数据结构（树链剖分，线段树）：SDOI 2016 游戏

  1 #include <iostream>
  2 #include <cstring>
  3 #include <cstdio>
  4 using namespace std;
  5 const int maxn=100010;
  6 const long long INF=123456789123456789LL;
  7 int cnt,fir[maxn],nxt[maxn<<1],to[maxn<<1],val[maxn<<1];
  8 void addedge(int a,int b,int v){
  9     nxt[++cnt]=fir[a];fir[a]=cnt;to[cnt]=b;val[cnt]=v;
 10 }
 11 
 12 int ID[maxn],top[maxn],rID[maxn],tot,n,Q;
 13 int sz[maxn],dep[maxn],fa[maxn],son[maxn];
 14 long long dis[maxn],Min[maxn<<2];
 15 
 16 void DFS(int x){
 17     sz[x]=1;
 18     for(int i=fir[x];i;i=nxt[i])
 19         if(to[i]!=fa[x]){
 20             fa[to[i]]=x;
 21             dep[to[i]]=dep[x]+1;
 22             dis[to[i]]=dis[x]+val[i];
 23             DFS(to[i]);
 24             sz[x]+=sz[to[i]];
 25             if(sz[son[x]]<sz[to[i]])
 26                 son[x]=to[i];
 27         }
 28 }
 29 
 30 void DFS(int x,int tp){
 31     top[x]=tp;
 32     ID[x]=++tot;rID[tot]=x;
 33     if(son[x])DFS(son[x],tp);
 34     for(int i=fir[x];i;i=nxt[i])
 35         if(to[i]!=fa[x]&&to[i]!=son[x])
 36             DFS(to[i],to[i]);
 37 }
 38 
 39 int Lca(int x,int y){
 40     while(top[x]!=top[y]){
 41         if(dep[top[x]]<dep[top[y]])swap(x,y);
 42         x=fa[top[x]];
 43     }
 44     return dep[x]<dep[y]?x:y;
 45 }
 46 
 47 void Build(int x,int l,int r){
 48     Min[x]=INF;
 49     if(l==r)return;
 50     int mid=(l+r)>>1;
 51     Build(x<<1,l,mid);
 52     Build(x<<1|1,mid+1,r);
 53 }
 54 
 55 struct Node{
 56     long long a,b;
 57     Node(long long a_=0,long long b_=INF){
 58         a=a_;b=b_;
 59     }
 60     long long Val(int x){
 61         return a*dis[rID[x]]+b;
 62     }
 63 }T[maxn<<2];
 64 
 65 int CmP(int l,int r,Node x,Node y){
 66     if(x.Val(l)<=y.Val(l)&&x.Val(r)<=y.Val(r))return 1;
 67     if(x.Val(l)>=y.Val(l)&&x.Val(r)>=y.Val(r))return -1;
 68     return 0;
 69 }
 70 
 71 void Update(int x,int l,int r,int a,int b,Node p){
 72     if(l>b||r<a)return;
 73     Min[x]=min(Min[x],min(p.Val(max(l,a)),p.Val(min(r,b))));
 74     int mid=(l+r)>>1;
 75     if(l>=a&&r<=b){
 76         int tmp=CmP(l,r,p,T[x]);
 77         if(tmp==1)T[x]=p;
 78         if(tmp!=0)return;//这里可以不用判断l==r 
 79         
 80         tmp=CmP(l,mid,p,T[x]);
 81         if(tmp!=1)Update(x<<1,l,mid,a,b,T[x]);
 82         tmp=CmP(mid+1,r,p,T[x]);
 83         if(tmp!=1)Update(x<<1|1,mid+1,r,a,b,T[x]);
 84     }
 85     Update(x<<1,l,mid,a,b,p);
 86     Update(x<<1|1,mid+1,r,a,b,p);
 87 }
 88 
 89 void Modify(int x,int y,Node p){
 90     while(top[x]!=top[y]){
 91         Update(1,1,n,ID[top[x]],ID[x],p);
 92         x=fa[top[x]];
 93     }
 94     Update(1,1,n,ID[y],ID[x],p);
 95 }
 96 
 97 long long Query(int x,int l,int r,int a,int b){
 98     if(l>b||r<a)return INF;
 99     if(l>=a&&r<=b)return Min[x];
100     int mid=(l+r)>>1;
101     long long ret=min(T[x].Val(max(l,a)),T[x].Val(min(r,b)));
102     if(mid>=a)ret=min(ret,Query(x<<1,l,mid,a,b));
103     if(mid<b)ret=min(ret,Query(x<<1|1,mid+1,r,a,b));
104     return ret; 
105 }
106 
107 long long Solve(int x,int y){
108     long long ret=INF;
109     while(top[x]!=top[y]){
110         if(dep[top[x]]<dep[top[y]])swap(x,y);
111         ret=min(ret,Query(1,1,n,ID[top[x]],ID[x]));
112         x=fa[top[x]];
113     }
114     if(dep[x]<dep[y])swap(x,y);
115     ret=min(ret,Query(1,1,n,ID[y],ID[x]));
116     return ret;
117 }
118 
119 int main(){
120 #ifndef ONLINE_JUDGE
121     freopen("menci_game.in","r",stdin);
122     freopen("menci_game.out","w",stdout);
123 #endif
124     scanf("%d%d",&n,&Q);
125     for(int i=1,u,v,w;i<n;i++){
126         scanf("%d%d%d",&u,&v,&w);
127         addedge(u,v,w);addedge(v,u,w);
128     }
129     DFS(1);
130     DFS(1,1);
131     Build(1,1,n);
132     
133     int type,s,t,lca;
134     long long a,b;
135     while(Q--){
136         scanf("%d",&type);
137         if(type==1){
138             scanf("%d%d%lld%lld",&s,&t,&a,&b);
139             lca=Lca(s,t);
140             Modify(s,lca,Node(-a,a*dis[s]+b));
141             Modify(t,lca,Node(a,a*(dis[s]-2*dis[lca])+b));
142         }
143         else{
144             scanf("%d%d",&s,&t);
145             printf("%lld\n",Solve(s,t));
146         }
147     }
148     return 0;    
149 }