4fd800b3a8 2011-02-23        kinaba: #include <iostream>
4fd800b3a8 2011-02-23        kinaba: #include <sstream>
4fd800b3a8 2011-02-23        kinaba: #include <iomanip>
4fd800b3a8 2011-02-23        kinaba: #include <vector>
4fd800b3a8 2011-02-23        kinaba: #include <string>
4fd800b3a8 2011-02-23        kinaba: #include <map>
4fd800b3a8 2011-02-23        kinaba: #include <set>
4fd800b3a8 2011-02-23        kinaba: #include <algorithm>
4fd800b3a8 2011-02-23        kinaba: #include <numeric>
4fd800b3a8 2011-02-23        kinaba: #include <iterator>
4fd800b3a8 2011-02-23        kinaba: #include <functional>
4fd800b3a8 2011-02-23        kinaba: #include <complex>
4fd800b3a8 2011-02-23        kinaba: #include <queue>
4fd800b3a8 2011-02-23        kinaba: #include <stack>
4fd800b3a8 2011-02-23        kinaba: #include <cmath>
4fd800b3a8 2011-02-23        kinaba: #include <cassert>
4fd800b3a8 2011-02-23        kinaba: #include <cstring>
4fd800b3a8 2011-02-23        kinaba: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: typedef complex<double> CMP;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: class BunnyExam { public:
4fd800b3a8 2011-02-23        kinaba: 	double getExpected(int m, int k, vector <int> linkage)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		// trivially impossible cases
4fd800b3a8 2011-02-23        kinaba: 		if( k==1 && m>1	)
4fd800b3a8 2011-02-23        kinaba: 			return -1;
4fd800b3a8 2011-02-23        kinaba: 		if( k==2 )
4fd800b3a8 2011-02-23        kinaba: 			for(int i=0; i<linkage.size(); i+=2)
4fd800b3a8 2011-02-23        kinaba: 				if( (linkage[i] ^ linkage[i+1])&1 )
4fd800b3a8 2011-02-23        kinaba: 					return -1;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<linkage.size(); i+=2)
4fd800b3a8 2011-02-23        kinaba: 			if( abs(linkage[i] - linkage[i+1]) == 1 )
4fd800b3a8 2011-02-23        kinaba: 				return -1;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		// interference graph
4fd800b3a8 2011-02-23        kinaba: 		int M = linkage.size()/2;
4fd800b3a8 2011-02-23        kinaba: 		vector< vector<int> > conflict(M);
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<M; ++i)
4fd800b3a8 2011-02-23        kinaba: 		for(int j=0; j<M; ++j)
4fd800b3a8 2011-02-23        kinaba: 			if( abs(linkage[2*i+0]-linkage[2*j+0])==1 || abs(linkage[2*i+1]-linkage[2*j+0])==1
4fd800b3a8 2011-02-23        kinaba: 			 || abs(linkage[2*i+0]-linkage[2*j+1])==1 || abs(linkage[2*i+1]-linkage[2*j+1])==1 )
4fd800b3a8 2011-02-23        kinaba: 				conflict[i].push_back(j);
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		// check k-colorability
4fd800b3a8 2011-02-23        kinaba: 		if( colorable(conflict, k) )
4fd800b3a8 2011-02-23        kinaba: 			return double(m)/k;
4fd800b3a8 2011-02-23        kinaba: 		else
4fd800b3a8 2011-02-23        kinaba: 			return -1;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	bool colorable(vector< vector<int> >& G, int k)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		if( G.size() <= k )
4fd800b3a8 2011-02-23        kinaba: 			return true;
4fd800b3a8 2011-02-23        kinaba: 		vector<int> color(G.size(), (1<<k)-1);
4fd800b3a8 2011-02-23        kinaba: 		color[0] = 1;
4fd800b3a8 2011-02-23        kinaba: 		return rec(G, color, 0);
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	bool rec(vector< vector<int> >& G, const vector<int>& color, int i)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		if( i == color.size() )
4fd800b3a8 2011-02-23        kinaba: 			return true;
4fd800b3a8 2011-02-23        kinaba: 		for(int k=1; k<=color[i]; k<<=1)
4fd800b3a8 2011-02-23        kinaba: 			if( color[i] & k ) // use color k
4fd800b3a8 2011-02-23        kinaba: 			{
4fd800b3a8 2011-02-23        kinaba: 				vector<int> c2 = color;
4fd800b3a8 2011-02-23        kinaba: 				for(int j=0; j<G[i].size(); ++j) // G[i][j] cannot use k
4fd800b3a8 2011-02-23        kinaba: 					c2[G[i][j]] &= ~k;
4fd800b3a8 2011-02-23        kinaba: 				if( rec(G, c2, i+1) )
4fd800b3a8 2011-02-23        kinaba: 					return true;
4fd800b3a8 2011-02-23        kinaba: 			}
4fd800b3a8 2011-02-23        kinaba: 		return false;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: };
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: #include <ctime>
4fd800b3a8 2011-02-23        kinaba: double start_time; string timer()
4fd800b3a8 2011-02-23        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
4fd800b3a8 2011-02-23        kinaba:  { os << "{ ";
4fd800b3a8 2011-02-23        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
4fd800b3a8 2011-02-23        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
4fd800b3a8 2011-02-23        kinaba: void verify_case(const double& Expected, const double& Received) {
4fd800b3a8 2011-02-23        kinaba:  bool ok = (abs(Expected - Received) < 1e-9);
4fd800b3a8 2011-02-23        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
4fd800b3a8 2011-02-23        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
4fd800b3a8 2011-02-23        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
4fd800b3a8 2011-02-23        kinaba: #define END	 verify_case(_, BunnyExam().getExpected(m, k, linkage));}
4fd800b3a8 2011-02-23        kinaba: int main(){
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: CASE(0)
4fd800b3a8 2011-02-23        kinaba: 	int m = 3;
4fd800b3a8 2011-02-23        kinaba: 	int k = 2;
4fd800b3a8 2011-02-23        kinaba: 	int linkage_[] = { 1, 3 };
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 1.5;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	int m = 4;
4fd800b3a8 2011-02-23        kinaba: 	int k = 2;
4fd800b3a8 2011-02-23        kinaba: 	int linkage_[] = { 1, 4 };
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = -1.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	int m = 2;
4fd800b3a8 2011-02-23        kinaba: 	int k = 8;
4fd800b3a8 2011-02-23        kinaba: 	vector <int> linkage;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0.25;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	int m = 1000000000;
4fd800b3a8 2011-02-23        kinaba: 	int k = 1;
4fd800b3a8 2011-02-23        kinaba: 	int linkage_[] = { 11, 13, 2010, 487 };
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = -1.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: 	int m = 128;
4fd800b3a8 2011-02-23        kinaba: 	int k = 64;
4fd800b3a8 2011-02-23        kinaba: 	int linkage_[] = { 32, 16, 8, 4, 2, 1 }
4fd800b3a8 2011-02-23        kinaba: ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = -1.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(5)
4fd800b3a8 2011-02-23        kinaba: 	int m = 13;
4fd800b3a8 2011-02-23        kinaba: 	int k = 3;
4fd800b3a8 2011-02-23        kinaba: 	int linkage_[] = { 1, 3, 7, 9, 13, 10, 6, 2  }
4fd800b3a8 2011-02-23        kinaba: ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 4.333333333333333;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(6)
4fd800b3a8 2011-02-23        kinaba: 	int m = 8;
4fd800b3a8 2011-02-23        kinaba: 	int k = 3;
4fd800b3a8 2011-02-23        kinaba: 	int linkage_[] = {1,4,2,6,3,8,5,7};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = -1;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(7)
4fd800b3a8 2011-02-23        kinaba: 	int m = 1000000000;
4fd800b3a8 2011-02-23        kinaba: 	int k = 4;
4fd800b3a8 2011-02-23        kinaba: 	int linkage_[] = {1,4,2,6,3,8,5,7,9,19,  10,20,11,21,12,22,13,23,14,24};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = -1;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(8)
4fd800b3a8 2011-02-23        kinaba: 	int m = 20;
4fd800b3a8 2011-02-23        kinaba: 	int k = 3;
4fd800b3a8 2011-02-23        kinaba: 	int linkage_[] = {19, 6, 1, 14, 13, 9, 20, 10, 15, 8, 17, 5, 12, 7, 16, 2, 18, 4, 3, 11};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 6.666666666666667;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE