#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
class BunnyExam { public:
double getExpected(int m, int k, vector <int> linkage)
{
// trivially impossible cases
if( k==1 && m>1 )
return -1;
if( k==2 )
for(int i=0; i<linkage.size(); i+=2)
if( (linkage[i] ^ linkage[i+1])&1 )
return -1;
for(int i=0; i<linkage.size(); i+=2)
if( abs(linkage[i] - linkage[i+1]) == 1 )
return -1;
// interference graph
int M = linkage.size()/2;
vector< vector<int> > conflict(M);
for(int i=0; i<M; ++i)
for(int j=0; j<M; ++j)
if( abs(linkage[2*i+0]-linkage[2*j+0])==1 || abs(linkage[2*i+1]-linkage[2*j+0])==1
|| abs(linkage[2*i+0]-linkage[2*j+1])==1 || abs(linkage[2*i+1]-linkage[2*j+1])==1 )
conflict[i].push_back(j);
// check k-colorability
if( colorable(conflict, k) )
return double(m)/k;
else
return -1;
}
bool colorable(vector< vector<int> >& G, int k)
{
if( G.size() <= k )
return true;
vector<int> color(G.size(), (1<<k)-1);
color[0] = 1;
return rec(G, color, 0);
}
bool rec(vector< vector<int> >& G, const vector<int>& color, int i)
{
if( i == color.size() )
return true;
for(int k=1; k<=color[i]; k<<=1)
if( color[i] & k ) // use color k
{
vector<int> c2 = color;
for(int j=0; j<G[i].size(); ++j) // G[i][j] cannot use k
c2[G[i][j]] &= ~k;
if( rec(G, c2, i+1) )
return true;
}
return false;
}
};
// 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 double& Expected, const double& Received) {
bool ok = (abs(Expected - Received) < 1e-9);
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(_, BunnyExam().getExpected(m, k, linkage));}
int main(){
CASE(0)
int m = 3;
int k = 2;
int linkage_[] = { 1, 3 };
vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
double _ = 1.5;
END
CASE(1)
int m = 4;
int k = 2;
int linkage_[] = { 1, 4 };
vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
double _ = -1.0;
END
CASE(2)
int m = 2;
int k = 8;
vector <int> linkage;
double _ = 0.25;
END
CASE(3)
int m = 1000000000;
int k = 1;
int linkage_[] = { 11, 13, 2010, 487 };
vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
double _ = -1.0;
END
CASE(4)
int m = 128;
int k = 64;
int linkage_[] = { 32, 16, 8, 4, 2, 1 }
;
vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
double _ = -1.0;
END
CASE(5)
int m = 13;
int k = 3;
int linkage_[] = { 1, 3, 7, 9, 13, 10, 6, 2 }
;
vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
double _ = 4.333333333333333;
END
CASE(6)
int m = 8;
int k = 3;
int linkage_[] = {1,4,2,6,3,8,5,7};
vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
double _ = -1;
END
CASE(7)
int m = 1000000000;
int k = 4;
int linkage_[] = {1,4,2,6,3,8,5,7,9,19, 10,20,11,21,12,22,13,23,14,24};
vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
double _ = -1;
END
CASE(8)
int m = 20;
int k = 3;
int linkage_[] = {19, 6, 1, 14, 13, 9, 20, 10, 15, 8, 17, 5, 12, 7, 16, 2, 18, 4, 3, 11};
vector <int> linkage(linkage_, linkage_+sizeof(linkage_)/sizeof(*linkage_));
double _ = 6.666666666666667;
END
}
// END CUT HERE