OJ-Problems-Source/HDOJ/3843_autoAC.cpp

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
const double pi = acos(-1.);
const double eps = 1e-8;
using namespace std;
int N;
int a[1000];
double ang[1000];
int dcmp( double x )
{
    if( x < eps )    return -1;
    if( x > eps )    return 1;
    return 0;
}
bool chk( int s, int e, double R )
{
    double t = 2*R*R;
    double sA = 0, mA = -1e30;
    int id;
    for( int i = s; i < e; ++i )
    {
        ang[i] = acos((t-a[i]*a[i])/t);
        sA += ang[i];
        if( mA < ang[i] )
            mA = ang[i], id = i;
    }
    if( dcmp(sA-mA-pi) >= 0 )
        return dcmp(sA-2*pi) <= 0;
    else
    {
        ang[id] *= -1;
        return dcmp(sA-mA+2*pi-mA - 2*pi) >= 0;
    }
}
int cal( int s, int e, double& S )
{
    double ll = 0, rr = 1000000, R;
    for( int i = s; i < e; ++i )
        ll = max(ll, a[i]*0.5);
    for( int T = 0; T < 80; ++T )
    {
        R = (ll+rr)/2;
        if( chk(s, e, R) )
            rr = R;
        else
            ll = R;
    }
    R = (ll+rr)/2;
    S = 0;
    for( int i = s; i < e; ++i )
        S += R*R*sin(ang[i]);
    S *= 0.5;
    for( int i = s; i < e; ++i )    if( ang[i] < 0 )
        return i;
    return -1;
}
double f( int s, int e )
{
    if( e-s < 3 )    return 0;
    int sum = 0, mv = a[s];
    int i, j, k, id = s;
    for( i = s; i < e; ++i )
    {
        sum += a[i];
        if( a[i] > mv )
            mv = a[i], id = i;
    }
    if( sum <= mv*2 )
        return f(s, id)+f(id+1, e);
    else
    {
        double S;
        k = cal(s, e, S);
        if( k < 0 )
            return S;
        return max(S, f(s, k)+f(k+1, e));
    }
}
int main()
{
    int i, cases = 1;
    while( scanf("%d", &N), N )
    {
        for( i = 0; i < N; ++i )
            scanf("%d", &a[i]);
        printf("Case %d: %.8lf\n", cases++, f(0, N));
    }
    return 0;
}