CF1019E Raining season

https://www.luogu.org/problemnew/show/CF1019E

题解

\[dis=day*a+b
\]

\[b=-day*a+dis
\]

然后就变成了斜率优化。

考虑边分治，每次把两边的凸包求出来。

然后再把两边的凸包做闵可夫斯基和求出新的凸包。

最后把分治求的的所有凸包上的点再做一次凸包即可得到答案凸包。

代码

#include<bits/stdc++.h>
#define N 200007
#define M 1000009
using namespace std;
typedef long long ll;
int head[N],tot=1,dp[N],sum,size[N],root,rootval,_rootval,top,n,m,num,cuu[2];
bool vis[N],jin[N<<1];
ll ans[M];
inline ll rd(){
  ll x=0;char c=getchar();bool f=0;
  while(!isdigit(c)){if(c=='-')f=1;c=getchar();}
  while(isdigit(c)){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
  return f?-x:x;
}
struct point{
    double x,y;
    inline point operator +(const point &b)const{return point{x+b.x,y+b.y};}
    inline point operator -(const point &b)const{return point{x-b.x,y-b.y};}
    inline double operator *(const point &b)const{return x*b.y-y*b.x;}
}cu[2][N],st[N*20];
inline double get_k(point y,point x){
    return (y.y-x.y)/(y.x-x.x);
}
inline bool cmp(point a,point b){
    if(a.x!=b.x)return a.x<b.x;
    return a.y>b.y;
}
struct nd{int to,a,b;};
vector<nd>vec[N];
vector<point>pt,tp[2];
struct edge{
    int n,to;
    ll a,b;
}e[N<<1];
inline void add(int u,int v,int a,int b){
    e[++tot].n=head[u];e[tot].to=v;head[u]=tot;e[tot].a=a;e[tot].b=b;
    e[++tot].n=head[v];e[tot].to=u;head[v]=tot;e[tot].a=a;e[tot].b=b;
}
inline void get_tb(int tag,int num){
  sort(cu[tag]+1,cu[tag]+num+1,cmp);
  tp[tag].clear();
  tp[tag].push_back(cu[tag][1]);
  int top=1;
  for(int i=2;i<=num;++i){
    if(cu[tag][i].x==tp[tag][top-1].x)continue;
    while(top>1&&get_k(cu[tag][i],tp[tag][top-2])>get_k(tp[tag][top-1],tp[tag][top-2]))tp[tag].pop_back(),top--;
    tp[tag].push_back(cu[tag][i]);top++;
  }
}
inline void merge(){
   point now=tp[0][0]+tp[1][0];
   pt.push_back(now);
   int sm=tp[0].size()+tp[1].size()-2,now1=0,now2=0;
   for(int i=1;i<=sm;++i){
    point xx,yy;
    if(now1+1<tp[0].size())xx=tp[0][now1+1]-tp[0][now1];
    if(now2+1<tp[1].size())yy=tp[1][now2+1]-tp[1][now2];
    if(now2+1>=tp[1].size()||((now1+1<tp[0].size())&&xx*yy<0))now=now+xx,now1++;
    else now=now+yy,now2++;
    pt.push_back(now);
   }
}
void dfs1(int u,int fa){
    int now=0;
    for(vector<nd>::iterator it=vec[u].begin();it!=vec[u].end();++it){
        int v=it->to,a=it->a,b=it->b;
        if(v==fa)continue;
        if(!now){add(u,v,a,b);now=u;}
        else{++num;add(now,num,0,0);add(num,v,a,b);now=num;}
        dfs1(v,u);
    }
}
void getroot(int u,int fa){
    size[u]=1;dp[u]=0;
    for(int i=head[u];i;i=e[i].n)if(e[i].to!=fa&&!jin[i]){
        int v=e[i].to;
        getroot(v,u);
        size[u]+=size[v];
        if(max(size[v],sum-size[v])<rootval){
            root=i;
            rootval=max(size[v],sum-size[v]);
            _rootval=size[v];
        }
    }
}
void getdeep(int u,int fa,int tag,ll suma,ll sumb){
    bool tg=0;
    for(int i=head[u];i;i=e[i].n)if(e[i].to!=fa&&!jin[i]){
        int v=e[i].to;tg=1;
        getdeep(v,u,tag,suma+e[i].a,sumb+e[i].b);
    }
    if(!tg){
        cu[tag][++cuu[tag]]=point{suma,sumb};
    }
}
void solve(int rot,int S){
     int u=e[rot].to,v=e[rot^1].to;
     jin[rot]=jin[rot^1]=1;
     int sm1=_rootval,sm2=S-_rootval;
     cuu[0]=cuu[1]=0;
     getdeep(u,0,0,e[rot].a,e[rot].b);
     getdeep(v,0,1,0ll,0ll);
     get_tb(0,cuu[0]);
     get_tb(1,cuu[1]);
     merge();
     if(sm1!=1){
       sum=sm1;rootval=num;getroot(u,0);
       solve(root,sm1);
     }
     if(sm2!=1){
       sum=sm2;rootval=num;getroot(v,0);
       solve(root,sm2);
     }
}
int main(){
    n=rd();m=rd();
    if(n==1){
        for(int i=1;i<=m;++i)printf("0 ");
        return 0;
    }
    int x,y,a,b;
    for(int i=1;i<n;++i){
        x=rd();y=rd();a=rd();b=rd();
        vec[x].push_back(nd{y,a,b});
        vec[y].push_back(nd{x,a,b});
    }
    num=n;
    dfs1(1,0);
    root=0;sum=num;rootval=num;
    getroot(1,0);
    solve(root,num);
    sort(pt.begin(),pt.end(),cmp);
    for(vector<point>::iterator it=pt.begin();it!=pt.end();++it){
      point now=*it;
      if(!top){st[top=1]=now;continue;}
      if(now.x==st[top].x)continue;
      while(top>1&&get_k(now,st[top-1])>get_k(st[top],st[top-1]))top--;
      st[++top]=now;
    }
    for(int i=m-1;i>=0;--i){
      while(top>1&&get_k(st[top],st[top-1])<-i)top--;
      ans[i]=1ll*i*st[top].x+st[top].y;
    }
    for(int i=0;i<m;++i)printf("%I64d ",ans[i]);
    return 0;
}