【题解】[NOI2019Route](70分)

占坑

做法是拆掉所有式子,拆完式子看一下,如果A=0,发现边被分为了终点走向n的边和不走向n的边。所以边就有了新的边权,并且可以相加。然后通过网络流建模的套路建模使得满足时间的限制,然后由于有负边,所以跑spfa,这里60分。然后还有两个点是一条链,送10分。

先放代码,还没测,可能会爆零。交上去的爆零了因为没写freopenQAQ


//@winlere
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#define ERP(t,a) for(register int t=head[a];t;t=e[t].nx)

using namespace std;  typedef long long ll;
inline int qr(){
      register int ret=0,f=0;
      register char c=getchar();
      while(c<48||c>57)f|=c==45,c=getchar();
      while(c>=48&&c<=57) ret=ret*10+c-48,c=getchar();
      return f?-ret:ret;
}
namespace sol1{

      const int maxn=3e5+5;
      struct E{
	    int fr,to,st,ed;
	    E(){to=fr=st=ed=0;}
	    E(const int&a,const int&b,const int&c,const int&d){
		  fr=a;to=b;st=c;ed=d;
	    }
      }data[maxn];
      ll w[maxn];
      int arc[maxn];
      int cnt;
      int nodecnt;
      typedef pair < ll , int > P;
      //priority_queue< P , vector<P>,greater <P> > q;
      queue<P> q;
      bool in[maxn<<2];
      vector < int > fr[maxn],to[maxn];
      vector < P >  e[maxn<<2];
      inline bool cmp(const int&a,const int&b){
	    return data[a].ed>data[b].ed;
      }
      int n,m,A,B,C;
      inline bool cmp2(const int&a,const int&b){
	    return data[a].st>data[b].st;
      }
      ll d[maxn<<2];
      inline ll spfa(){
	    for(register int t=1;t<maxn<<2;++t) d[t]=2e18;
	    d[0]=0;in[0]=1;
	    q.push(make_pair(0,0));
	    while(!q.empty()){
		  P cur=q.front();
		  q.pop();in[cur.second]=0;
		  for(register int t=0,edd=e[cur.second].size();t<edd;++t){
			//cout<<d[e[cur.second][t].second]<<' '<<d[cur.second]+e[cur.second][t].first<<endl;
			if(d[e[cur.second][t].second]>d[cur.second]+e[cur.second][t].first){
			      d[e[cur.second][t].second]=d[cur.second]+e[cur.second][t].first;
			      if(!in[e[cur.second][t].second])
				    q.push(make_pair(d[e[cur.second][t].second],e[cur.second][t].second)),in[e[cur.second][t].second]=1;
			}
		  }
	    }
	    return d[m+1];
      }
      
      inline void add(const int&fr,const int&to,const ll&w){
	    //cout<<"fr="<<fr<<' '<<"to="<<to<<" w="<<w<<endl;
	    e[fr].push_back(make_pair(w,to));
      }
      
      
      inline int init(const int&a,const int&b,const int&c,const int&d1,const int&e1){
	    n=a;m=b;A=c;B=d1;C=e1;
	    nodecnt=n;
	    for(register int t=1,x,y,p,q;t<=m;++t){
		  x=qr();y=qr();p=qr();q=qr();
		  //cout<<x<<' '<<y<<' '<<p<<' '<<q<<endl;
		  data[t]=E(x,y,p,q);
		  w[t]=C+1ll*B*p+1ll*A*p*p;
		  if(y!=n) w[t]=w[t]+1ll*A*q*q-1ll*B*q;
		  if(y==n) w[t]=w[t]+0ll+q;
		  fr[x].push_back(t);to[y].push_back(t);
		  if(x==1) add(0,t,w[t]);
		  if(y==n) add(t,m+1,0);
	    }
	    for(register int t=1;t<=n;++t){
		  //if(fr[t].empty()||to[t].empty())continue;
		  sort(to[t].begin(),to[t].end(),cmp);
		  sort(fr[t].begin(),fr[t].end(),cmp2);
		  int k=0;/*
			    
			    cout<<t<<' '<<fr[t].size()<<' '<<to[t].size()<<endl;
			    cout<<"fr=";
			    for(auto f:fr[t])
			    cout<<f<<"   ";
			    putchar('
');
			    cout<<"to=";
			    for(auto f:to[t])
			    cout<<f<<"   ";
			    putchar('
');

			   */
		  for(register int i=0,edd=to[t].size(),ed2=fr[t].size();i<edd;++i){
			if(i<edd-1)add(to[t][i+1],to[t][i],0);
			while(k<ed2&&data[fr[t][k]].st>=data[to[t][i]].ed) add(to[t][i],fr[t][k],w[fr[t][k]]),++k;
		  }
	    }
	    cout<<spfa()<<endl;
	    return 0;
      }
      
}

int main(){
      freopen("route.in","r",stdin);
      freopen("route.out","w",stdout);

      int a=qr(),b=qr(),c=qr(),d=qr(),e=qr();
      if(a<=100&&b==a-1&&c!=0){
	    ll A=c,B=d,C=e;
	    ll ans=1ll*a*C;
	    ll t1=0,t2=0,t3=0;
	    for(register int t=1;t<=b;++t){
		  qr();qr();t1=qr();t2=qr();
		  ans+=B*(t1-t3)+A*(t1-t3)*(t1-t3);
		  t3=t2;
	    }
	    cout<<ans+t3<<endl;
	    return 0;
      }
      return sol1::init(a,b,c,d,e);
      return 0;
}



原文地址:https://www.cnblogs.com/winlere/p/11195100.html