccb20270 2014-05-17        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
e6ccb20270 2014-05-17        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
e6ccb20270 2014-05-17        kinaba:  { os << "{ ";
e6ccb20270 2014-05-17        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
e6ccb20270 2014-05-17        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
e6ccb20270 2014-05-17        kinaba: void verify_case(const string& Expected, const string& Received) {
e6ccb20270 2014-05-17        kinaba:  bool ok = (Expected == Received);
e6ccb20270 2014-05-17        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
e6ccb20270 2014-05-17        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
e6ccb20270 2014-05-17        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
e6ccb20270 2014-05-17        kinaba: #define END	 verify_case(_, CandidatesSelection().possible(score, result));}
e6ccb20270 2014-05-17        kinaba: int main(){
e6ccb20270 2014-05-17        kinaba: 
e6ccb20270 2014-05-17        kinaba: CASE(0)
e6ccb20270 2014-05-17        kinaba: 	string score_[] = {"CC", "AA", "BB"};
e6ccb20270 2014-05-17        kinaba: 	  vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
e6ccb20270 2014-05-17        kinaba: 	int result_[] = {1,2,0};
e6ccb20270 2014-05-17        kinaba: 	  vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
e6ccb20270 2014-05-17        kinaba: 	string _ = "Possible";
e6ccb20270 2014-05-17        kinaba: END
e6ccb20270 2014-05-17        kinaba: CASE(1)
e6ccb20270 2014-05-17        kinaba: 	string score_[] = {"BAB", "ABB", "AAB", "ABA"};
e6ccb20270 2014-05-17        kinaba: 	  vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
e6ccb20270 2014-05-17        kinaba: 	int result_[] = {2,0,1,3};
e6ccb20270 2014-05-17        kinaba: 	  vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
e6ccb20270 2014-05-17        kinaba: 	string _ = "Possible";
e6ccb20270 2014-05-17        kinaba: END
e6ccb20270 2014-05-17        kinaba: CASE(2)
e6ccb20270 2014-05-17        kinaba: 	string score_[] = {"BAB", "ABB", "AAB", "ABA"};
e6ccb20270 2014-05-17        kinaba: 	  vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
e6ccb20270 2014-05-17        kinaba: 	int result_[] = {0, 1, 3, 2};
e6ccb20270 2014-05-17        kinaba: 	  vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
e6ccb20270 2014-05-17        kinaba: 	string _ = "Impossible";
e6ccb20270 2014-05-17        kinaba: END
e6ccb20270 2014-05-17        kinaba: CASE(3)
e6ccb20270 2014-05-17        kinaba: 	string score_[] = {"AAA", "ZZZ"};
e6ccb20270 2014-05-17        kinaba: 	  vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
e6ccb20270 2014-05-17        kinaba: 	int result_[] = {1, 0};
e6ccb20270 2014-05-17        kinaba: 	  vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
e6ccb20270 2014-05-17        kinaba: 	string _ = "Impossible";
e6ccb20270 2014-05-17        kinaba: END
e6ccb20270 2014-05-17        kinaba: CASE(4)
e6ccb20270 2014-05-17        kinaba: 	string score_[] = {"ZZZ", "AAA"};
e6ccb20270 2014-05-17        kinaba: 	  vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
e6ccb20270 2014-05-17        kinaba: 	int result_[] = {0, 1};
e6ccb20270 2014-05-17        kinaba: 	  vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
e6ccb20270 2014-05-17        kinaba: 	string _ = "Possible";
e6ccb20270 2014-05-17        kinaba: END
e6ccb20270 2014-05-17        kinaba: CASE(5)
e6ccb20270 2014-05-17        kinaba: 	string score_[] = {"ZYYYYX","YXZYXY","ZZZZXX","XZXYYX","ZZZYYZ","ZZXXYZ","ZYZZXZ","XZYYZX"};
e6ccb20270 2014-05-17        kinaba: 	  vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
e6ccb20270 2014-05-17        kinaba: 	int result_[] = {3,7,1,0,2,5,6,4};
e6ccb20270 2014-05-17        kinaba: 	  vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
e6ccb20270 2014-05-17        kinaba: 	string _ = "Possible";
e6ccb20270 2014-05-17        kinaba: END
e6ccb20270 2014-05-17        kinaba: /*
e6ccb20270 2014-05-17        kinaba: CASE(6)
e6ccb20270 2014-05-17        kinaba: 	string score_[] = ;
e6ccb20270 2014-05-17        kinaba: 	  vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
e6ccb20270 2014-05-17        kinaba: 	int result_[] = ;
e6ccb20270 2014-05-17        kinaba: 	  vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
e6ccb20270 2014-05-17        kinaba: 	string _ = ;
e6ccb20270 2014-05-17        kinaba: END
e6ccb20270 2014-05-17        kinaba: CASE(7)
e6ccb20270 2014-05-17        kinaba: 	string score_[] = ;
e6ccb20270 2014-05-17        kinaba: 	  vector <string> score(score_, score_+sizeof(score_)/sizeof(*score_));
e6ccb20270 2014-05-17        kinaba: 	int result_[] = ;
e6ccb20270 2014-05-17        kinaba: 	  vector <int> result(result_, result_+sizeof(result_)/sizeof(*result_));
e6ccb20270 2014-05-17        kinaba: 	string _ = ;
e6ccb20270 2014-05-17        kinaba: END
e6ccb20270 2014-05-17        kinaba: */
e6ccb20270 2014-05-17        kinaba: }
e6ccb20270 2014-05-17        kinaba: // END CUT HERE