【bzoj4009 hnoi2015】接水果

题目描述

风见幽香非常喜欢玩一个叫做 osu!的游戏，其中她最喜欢玩的模式就是接水果。由于她已经DT FC 了The big black, 她觉得这个游戏太简单了，于是发明了一个更加难的版本。

首先有一个地图，是一棵由 n 个顶点、n-1 条边组成的树（例如图 1给出的树包含 8 个顶点、7 条边）。

这颗树上有 P 个盘子，每个盘子实际上是一条路径（例如图 1 中顶点 6 到顶点 8 的路径），并且每个盘子还有一个权值。第 i 个盘子就是顶点a_i到顶点b_i的路径(由于是树，所以从a_i到b_i的路径是唯一的)，权值为c_i。

接下来依次会有Q个水果掉下来，每个水果本质上也是一条路径，第i 个水果是从顶点 u_i 到顶点v_i 的路径。

幽香每次需要选择一个盘子去接当前的水果：一个盘子能接住一个水果，当且仅当盘子的路径是水果的路径的子路径（例如图1中从 3到7 的路径是从1到8的路径的子路径）。这里规定:从a 到b的路径与从b到 a的路径是同一条路径。

当然为了提高难度，对于第 i 个水果，你需要选择能接住它的所有盘子中，权值第 k_i 小的那个盘子，每个盘子可重复使用（没有使用次数的上限：一个盘子接完一个水果后，后面还可继续接其他水果，只要它是水果路径的子路径）。幽香认为这个游戏很难，你能轻松解决给她看吗？

输入输出格式

输入格式：

第一行三个数 n和P 和Q，表示树的大小和盘子的个数和水果的个数。 接下来n-1 行，每行两个数 a、b，表示树上的a和b 之间有一条边。树中顶点按1到 n标号。 接下来 P 行，每行三个数 a、b、c，表示路径为 a 到 b、权值为 c 的盘子，其中0<=c<=10^9，a不等于b。 接下来Q行，每行三个数 u、v、k，表示路径为 u到 v的水果，其中 u不等于v，你需要选择第 k小的盘子，第k 小一定存在。

输出格式：

对于每个果子，输出一行表示选择的盘子的权值。

题意：统计对于给出一些有权值的点对（盘子），再给出一些询问点对（水果），每个水果能被一个盘子接住当且仅当盘子的两点间的路径是水果两点之间路径的子路径。

题解：

①转化一下：一个盘子A可以接住一个水果B，意思是要么是A.x和A.y无祖先关系时，B.x和B.y都在A.x和A.y(可以交换位置)的子树里，要么是A.x和A.y有祖先关系：假设A.x是A.y的祖先，B.x一定在A.y的子树里且B.y一定不在A.x到A.y路径上的第二个点(第一个点为A.x)的子树里(同样可以交换)。

(还是给个图吧)aaarticlea/png;base64,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" alt="" />

②用dfs序维护一下子树信息，一个子树成为一个连续的一段，找x到y的第二个点可以LCA或者树剖每次往上跳即可。

③现在相当于每个盘子可以转化成一个矩形：整体二分，用扫描线的思想维护一下每次的答案。把所有矩形和询问点按横坐标的大小排序，想像有一条从左向右的直线，扫到的横坐标为一个矩形的起点是把这个区间的[l,r]加入树状数组里，终点时再去掉。询问变为纵坐标的询问就可以在树状数组内完成。

aaarticlea/png;base64,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" alt="" />

 #include<cstdio>
 #include<iostream>
 #include<algorithm>
 using namespace std;
 const int N = ;
 int n,m;
 int o,hd[N],v[*N],nt[*N],son[N],top[N],size[N],st[N],ed[N],dep[N],idx,fa[N],ans[N],k;
 char gc(){
     static char *p1,*p2,s[];
     if(p1==p2) p2=(p1=s)+fread(s,,,stdin);
     return(p1==p2)?EOF:*p1++;
 }
 int rd(){
     int x = ,f = ; char c = gc();
     while(c<''||c>'') {if(c=='-') f=-;c = gc();}
     while(c>=''&&c<='') x=x*+c-'',c=gc();
     return x*f;
 }///
 void adde(int x,int y){v[o]=y;nt[o]=hd[x];hd[x]=o++;} ///
 void Adde(int u,int v){adde(u,v);adde(v,u);}///
 void dfsA(int u){
     size[u] = ; st[u] = ++idx;
     for(int i=hd[u];i!=-;i=nt[i]){
         if(v[i]==fa[u]) continue;
         fa[v[i]] = u;
         dfsA(v[i]);
         size[u] += size[v[i]];
         if(size[v[i]]>size[son[u]]) son[u] = v[i];
     }
     ed[u] = idx;
 }///
 void dfsB(int u,int Top){
     top[u] = Top; dep[u]=dep[fa[u]]+;
     if(son[u]) dfsB(son[u],Top);
     for(int i=hd[u];i!=-;i=nt[i]){
         if(v[i]==fa[u]||v[i]==son[u]) continue;
         dfsB(v[i],v[i]);
     }
 }///
 int find(int x,int y){
     int tmp=x;
     while(top[x]!=top[y]) tmp=top[x],x=fa[top[x]];
     return x==y?tmp:son[y];
 }///
 struct edge{int l,r,x1,y1,x2,y2,w;
 bool operator <(const edge &a)const{return w<a.w;}
 }e[N];///
 struct A{int id,x,y,k;}a[N],tmp[N];///
 struct B{int p,x,y,d;
 bool operator<(const B&a)const{return p<a.p;}
 }b[*N];///
 struct C{int id,x,y;
 bool operator<(const C&a)const{return x<a.x;}
 }c[*N];///
 int tot,cnt,bit[N],now[N];
 void add(int x,int y){for(;x<=n;x+=x&-x)bit[x]+=y;}
 int ask(int x){int ret=;for(;x;x-=x&-x)ret+=bit[x];return ret;}//
 void erfn(int l,int r,int L,int R){
     if(L>R) return ;
     if(l==r){
         for(int i=L;i<=R;i++) ans[a[i].id]=e[l].w;
         return;
     }
     int mid=l+r>>,tb=,tc=,tl=L,tr=;
     for(int i=l;i<=mid;i++){
         if(e[i].x1<=e[i].y1){
             b[++tb] = (B){e[i].l,e[i].x1,e[i].y1,};
             b[++tb] = (B){e[i].r+,e[i].x1,e[i].y1,-};
         }
         if(e[i].x2<=e[i].y2){
             b[++tb] = (B){e[i].l,e[i].x2,e[i].y2,};
             b[++tb] = (B){e[i].r+,e[i].x2,e[i].y2,-};
         }
     }
     sort(b+,b+tb+);
     for(int i=L;i<=R;i++){
         c[++tc] = (C){i,a[i].x,a[i].y};
         c[++tc] = (C){i,a[i].y,a[i].x};
         now[i] = ;
     }
     sort(c+,c+tc+);
     int j=;
     for(int i=;i <= tc;i++){
         while(j<=tb&&b[j].p<=c[i].x) add(b[j].x,b[j].d),add(b[j].y+,-b[j].d),j++;
         now[c[i].id]+=ask(c[i].y);
     }
     for(int i=j;i<=tb;i++) add(b[i].x,b[i].d),add(b[i].y+,-b[i].d);
     for(int i=L;i<=R;i++){
         if(now[i]>=a[i].k) a[tl++] = a[i]; else a[i].k-=now[i],tmp[tr++] = a[i];
     }
     for(int i=tl;i<=R;i++) a[i] = tmp[i-tl];
     erfn(l,mid,L,tl-); erfn(mid+,r,tl,R);
 }//
 int main()
 {    freopen("bzoj4009.in","r",stdin);
     freopen("bzoj4009.out","w",stdout);
      n=rd(); m=rd(); k=rd();
     for(int i=;i<=n;i++) hd[i]=-;
     for(int i=;i<n;i++) Adde(rd(),rd());
     dfsA();
     dfsB(,);
     for(int i=,x,y,w;i<=m;i++){
         x=rd(),y=rd(),w=rd();
         if(dep[x]<dep[y]) swap(x,y);
         if(st[x]>=st[y]&&ed[x]<=ed[y])
         {
         y=find(x,y);
         e[++tot]=(edge){st[x],ed[x],,st[y]-,ed[y]+,n,w};
         }
         else e[++tot]=(edge){st[x],ed[x],st[y],ed[y],,,w};
     }
     sort(e+,e+tot+);
     for(int i=,x,y,w;i<=k;i++){
         x=rd(),y=rd(),w=rd();
         a[++cnt]=(A){i,st[x],st[y],w};
     }
     erfn(,tot,,cnt);
     for(int i =;i <= k;i++) printf("%d\n",ans[i]);//
 }//by tkys_Austin;