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 <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: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: int INF = 10000000;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: class TwinTowns
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba: 	vector <int> optimalTwinTowns(vector <int> x, vector <int> y, int maxPartners, int minDistance)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		int N = x.size();
4fd800b3a8 2011-02-23        kinaba: 		int cost[10][10];
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<N; ++i)
4fd800b3a8 2011-02-23        kinaba: 		for(int j=0; j<N; ++j)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			int d = abs(x[i]-x[j]) + abs(y[i]-y[j]);
4fd800b3a8 2011-02-23        kinaba: 			cost[i][j] = (d < minDistance ? INF : d);
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		vector<int> v(N, maxPartners);
4fd800b3a8 2011-02-23        kinaba: 		pair<int,int> r = rec(0, N, v, cost);
4fd800b3a8 2011-02-23        kinaba: 		vector<int> ans(2);
4fd800b3a8 2011-02-23        kinaba: 		ans[0] = -r.first;
4fd800b3a8 2011-02-23        kinaba: 		ans[1] = r.second;
4fd800b3a8 2011-02-23        kinaba: 		return ans;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	map< vector<int>,pair<int,int> > memo;
4fd800b3a8 2011-02-23        kinaba: 	pair<int,int> rec(int i, int N, vector<int>& v, int cost[10][10])
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		if( i==N )
4fd800b3a8 2011-02-23        kinaba: 			return make_pair(0, 0);
4fd800b3a8 2011-02-23        kinaba: 		vector<int> key(v.begin()+i, v.end());
4fd800b3a8 2011-02-23        kinaba: 		if( memo.count(key) )
4fd800b3a8 2011-02-23        kinaba: 			return memo[key];
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		// choose at most v[i] js s.t. cost[i][j]!=INF && v[j]!=0
4fd800b3a8 2011-02-23        kinaba: 		pair<int,int> best = rec(i+1, N, v, cost);
4fd800b3a8 2011-02-23        kinaba: 		if( v[i] >= 1 )
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			for(int j1= i+1; j1<N; ++j1) if(cost[i][j1]!=INF && v[j1])
4fd800b3a8 2011-02-23        kinaba: 			{
4fd800b3a8 2011-02-23        kinaba: 				v[j1]--;
4fd800b3a8 2011-02-23        kinaba: 				pair<int,int> a = rec(i+1, N, v, cost);
4fd800b3a8 2011-02-23        kinaba: 				a.first  -= 1;
4fd800b3a8 2011-02-23        kinaba: 				a.second += cost[i][j1];
4fd800b3a8 2011-02-23        kinaba: 				best = min(best, a);
4fd800b3a8 2011-02-23        kinaba: 				v[j1]++;
4fd800b3a8 2011-02-23        kinaba: 			}
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		if( v[i] >= 2 )
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			for(int j1= i+1; j1<N; ++j1) if(cost[i][j1]!=INF && v[j1])
4fd800b3a8 2011-02-23        kinaba: 			for(int j2=j1+1; j2<N; ++j2) if(cost[i][j2]!=INF && v[j2])
4fd800b3a8 2011-02-23        kinaba: 			{
4fd800b3a8 2011-02-23        kinaba: 				v[j1]--;
4fd800b3a8 2011-02-23        kinaba: 				v[j2]--;
4fd800b3a8 2011-02-23        kinaba: 				pair<int,int> a = rec(i+1, N, v, cost);
4fd800b3a8 2011-02-23        kinaba: 				a.first  -= 2;
4fd800b3a8 2011-02-23        kinaba: 				a.second += cost[i][j1] + cost[i][j2];
4fd800b3a8 2011-02-23        kinaba: 				best = min(best, a);
4fd800b3a8 2011-02-23        kinaba: 				v[j1]++;
4fd800b3a8 2011-02-23        kinaba: 				v[j2]++;
4fd800b3a8 2011-02-23        kinaba: 			}
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		if( v[i] >= 3 )
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			for(int j1= i+1; j1<N; ++j1) if(cost[i][j1]!=INF && v[j1])
4fd800b3a8 2011-02-23        kinaba: 			for(int j2=j1+1; j2<N; ++j2) if(cost[i][j2]!=INF && v[j2])
4fd800b3a8 2011-02-23        kinaba: 			for(int j3=j2+1; j3<N; ++j3) if(cost[i][j3]!=INF && v[j3])
4fd800b3a8 2011-02-23        kinaba: 			{
4fd800b3a8 2011-02-23        kinaba: 				v[j1]--;
4fd800b3a8 2011-02-23        kinaba: 				v[j2]--;
4fd800b3a8 2011-02-23        kinaba: 				v[j3]--;
4fd800b3a8 2011-02-23        kinaba: 				pair<int,int> a = rec(i+1, N, v, cost);
4fd800b3a8 2011-02-23        kinaba: 				a.first  -= 3;
4fd800b3a8 2011-02-23        kinaba: 				a.second += cost[i][j1] + cost[i][j2] + cost[i][j3];
4fd800b3a8 2011-02-23        kinaba: 				best = min(best, a);
4fd800b3a8 2011-02-23        kinaba: 				v[j1]++;
4fd800b3a8 2011-02-23        kinaba: 				v[j2]++;
4fd800b3a8 2011-02-23        kinaba: 				v[j3]++;
4fd800b3a8 2011-02-23        kinaba: 			}
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		return memo[key] = best;
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() { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: int verify_case(const vector <int> &Expected, const vector <int> &Received) { if (Expected == Received) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: " << print_array(Expected) << endl; cerr << "\tReceived: " << print_array(Received) << endl; } return 0;}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template<int N> struct Case_ { Case_(){start_time=clock();} };
4fd800b3a8 2011-02-23        kinaba: char Test_(...);
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<0>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,0,10};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {0,10,4};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int maxPartners = 1;
4fd800b3a8 2011-02-23        kinaba: 	int minDistance = 1;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal_[] = {1, 10 };
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<1>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,0,10};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {0,10,4};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int maxPartners = 1;
4fd800b3a8 2011-02-23        kinaba: 	int minDistance = 11;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal_[] = {1, 14 };
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<2>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,10,0,10};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {0,0,20,20};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int maxPartners = 1;
4fd800b3a8 2011-02-23        kinaba: 	int minDistance = 1;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal_[] = {2, 20 };
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<3>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,10,0,10};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {0,0,20,20};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int maxPartners = 2;
4fd800b3a8 2011-02-23        kinaba: 	int minDistance = 10;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal_[] = {4, 60 };
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<4>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,0,0,0,0,0,0,0,0};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {1,2,3,4,5,6,7,8,9};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int maxPartners = 3;
4fd800b3a8 2011-02-23        kinaba: 	int minDistance = 6;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal_[] = {6, 40 };
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> RetVal(RetVal_, RetVal_+sizeof(RetVal_)/sizeof(*RetVal_));
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, TwinTowns().optimalTwinTowns(x, y, maxPartners, minDistance)); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
4fd800b3a8 2011-02-23        kinaba: template<>      void Run_<-1>() {}
4fd800b3a8 2011-02-23        kinaba: int main() { Run_<0>(); }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE
4fd800b3a8 2011-02-23        kinaba: