UVa 10911 – Forming Quiz Teams


/*
User ID: turing_13
Link: https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=1852
*/

/*
         +-+ +-+ +-+
         |R| |.| |S|
         +-+ +-+ +-+
 */

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             10000
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sfl(a)          scanf("%lld",&a)
#define sff(a,b)        scanf("%d %d",&a,&b)
#define sffl(a,b)       scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)     scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)    scanf("%lld %lld %lld",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define CASE_PRINT      cout<<"Case "<<z<<": ";
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
int Set(int N,int pos)
{
    return N=N | (1<<pos);
}
int reset(int N,int pos)
{
    return N= N & ~(1<<pos);
}
bool check(int N,int pos)
{
    return (bool)(N & (1<<pos));
}
/*------------------------------------------------*/

vector<pii>v;

double dp[1<<17][16][2];
int vis[1<<17][16][2];
int n,z;

double dist(pii x, pii y)
{
    return sqrt((1.0*(x.ff-y.ff)*(x.ff-y.ff))+(1.0*(x.ss-y.ss)*(x.ss-y.ss)));
}

double call(int mask,int last, int pp)
{
    if(__builtin_popcount(mask)==2*n) return 0.0;

    double &ret=dp[mask][last][pp];
    int &state=vis[mask][last][pp];
    if(state==z) return ret;
    state=z;

    double temp=100000000.0;
//    ret=100000000.0;
    if(pp==0)
    {
        loop(i,2*n)
        {
            if(!check(mask,i))
            {
                temp=min(temp,call(Set(mask,i),i,1));
                break;
            }
        }
    }
    else
    {
        loop(i,2*n)
        {
            if(!check(mask,i))
                temp=min(temp,dist(v[last],v[i])+call(Set(mask,i),i,0));
        }
    }

    return ret=temp;
}

int main()
{
//    freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);
    CIN;
    while(cin>>n && n)
    {
        z++;
        loop(i,2*n)
        {
            string str;
            cin>>str;
            int a,b;
            cin>>a>>b;
            v.pb(MP(a,b));
        }
        CASE_PRINT;
        cout<<setprecision(2)<<fixed<<call(0,0,0)<<endl;
        v.clear();
    }


    return 0;
}


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