743781a2d9 2012-06-26        kinaba: #include <iostream>
743781a2d9 2012-06-26        kinaba: #include <sstream>
743781a2d9 2012-06-26        kinaba: #include <iomanip>
743781a2d9 2012-06-26        kinaba: #include <vector>
743781a2d9 2012-06-26        kinaba: #include <string>
743781a2d9 2012-06-26        kinaba: #include <map>
743781a2d9 2012-06-26        kinaba: #include <set>
743781a2d9 2012-06-26        kinaba: #include <algorithm>
743781a2d9 2012-06-26        kinaba: #include <numeric>
743781a2d9 2012-06-26        kinaba: #include <iterator>
743781a2d9 2012-06-26        kinaba: #include <functional>
743781a2d9 2012-06-26        kinaba: #include <complex>
743781a2d9 2012-06-26        kinaba: #include <queue>
743781a2d9 2012-06-26        kinaba: #include <stack>
743781a2d9 2012-06-26        kinaba: #include <cmath>
743781a2d9 2012-06-26        kinaba: #include <cassert>
743781a2d9 2012-06-26        kinaba: using namespace std;
743781a2d9 2012-06-26        kinaba: typedef long long LL;
743781a2d9 2012-06-26        kinaba: typedef long double LD;
743781a2d9 2012-06-26        kinaba: typedef complex<LD> CMP;
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: //-------------------------------------------------------------
743781a2d9 2012-06-26        kinaba: // Dinic's Algorithm
743781a2d9 2012-06-26        kinaba: //   O(V E)
743781a2d9 2012-06-26        kinaba: //
743781a2d9 2012-06-26        kinaba: // G : bidirectional (G[i].has(j) <==> G[j].has(i))
743781a2d9 2012-06-26        kinaba: // F : flow-capacity F[i][j] = Capacity, F[j][i] = 0
743781a2d9 2012-06-26        kinaba: //
743781a2d9 2012-06-26        kinaba: // Verified by
743781a2d9 2012-06-26        kinaba: //   - SRM 399 Div1 LV3
743781a2d9 2012-06-26        kinaba: //   - PKU 1459
743781a2d9 2012-06-26        kinaba: //   - CodeCraft 09 CUTS
743781a2d9 2012-06-26        kinaba: //   - SRM 465 Div1 LV2
743781a2d9 2012-06-26        kinaba: //   - SRM 543 Div1 LV3
743781a2d9 2012-06-26        kinaba: //-------------------------------------------------------------
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: template<typename T>
743781a2d9 2012-06-26        kinaba: class IdGen
743781a2d9 2012-06-26        kinaba: {
743781a2d9 2012-06-26        kinaba: 	map<T, int> v2id_;
743781a2d9 2012-06-26        kinaba: 	vector<T>   id2v_;
743781a2d9 2012-06-26        kinaba: public:
743781a2d9 2012-06-26        kinaba: 	int v2id(const T& v) {
743781a2d9 2012-06-26        kinaba: 		if( !v2id_.count(v) ) { v2id_[v] = size(); id2v_.push_back(v); }
743781a2d9 2012-06-26        kinaba: 		return v2id_[v];
743781a2d9 2012-06-26        kinaba: 	}
743781a2d9 2012-06-26        kinaba: 	const T& id2v(int i) const { return id2v_[i]; }
743781a2d9 2012-06-26        kinaba: 	int size() const { return id2v_.size(); }
743781a2d9 2012-06-26        kinaba: };
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: template<typename Vert, typename Flow, int NV=2048>
743781a2d9 2012-06-26        kinaba: class MaxFlow
743781a2d9 2012-06-26        kinaba: {
743781a2d9 2012-06-26        kinaba: 	IdGen<Vert> idgen;
743781a2d9 2012-06-26        kinaba: 	vector<int> G[NV];
743781a2d9 2012-06-26        kinaba: 	Flow F[NV][NV];
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: public:
743781a2d9 2012-06-26        kinaba: 	void addEdge( Vert s_, Vert t_, Flow f )
743781a2d9 2012-06-26        kinaba: 	{
743781a2d9 2012-06-26        kinaba: 		const int s = idgen.v2id(s_), t = idgen.v2id(t_);
743781a2d9 2012-06-26        kinaba: 		G[s].push_back(t);
743781a2d9 2012-06-26        kinaba: 		G[t].push_back(s);
743781a2d9 2012-06-26        kinaba: 		F[s][t] = f;
743781a2d9 2012-06-26        kinaba: 		F[t][s] = 0;
743781a2d9 2012-06-26        kinaba: 	}
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 	Flow calc( Vert s_, Vert t_ )
743781a2d9 2012-06-26        kinaba: 	{
743781a2d9 2012-06-26        kinaba: 		const int S = idgen.v2id(s_), D = idgen.v2id(t_);
743781a2d9 2012-06-26        kinaba: 		for( Flow total=0 ;; ) {
743781a2d9 2012-06-26        kinaba: 			// Do BFS and compute the level for each node.
743781a2d9 2012-06-26        kinaba: 			int LV[NV] = {0};
743781a2d9 2012-06-26        kinaba: 			vector<int> Q(1, S);
743781a2d9 2012-06-26        kinaba: 			for(int lv=1; !Q.empty(); ++lv) {
743781a2d9 2012-06-26        kinaba: 				vector<int> Q2;
743781a2d9 2012-06-26        kinaba: 				for(size_t i=0; i!=Q.size(); ++i) {
743781a2d9 2012-06-26        kinaba: 					const vector<int>& ne = G[Q[i]];
743781a2d9 2012-06-26        kinaba: 					for(size_t j=0; j!=ne.size(); ++j)
743781a2d9 2012-06-26        kinaba: 						if( F[Q[i]][ne[j]] && !LV[ne[j]] && ne[j]!=S )
743781a2d9 2012-06-26        kinaba: 							LV[ne[j]]=lv, Q2.push_back(ne[j]);
743781a2d9 2012-06-26        kinaba: 				}
743781a2d9 2012-06-26        kinaba: 				Q.swap(Q2);
743781a2d9 2012-06-26        kinaba: 			}
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 			// Destination is now unreachable. Done.
743781a2d9 2012-06-26        kinaba: 			if( !LV[D] )
743781a2d9 2012-06-26        kinaba: 				return total;
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 			// Iterating DFS.
743781a2d9 2012-06-26        kinaba: 			bool blocked[NV] = {};
743781a2d9 2012-06-26        kinaba: 			total += dinic_dfs( S, D, LV, 0x7fffffff, blocked );
743781a2d9 2012-06-26        kinaba: 		}
743781a2d9 2012-06-26        kinaba: 	}
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: private:
743781a2d9 2012-06-26        kinaba: 	Flow dinic_dfs( int v, int D, int LV[], Flow flow_in, bool blocked[] )
743781a2d9 2012-06-26        kinaba: 	{
743781a2d9 2012-06-26        kinaba: 		Flow flow_out = 0;
743781a2d9 2012-06-26        kinaba: 		for(size_t i=0; i!=G[v].size(); ++i) {
743781a2d9 2012-06-26        kinaba: 			int u = G[v][i];
743781a2d9 2012-06-26        kinaba: 			if( LV[v]+1==LV[u] && F[v][u] ) {
743781a2d9 2012-06-26        kinaba: 				Flow f = min(flow_in-flow_out, F[v][u]);
743781a2d9 2012-06-26        kinaba: 				if( u==D || !blocked[u] && (f=dinic_dfs(u,D,LV,f,blocked))>0 ) {
743781a2d9 2012-06-26        kinaba: 					F[v][u]  -= f;
743781a2d9 2012-06-26        kinaba: 					F[u][v]  += f;
743781a2d9 2012-06-26        kinaba: 					flow_out += f;
743781a2d9 2012-06-26        kinaba: 					if( flow_in == flow_out ) return flow_out;
743781a2d9 2012-06-26        kinaba: 				}
743781a2d9 2012-06-26        kinaba: 			}
743781a2d9 2012-06-26        kinaba: 		}
743781a2d9 2012-06-26        kinaba: 		blocked[v] = (flow_out==0);
743781a2d9 2012-06-26        kinaba: 		return flow_out;
743781a2d9 2012-06-26        kinaba: 	}
743781a2d9 2012-06-26        kinaba: };
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: class FoxAndCake { public:
743781a2d9 2012-06-26        kinaba: 	string ableToDivide(int W, int H, vector <int> x, vector <int> y)
743781a2d9 2012-06-26        kinaba: 	{
743781a2d9 2012-06-26        kinaba: 		vector< vector<char> > M = compress(W, H, x, y);
743781a2d9 2012-06-26        kinaba: 		H = M.size();
743781a2d9 2012-06-26        kinaba: 		W = M[0].size();
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 		typedef pair< int, pair<int,int> > Vert;
743781a2d9 2012-06-26        kinaba: 		enum {IN, OUT, SPECIAL};
743781a2d9 2012-06-26        kinaba: 		Vert Src(SPECIAL, make_pair(0, 0));
743781a2d9 2012-06-26        kinaba: 		Vert Sink(SPECIAL, make_pair(1, 1));
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 		MaxFlow<Vert,int,7*7*7*2+2> G;
743781a2d9 2012-06-26        kinaba: 		for(int y=0; y<H; ++y)
743781a2d9 2012-06-26        kinaba: 		for(int x=0; x<W; ++x) if( M[y][x]!='#' )
743781a2d9 2012-06-26        kinaba: 		{
743781a2d9 2012-06-26        kinaba: 			int dy[] = {-1,+1,0,0};
743781a2d9 2012-06-26        kinaba: 			int dx[] = {0,0,-1,+1};
743781a2d9 2012-06-26        kinaba: 			for(int d=0; d<4; ++d) {
743781a2d9 2012-06-26        kinaba: 				int yy = y + dy[d];
743781a2d9 2012-06-26        kinaba: 				int xx = x + dx[d];
743781a2d9 2012-06-26        kinaba: 				if(0<=yy&&yy<H&&0<=xx&&xx<W&&M[yy][xx]!='#')
743781a2d9 2012-06-26        kinaba: 					G.addEdge(Vert(OUT, make_pair(y,x)), Vert(IN, make_pair(yy,xx)), 1);
743781a2d9 2012-06-26        kinaba: 			}
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 			G.addEdge(Vert(IN, make_pair(y,x)), Vert(OUT, make_pair(y,x)), 1);
743781a2d9 2012-06-26        kinaba: 			if(M[y][x]=='C') G.addEdge(Src, Vert(IN, make_pair(y,x)), 1);
743781a2d9 2012-06-26        kinaba: 			if(M[y][x]=='S') G.addEdge(Vert(OUT, make_pair(y,x)), Sink, 1);
743781a2d9 2012-06-26        kinaba: 		}
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 		return G.calc(Src, Sink)==3 ? "Yes" : "No";
743781a2d9 2012-06-26        kinaba: 	}
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 	vector< vector<char> > compress(int W, int H, vector<int>& x, vector<int>& y)
743781a2d9 2012-06-26        kinaba: 	{
743781a2d9 2012-06-26        kinaba: 		for(int i=0; i<7; ++i)
743781a2d9 2012-06-26        kinaba: 			--x[i], --y[i];
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 		set<int> sigx, sigy;
743781a2d9 2012-06-26        kinaba: 		for(int i=0; i<7; ++i)
743781a2d9 2012-06-26        kinaba: 			for(int d=-3; d<=+3; ++d) {
743781a2d9 2012-06-26        kinaba: 				if(0<=x[i]+d && x[i]+d<W)
743781a2d9 2012-06-26        kinaba: 					sigx.insert(x[i]+d);
743781a2d9 2012-06-26        kinaba: 				if(0<=y[i]+d && y[i]+d<H)
743781a2d9 2012-06-26        kinaba: 					sigy.insert(y[i]+d);
743781a2d9 2012-06-26        kinaba: 			}
743781a2d9 2012-06-26        kinaba: 		vector<int> sx(sigx.begin(), sigx.end());
743781a2d9 2012-06-26        kinaba: 		vector<int> sy(sigy.begin(), sigy.end());
743781a2d9 2012-06-26        kinaba: 		map<int,int> inv_sx; for(int i=0; i<sx.size(); ++i) inv_sx[sx[i]] = i;
743781a2d9 2012-06-26        kinaba: 		map<int,int> inv_sy; for(int i=0; i<sy.size(); ++i) inv_sy[sy[i]] = i;
743781a2d9 2012-06-26        kinaba: 		W = sx.size();
743781a2d9 2012-06-26        kinaba: 		H = sy.size();
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: 		vector< vector<char> > result(H, vector<char>(W, ' '));
743781a2d9 2012-06-26        kinaba: 		for(int i=0; i<7; ++i) {
743781a2d9 2012-06-26        kinaba: 			int xx = inv_sx[x[i]];
743781a2d9 2012-06-26        kinaba: 			int yy = inv_sy[y[i]];
743781a2d9 2012-06-26        kinaba: 			result[yy][xx] = (i==0?'#':i<4?'C':'S');
743781a2d9 2012-06-26        kinaba: 		}
743781a2d9 2012-06-26        kinaba: 		return result;
743781a2d9 2012-06-26        kinaba: 	}
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: };
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: // BEGIN CUT HERE
743781a2d9 2012-06-26        kinaba: #include <ctime>
743781a2d9 2012-06-26        kinaba: double start_time; string timer()
743781a2d9 2012-06-26        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
743781a2d9 2012-06-26        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
743781a2d9 2012-06-26        kinaba:  { os << "{ ";
743781a2d9 2012-06-26        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
743781a2d9 2012-06-26        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
743781a2d9 2012-06-26        kinaba: void verify_case(const string& Expected, const string& Received) {
743781a2d9 2012-06-26        kinaba:  bool ok = (Expected == Received);
743781a2d9 2012-06-26        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
743781a2d9 2012-06-26        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
743781a2d9 2012-06-26        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
743781a2d9 2012-06-26        kinaba: #define END	 verify_case(_, FoxAndCake().ableToDivide(n, m, x, y));}
743781a2d9 2012-06-26        kinaba: int main(){
743781a2d9 2012-06-26        kinaba: 
743781a2d9 2012-06-26        kinaba: CASE(0)
743781a2d9 2012-06-26        kinaba: 	int n = 2;
743781a2d9 2012-06-26        kinaba: 	int m = 4;
743781a2d9 2012-06-26        kinaba: 	int x_[] = {1,1,1,1,2,2,2};
743781a2d9 2012-06-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
743781a2d9 2012-06-26        kinaba: 	int y_[] = {1,2,3,4,2,3,4};
743781a2d9 2012-06-26        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
743781a2d9 2012-06-26        kinaba: 	string _ = "Yes";
743781a2d9 2012-06-26        kinaba: END
743781a2d9 2012-06-26        kinaba: CASE(1)
743781a2d9 2012-06-26        kinaba: 	int n = 2;
743781a2d9 2012-06-26        kinaba: 	int m = 4;
743781a2d9 2012-06-26        kinaba: 	int x_[] = {1,1,2,1,2,1,2};
743781a2d9 2012-06-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
743781a2d9 2012-06-26        kinaba: 	int y_[] = {1,2,2,3,3,4,4};
743781a2d9 2012-06-26        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
743781a2d9 2012-06-26        kinaba: 	string _ = "No";
743781a2d9 2012-06-26        kinaba: END
743781a2d9 2012-06-26        kinaba: CASE(2)
743781a2d9 2012-06-26        kinaba: 	int n = 6;
743781a2d9 2012-06-26        kinaba: 	int m = 6;
743781a2d9 2012-06-26        kinaba: 	int x_[] = {1,1,3,4,3,4,5};
743781a2d9 2012-06-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
743781a2d9 2012-06-26        kinaba: 	int y_[] = {2,6,4,5,5,4,2};
743781a2d9 2012-06-26        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
743781a2d9 2012-06-26        kinaba: 	string _ = "Yes";
743781a2d9 2012-06-26        kinaba: END
743781a2d9 2012-06-26        kinaba: CASE(3)
743781a2d9 2012-06-26        kinaba: 	int n = 999999999;
743781a2d9 2012-06-26        kinaba: 	int m = 999999999;
743781a2d9 2012-06-26        kinaba: 	int x_[] = {500000000,1,1,1,999999999,999999999,999999999};
743781a2d9 2012-06-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
743781a2d9 2012-06-26        kinaba: 	int y_[] = {500000000,1,2,3,999999997,999999998,999999999};
743781a2d9 2012-06-26        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
743781a2d9 2012-06-26        kinaba: 	string _ = "Yes";
743781a2d9 2012-06-26        kinaba: END
743781a2d9 2012-06-26        kinaba: CASE(4)
743781a2d9 2012-06-26        kinaba: 	int n = 1000000000;
743781a2d9 2012-06-26        kinaba: 	int m = 1000000000;
743781a2d9 2012-06-26        kinaba: 	int x_[] = {500000000,1,1,2,999999998,999999999,999999999};
743781a2d9 2012-06-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
743781a2d9 2012-06-26        kinaba: 	int y_[] = {500000000,1,2,1,999999999,999999998,999999999};
743781a2d9 2012-06-26        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
743781a2d9 2012-06-26        kinaba: 	string _ = "No";
743781a2d9 2012-06-26        kinaba: END
743781a2d9 2012-06-26        kinaba: CASE(5)
743781a2d9 2012-06-26        kinaba: 	int n = 7;
743781a2d9 2012-06-26        kinaba: 	int m = 2;
743781a2d9 2012-06-26        kinaba: 	int x_[] = {4,1,2,3,5,6,7};
743781a2d9 2012-06-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
743781a2d9 2012-06-26        kinaba: 	int y_[] = {2,1,2,2,2,2,1};
743781a2d9 2012-06-26        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
743781a2d9 2012-06-26        kinaba: 	string _ = "No";
743781a2d9 2012-06-26        kinaba: END
743781a2d9 2012-06-26        kinaba: CASE(6)
743781a2d9 2012-06-26        kinaba: 	int n = 7;
743781a2d9 2012-06-26        kinaba: 	int m = 2;
743781a2d9 2012-06-26        kinaba: 	int x_[] = {5,1,2,4,3,6,7};
743781a2d9 2012-06-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
743781a2d9 2012-06-26        kinaba: 	  int y_[] = {1,1,1,1,1,1,1};
743781a2d9 2012-06-26        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
743781a2d9 2012-06-26        kinaba: 	string _ = "No";
743781a2d9 2012-06-26        kinaba: END
743781a2d9 2012-06-26        kinaba: }
743781a2d9 2012-06-26        kinaba: // END CUT HERE