Data structure (tree link Division): noi2014 ticket purchase

 

 

Use the line tree to optimize the convex hull.

Note the following:

1. Recursive non-duplicated son must be performed first. If recursive re-son is performed first, a useful solution may be kicked out.

2. You cannot create only one Convex Hull for each chain, because the convex hull cannot be updated with only a certain part of the answer (it may not be considered that the point in the range is combined with a certain point to kill the optimal point ).

Another is to use double to compare the slope in the old field. Otherwise, long will be cracked.

  1 #include <algorithm>  2 #include <iostream>  3 #include <cstring>  4 #include <cstdio>  5 #include <vector>  6 using namespace std;  7 const long long INF=(long long)1e18;  8 const int maxn=200010;  9 int cnt,fir[maxn],to[maxn],nxt[maxn],son[maxn],sz[maxn],fa[maxn],n,t; 10 long long val[maxn],P[maxn],Q[maxn],S[maxn],F[maxn],L[maxn]; 11 void addedge(int a,int b,long long c){ 12     nxt[++cnt]=fir[a];fir[a]=cnt;to[cnt]=b;val[cnt]=c; 13 } 14  15 void DFS(int x){ 16     sz[x]=1; 17     for(int i=fir[x];i;i=nxt[i]) 18         if(to[i]!=fa[x]){ 19             fa[to[i]]=x; 20             S[to[i]]=S[x]+val[i]; 21             DFS(to[i]); 22             sz[x]+=sz[to[i]]; 23             if(sz[son[x]]<sz[to[i]]) 24                 son[x]=to[i]; 25         } 26 } 27  28 int top[maxn],ID[maxn],RID[maxn],tot; 29 void DFS(int x,int tp){ 30     ID[x]=++tot;RID[tot]=x;top[x]=tp; 31     if(son[x])DFS(son[x],tp); 32     for(int i=fir[x];i;i=nxt[i]) 33         if(to[i]!=fa[x]&&to[i]!=son[x]) 34             DFS(to[i],to[i]); 35 } 36  37 struct Slope{ 38     vector<int>id; 39     void Insert(int x){ 40         int p=id.size()-1; 41         id.push_back(x); 42         while(true){ 43             if(p<=0)break; 44             if(1.0*(F[id[p]]-F[id[p-1]])/(S[id[p]]-S[id[p-1]])<1.0*(F[id[p+1]]-F[id[p]])/(S[id[p+1]]-S[id[p]]))break; 45             id.pop_back();id.pop_back();id.push_back(x);p--; 46         } 47         return;  48     } 49      50     long long Query(int p){ 51         int p1=-1,p2; 52         for(int i=20;i>=0;i--){ 53             p2=p1+(1<<i); 54             if(p2>=id.size()-1)continue; 55             if(1.0*(F[id[p2+1]]-F[id[p2]])/P[p]<=1.0*(S[id[p2+1]]-S[id[p2]])) 56                 p1+=1<<i; 57         } 58         p1+=1; 59         return F[id[p1]]+(S[p]-S[id[p1]])*P[p]+Q[p]; 60     } 61 }slope[maxn<<2]; 62  63 long long Query(int x,int l,int r,int a,int b,int p){ 64     if(l>=a&&r<=b) 65         return slope[x].Query(p); 66          67     int mid=(l+r)>>1; 68     long long ret=INF; 69     if(a<=mid) 70         ret=Query(x<<1,l,mid,a,b,p); 71     if(mid<b) 72         ret=min(ret,Query(x<<1|1,mid+1,r,a,b,p)); 73     return ret;         74 } 75  76 void Insert(int x,int l,int r,int p){ 77     slope[x].Insert(p); 78     if(l==r)return; 79     int mid=(l+r)>>1; 80     if(mid>=ID[p]) 81         Insert(x<<1,l,mid,p); 82     else 83         Insert(x<<1|1,mid+1,r,p);     84 } 85  86 long long Get_ans(int p){  87     int pos=fa[p]; 88     long long ret=INF; 89     while(pos){ 90         if(S[p]-L[p]>S[pos])break; 91         int p1=ID[top[pos]]-1; 92         for(int i=20;i>=0;i--) 93             if(p1+(1<<i)<ID[pos]&&S[RID[p1+(1<<i)]]<S[p]-L[p]) 94                 p1+=1<<i;         95         ret=min(ret,Query(1,1,n,p1+1,ID[pos],p)); 96         pos=fa[top[pos]]; 97     } 98     return ret; 99 }100 101 void Solve(int x){102     F[x]=x==1?0:Get_ans(x);103     Insert(1,1,n,x);104     for(int i=fir[x];i;i=nxt[i])105         if(to[i]!=son[x])106             Solve(to[i]);107     if(son[x])108         Solve(son[x]);        109     return;110 }111 112 int main(){113 #ifndef ONLINE_JUDGE 114     freopen("ticket.in","r",stdin);115     freopen("ticket.out","w",stdout);116 #endif 117     scanf("%d%d",&n,&t);118     for(int i=2,a,b;i<=n;i++){119         scanf("%d%d%lld%lld%lld",&a,&b,&P[i],&Q[i],&L[i]);120         addedge(a,i,b*1ll);121     }122     123     DFS(1);124     DFS(1,1);125     126     Solve(1);127     for(int i=2;i<=n;i++)128         printf("%lld\n",F[i]);129     return 0;130 }

 

Data structure (tree link Division): noi2014 ticket purchase