Gym 100269 L Lonely Mountain

分段函数+积分

/*
{
######################
#       Author       #
#        Gary        #
#        2021        #
######################
*/
#include<bits/stdc++.h>
#define rb(a,b,c) for(int a=b;a<=c;++a)
#define rl(a,b,c) for(int a=b;a>=c;--a)
#define LL long long
#define IT iterator
#define PB push_back
#define II(a,b) make_pair(a,b)
#define FIR first
#define SEC second
#define FREO freopen("check.out","w",stdout)
#define rep(a,b) for(int a=0;a<b;++a)
#define SRAND mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define random(a) rng()%a
#define ALL(a) a.begin(),a.end()
#define POB pop_back
#define ff fflush(stdout)
#define fastio ios::sync_with_stdio(false)
#define check_min(a,b) a=min(a,b)
#define check_max(a,b) a=max(a,b)
using namespace std;
//inline int read(){
//    int x=0;
//    char ch=getchar();
//    while(ch<'0'||ch>'9'){
//        ch=getchar();
//    }
//    while(ch>='0'&&ch<='9'){
//        x=(x<<1)+(x<<3)+(ch^48);
//        ch=getchar();
//    }
//    return x;
//}
const int INF=0x3f3f3f3f;
typedef pair<int,int> mp;
typedef long double lb;
/*}
*/
lb get(lb l){
	l=l*l*l;
	l*=1.0;
	l/=3.0;
	return l;
}
lb integral2(lb a,lb l,lb r){
	return (get(r)-get(l))*a;
}
lb integral1(lb a,lb l,lb r){
	lb l_,r_;
	l_=l*a;
	r_=r*a;
	return (r_+l_)*(r-l)/2.0;
}
lb integral0(lb a,lb l,lb r){
	return a*(r-l);
}
struct line{
	lb k,b;
	inline bool operator < (line oth)const{
		return 0;
	}
	inline bool operator > (line oth)const{
		return 0;
	}
	line (lb k_,lb b_){
		k=k_,b=b_;
	}
	line operator + (line oth){
		return line(k+oth.k,b+oth.b);
	}
	line operator - (line oth){
		return line(k-oth.k,b-oth.b);
	}
	line (pair<lb,lb> A,pair<lb,lb> B,bool rev=0){
		swap(A.FIR,A.SEC);
		swap(B.FIR,B.SEC);
		k=(A.SEC-B.SEC)/(A.FIR-B.FIR);
		b=A.SEC-k*A.FIR;
//		if(rev) k=-k;
	}
};
lb get(line A,line B,lb l,lb r){
//	printf("A:%.10Lf %.10Lf\n",A.k,A.b);
//	printf("B:%.10Lf %.10Lf\n",B.k,B.b);
//	printf("l:r %.10Lf %.10Lf\n",l,r); 
	lb a,b,c;
	a=A.k*B.k;
	b=A.k*B.b+B.k*A.b;
	c=A.b*B.b;
//	printf("a,b,c[ret] : %.10Lf %.10Lf %.10Lf %.10Lf \n",a,b,c,integral0(c,l,r)+integral1(b,l,r)+integral2(a,l,r)); 
	return integral0(c,l,r)+integral1(b,l,r)+integral2(a,l,r);
}
const int MAXN=1e5+23;
pair<lb,lb> a[MAXN],b[MAXN];
int n,m;
int main(){
	scanf("%d",&n);
	lb maxa,maxb;
	maxa=maxb=0;
	rb(i,1,n) scanf("%Lf%Lf",&a[i].FIR,&a[i].second),check_max(maxa,a[i].second);
	scanf("%d",&m);
	rb(i,1,m) scanf("%Lf%Lf",&b[i].FIR,&b[i].second),check_max(maxb,b[i].second);
	if(maxa!=maxb){
		printf("Invalid plan\n");
		return 0;
	}
	priority_queue<pair<lb,pair<int,line> > ,vector<pair<lb,pair<int,line> > > ,greater<pair<lb,pair<int,line> >  > > heap;
	lb rest=0;
	rb(i,1,n){
		if(i!=1&&a[i-1].second>a[i].second){
//			cout<<"$"<<i<<endl;	
//			cout<<line(a[i],a[i-1]).k<<endl;
			heap.push(II(a[i].second,II(1,line(a[i],a[i-1],1))));
			heap.push(II(a[i-1].SEC,II(-1,line(a[i],a[i-1],1))));
		}
		if(i!=n&&a[i+1].second>a[i].second){
			heap.push(II(a[i].second,II(-1,line(a[i],a[i+1],1))));
			heap.push(II(a[i+1].SEC,II(1,line(a[i],a[i+1],1))));
		}
	}
	rb(i,1,m){
		if(i!=1&&b[i-1].second>b[i].second){
			heap.push(II(b[i].second,II(2,line(b[i],b[i-1],1))));
			heap.push(II(b[i-1].SEC,II(-2,line(b[i],b[i-1],1))));
		}
		if(i!=m&&b[i+1].second>b[i].second){
			heap.push(II(b[i].second,II(-2,line(b[i],b[i+1],1))));
			heap.push(II(b[i+1].SEC,II(2,line(b[i],b[i+1],1))));
		}
	}
	line basea(0,0),baseb(0,0);
	while(!heap.empty()){
		lb tim=heap.top().FIR;
		while(!heap.empty()&&heap.top().FIR==tim){
			pair<lb,pair<int,line> >  now=heap.top();
			heap.pop();
			if(now.second.FIR==1){
				basea=basea+now.second.SEC;
			}
			if(now.second.FIR==-1){
				basea=basea-now.second.SEC;
			}
			if(now.second.FIR==2){
				baseb=baseb+now.second.SEC;
			}
			if(now.second.FIR==-2){
				baseb=baseb-now.second.SEC;	
			}
		}
		if(heap.empty()) break;
		lb r=heap.top().FIR;
		rest+=get(basea,baseb,tim,r);
	}
	printf("%.18Lf\n",rest); 
	return 0;
}