bzoj2588

题目：http://www.lydsy.com/JudgeOnline/problem.php?id=2588

就是静态区间第K大的变形。

每个节点为一棵线段树，表示到根的路径中，以权值为下标的线段树。

每个节点建树的时候，以父亲为历史版本。

对于询问点x和点y的时候，就是求ask(x)+ask(y)-ask(lca)-ask(fa[lca])，然后用类似于静态区间第K的方法决定是去左子树还是右子树。

#include<cstdio>

#include<cstdlib>

#include<iostream>

#include<fstream>

#include<algorithm>

#include<cstring>

#include<string>

#include<cmath>

#include<queue>

#include<stack>

#include<map>

#include<utility>

#include<set>

#include<bitset>

#include<vector>

#include<functional>

#include<deque>

#include<cctype>

#include<climits>

#include<complex>

//#include<bits/stdc++.h>适用于CF,UOJ，但不适用于poj

 

using namespace std;



typedef long long LL;

typedef double DB;

typedef pair<int,int> PII;

typedef complex<DB> CP;



#define mmst(a,v) memset(a,v,sizeof(a))

#define mmcy(a,b) memcpy(a,b,sizeof(a))

#define re(i,a,b)  for(i=a;i<=b;i++)

#define red(i,a,b) for(i=a;i>=b;i--)

#define fi first

#define se second

#define m_p(a,b) make_pair(a,b)

#define SF scanf

#define PF printf

#define two(k) (1<<(k))



template<class T>inline T sqr(T x){return x*x;}

template<class T>inline void upmin(T &t,T tmp){if(t>tmp)t=tmp;}

template<class T>inline void upmax(T &t,T tmp){if(t<tmp)t=tmp;}



const DB EPS=1e-9;

inline int sgn(DB x){if(abs(x)<EPS)return 0;return(x>0)?1:-1;}

const DB Pi=acos(-1.0);



inline int gint()

  {

        int res=0;bool neg=0;char z;

        for(z=getchar();z!=EOF && z!='-' && !isdigit(z);z=getchar());

        if(z==EOF)return 0;

        if(z=='-'){neg=1;z=getchar();}

        for(;z!=EOF && isdigit(z);res=res*10+z-'0',z=getchar());

        return (neg)?-res:res; 

    }

inline LL gll()

  {

      LL res=0;bool neg=0;char z;

        for(z=getchar();z!=EOF && z!='-' && !isdigit(z);z=getchar());

        if(z==EOF)return 0;

        if(z=='-'){neg=1;z=getchar();}

        for(;z!=EOF && isdigit(z);res=res*10+z-'0',z=getchar());

        return (neg)?-res:res; 

    }



const int maxN=100000;



int N,M;

int a[maxN+100];

int bak[maxN+100],cnt;

int first[maxN+100],now;

struct Tedge{int v,next;}edge[2*maxN+100];



inline void addedge(int u,int v){now++;edge[now].v=v;edge[now].next=first[u];first[u]=now;}



int head,tail,que[maxN+100];

int fa[maxN+100],dep[maxN+100];

int jump[35][maxN+100];



struct Tnode{int val,son[2];}sn[maxN*70+100000];int idx;



int root[maxN+100];



inline void update(int past,int p,int l,int r,int x)

  {

      if(x<=l && r<=x){sn[p].val=sn[past].val+1;return;}

      int mid=(l+r)/2,f=(x<=mid);

      sn[p].son[f]=sn[past].son[f];

      sn[p].son[f^1]=++idx;

      if(x<=mid) update(sn[past].son[0],sn[p].son[0],l,mid,x); else update(sn[past].son[1],sn[p].son[1],mid+1,r,x);

      sn[p].val=sn[sn[p].son[0]].val+sn[sn[p].son[1]].val;

  }

inline int ask(int r1,int r2,int r3,int r4,int l,int r,int k)

  {

      if(l==r)return bak[l];

      int mid=(l+r)/2;

      int ge=sn[sn[r1].son[0]].val+sn[sn[r2].son[0]].val-sn[sn[r3].son[0]].val-sn[sn[r4].son[0]].val;

      if(ge<k)

        return ask(sn[r1].son[1],sn[r2].son[1],sn[r3].son[1],sn[r4].son[1],mid+1,r,k-ge);

      else

        return ask(sn[r1].son[0],sn[r2].son[0],sn[r3].son[0],sn[r4].son[0],l,mid,k);

  }



inline void BFS()

  {

      int i,j;

      mmst(fa,-1);

      fa[que[head=tail=0]=1]=0;

      dep[1]=1;

      while(head<=tail)

        {

            int u=que[head++],v;

            for(i=first[u],v=edge[i].v;i!=-1;i=edge[i].next,v=edge[i].v)if(fa[v]==-1){fa[que[++tail]=v]=u;dep[v]=dep[u]+1;}

        }

      re(i,0,N)root[i]=++idx;

      re(i,0,tail)

          {

              int u=que[i];

                update(root[fa[u]],root[u],1,cnt,a[u]);

            }

      re(j,0,30)jump[j][1]=1;

      re(i,1,tail)

        {

            int u=que[i];

            jump[0][u]=fa[u];

            re(j,1,30)jump[j][u]=jump[j-1][jump[j-1][u]];

        }

  }



inline void swim(int &x,int H){int i;for(i=0;H!=0;H/=2,i++)if(H&1)x=jump[i][x];}

inline int ask_lca(int x,int y)

  {

      if(dep[x]<dep[y])swap(x,y);

      swim(x,dep[x]-dep[y]);

      if(x==y)return x;

      int i;

      red(i,30,0)if(jump[i][x]!=jump[i][y]){x=jump[i][x];y=jump[i][y];}

      return jump[0][x];

  }



int main()

  {

      freopen("bzoj2588.in","r",stdin);

      freopen("bzoj2588.out","w",stdout);

      int i;

      N=gint();M=gint();

      re(i,1,N)a[i]=gint();

      re(i,1,N)bak[i]=a[i];

      sort(bak+1,bak+N+1);

      cnt=unique(bak+1,bak+N+1)-bak-1;

      re(i,1,N)a[i]=lower_bound(bak+1,bak+cnt+1,a[i])-bak;

      mmst(first,-1);now=-1;

      re(i,1,N-1){int x=gint(),y=gint();addedge(x,y);addedge(y,x);}

      BFS();

      int lastans=0;

      while(M--)

        {

            int x=gint()^lastans,y=gint(),lca=ask_lca(x,y),k=gint();

            lastans=ask(root[x],root[y],root[lca],root[fa[lca]],1,cnt,k);

            printf("%d",lastans);if(M!=0)printf("\n");

        }

      return 0;

  }

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