HK 2016(Peak Tower-矩形面积并)

在$W*H$($m^2$)的方框里，由n个矩形（坐标平行于坐标轴），每个矩形开始在$(sx,sy)$，且以$(vx,vy)$的速度匀速移动。问在0~Es的时间里，方框内被矩形覆盖的最小面积。

矩形面积并，处理出若干个关键时间点（线线相撞的时刻）。

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<' ';\
                        cout<<a[i][m]<<endl; \
                        } 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
#define MAXN (2000)
int n;
double W,H,E,w[MAXN],h[MAXN],sx[MAXN],vx[MAXN],sy[MAXN],vy[MAXN];
const double eps = 1e-8;
vector<double> v;
//si+vit==sj+vjt si-sj=(vj-vi)t
void pre(int n) {
    v.pb(0);
    For(i,n) {
        Fork(j,i+1,n) {
            if (fabs(vx[j]-vx[i])>eps) {
                double tt=(sx[i]-sx[j])/(vx[j]-vx[i]);
                if (tt>0 && tt<E) v.pb(tt);
            }
            if (fabs(vy[j]-vy[i])>eps) {
                double tt=(sy[i]-sy[j])/(vy[j]-vy[i]);
                if (tt>0 && tt<E) v.pb(tt);
            }
        }
    }
    v.pb(E);
}
namespace RectUnion{
    struct data
    {
        double x1,x2,y;
        int flag;
        }a[3000];
    double hash[3000];
    double sum[3000];
    int col[3000];
    inline bool cp(data a,data b){return a.y<b.y;}
    void pushup(int size,int l,int r)
    {
        if(col[size])sum[size]=hash[r+1]-hash[l];
        else if(l==r)sum[size]=0;
        else sum[size]=sum[size*2]+sum[size*2+1];
    }
    void update(int L,int R,int flag,int l,int r,int size)
    {
        if(L<=l&&R>=r)
        {
            col[size]+=flag;
            pushup(size,l,r);
            return;
        }
        int m=(l+r)/2;
        if(L<=m)update(L,R,flag,l,m,size*2);
        if(R>m)update(L,R,flag,m+1,r,size*2+1);
        pushup(size,l,r);
    }
    double work(double t,int n) {
        double x1,y1,x2,y2;
        int cnt=0;
        for(int i=1;i<=n;i++)
        {
            x1=sx[i]+ t* vx[i];
            y1=sy[i]+ t* vy[i];
            x2=x1+w[i];
            y2=y1+h[i];
            x1=max(x1,0.),x2=min(x2,W);
            x2=max(x2,0.),x1=min(x1,W);
            y1=max(y1,0.),y2=min(y2,H);
            y2=max(y2,0.),y1=min(y1,H);
            if(x1>=x2 || y1>=y2) continue;
            ++cnt;
            a[2*cnt-1].x1=a[2*cnt].x1=x1;
            a[2*cnt-1].x2=a[2*cnt].x2=x2;
            a[2*cnt-1].y=y1;a[2*cnt].y=y2;
            a[2*cnt-1].flag=1;a[2*cnt].flag=-1;
            hash[2*cnt-1]=x1;hash[2*cnt]=x2;
        }
        sort(a+1,a+2*cnt+1,cp);sort(hash+1,hash+2*cnt+1);
        memset(col,0,sizeof(col));
        memset(sum,0,sizeof(sum));
        double ans=0;
        for(int i=1;i<=2*cnt;i++)
        {
            int l=lower_bound(hash+1,hash+2*cnt+1,a[i].x1)-hash;
            int r=lower_bound(hash+1,hash+2*cnt+1,a[i].x2)-hash-1;
            if(l<=r)update(l,r,a[i].flag,1,2*cnt,1);
            ans+=sum[1]*(a[i+1].y-a[i].y);
        }
        return ans;
        printf("%.2lf\n",ans);
    }
};
int main()
{
//  freopen("C.in","r",stdin);
//  freopen(".out","w",stdout);
    n=read();
    cin>>W>>H>>E;   
    For(i,n) {
        cin>>w[i]>>h[i]>>sx[i]>>sy[i]>>vx[i]>>vy[i];
    }
    Fork(i,n+1,2*n) {
        sx[i] = sx[i-n]+w[i-n];
        vx[i] = vx[i-n];
        sy[i] = sy[i-n]+h[i-n];
        vy[i] = vy[i-n];
    }
    sx[n*2+1]=0,vx[n*2+1]=0;
    sy[n*2+1]=0,vx[n*2+1]=0;
    sx[n*2+2]=W,vy[n*2+2]=0;
    sy[n*2+2]=H,vy[n*2+2]=0;
    pre(n*2+2);

    double ans=RectUnion::work(0,n);
    sort(ALL(v));
    for(double t:v) {
        double p=RectUnion::work(t,n);
        gmin(ans,p)
    }
    for(double t=0;t<=E;t+=0.01) {
        double p=RectUnion::work(t,n);
//      if (p<ans) cout<<t<<endl;
//      cout<<t;
        gmin(ans,p)
    }
    cout<<setiosflags(ios::fixed)<<setprecision(10)<<ans<<endl;
    return 0;
}