[ZJOI2010]贪吃的老鼠

#include<bits/stdc++.h>
#define reg register int
#define il inline
#define fi first
#define se second
#define mk(a,b) make_pair(a,b)
#define numb (ch^‘0‘)
#define pb push_back
#define solid const auto &
#define enter cout<<endl
#define pii pair<int,int>
#define double long double
using namespace std;
typedef long long ll;
template<class T>il void rd(T &x){
    char ch;x=0;bool fl=false;
    while(!isdigit(ch=getchar()))(ch==‘-‘)&&(fl=true);
    for(x=numb;isdigit(ch=getchar());x=x*10+numb);
    (fl==true)&&(x=-x);
}
template<class T>il void output(T x){if(x/10)output(x/10);putchar(x%10+‘0‘);}
template<class T>il void ot(T x){if(x<0) putchar(‘-‘),x=-x;output(x);putchar(‘ ‘);}
template<class T>il void prt(T a[],int st,int nd){for(reg i=st;i<=nd;++i) ot(a[i]);putchar(‘\n‘);}

namespace Miracle{
const int N=33;
const int P=33*33*2+44;
const double inf=1e9;
const double eps=1e-8;
int n,m;
struct node{
    int nxt,to;
    double w;
}e[2*(P*N+N+P)];
int hd[P],cnt=1;
int p[N],st[N],nd[N];
int sp[N];
double mem[2*N];
int num;
int sum;
void add(int x,int y,double z){
    e[++cnt].nxt=hd[x];
    e[cnt].to=y;
    e[cnt].w=z;
    hd[x]=cnt;

    e[++cnt].nxt=hd[y];
    e[cnt].to=x;
    e[cnt].w=0;
    hd[y]=cnt;
}
int d[P];
int s,t;
double dfs(int x,double flow){
    if(x==t) return flow;
    double res=flow;
    for(reg i=hd[x];i&&res>eps;i=e[i].nxt){
        int y=e[i].to;
        if(e[i].w>eps&&d[y]==d[x]+1){
            double k=dfs(y,min(res,e[i].w));
            if(!k) d[y]=0;
            res-=k;
            e[i].w-=k;
            e[i^1].w+=k;
        }
    }
    return flow-res;
}
int q[P],l,r;
bool bfs(){
    memset(d,0,sizeof d);
    l=1;r=0;
    q[++r]=s;
    d[s]=1;
    while(l<=r){
        int x=q[l++];
        for(reg i=hd[x];i;i=e[i].nxt){
            int y=e[i].to;
            if(e[i].w>eps&&!d[y]){
                d[y]=d[x]+1;
                q[++r]=y;
                if(y==t) return true;
            }
        }
    }
    return false;
}
int id(int x,int y){
    return m+(x-1)*num+y;
}
bool che(double mid){
    memset(hd,0,sizeof hd);
    cnt=1;
    num=0;
    for(reg i=1;i<=m;++i){
        mem[++num]=st[i];mem[++num]=nd[i]+mid;
    }
    sort(mem+1,mem+num+1);
    num=unique(mem+1,mem+num+1)-mem-1;
    --num;//warning!!!

    s=0,t=id(n,num)+1;
    for(reg i=1;i<=m;++i){
        add(i,t,p[i]);
    }
    for(reg i=1;i<=n;++i){
        for(reg j=1;j<=num;++j){
            for(reg k=1;k<=m;++k){
                if(st[k]<=mem[j]&&mem[j+1]<=nd[k]+mid){
                    add(id(i,j),k,(double)sp[i]*(mem[j+1]-mem[j]));
                }
            }
            add(s,id(i,j),(double)sp[i]*i*(mem[j+1]-mem[j]));
        }
    }
    double flow=0,ret=0;
    while(bfs()){
        while(1){
            flow=dfs(s,inf);
            if(flow<eps) break;
            ret+=flow;
        }
    }
    if(ret+eps>sum) return true;
    return false;
}
void clear(){
    sum=0;
    s=0;t=0;
}
bool cmp(int x,int y){
    return x>y;
}
int main(){
    int T;
    rd(T);
    while(T--){
        clear();
        rd(m);rd(n);    
        for(reg i=1;i<=m;++i){
            rd(p[i]);rd(st[i]);rd(nd[i]);
            sum+=p[i];
        }
        for(reg i=1;i<=n;++i){
            rd(sp[i]);
        }
        sort(sp+1,sp+n+1,cmp);
        sp[n+1]=0;
        for(reg i=1;i<=n;++i){
            sp[i]-=sp[i+1];
        }
        double L=0.0,R=1e7+3;
        for(reg i=1;i<=60;++i){
            double mid=(R+L)/2;
            if(che(mid)) R=mid;
            else L=mid;
        }
        printf("%.10Lf\n",L);
    }
    return 0;
}

}
signed main(){
    Miracle::main();
    return 0;
}

/*
   Author: *Miracle*
*/