Tsinsen A1505. 树（张闻涛） 倍增LCA,可持久化线段树,DFS序

  1 #include<bits/stdc++.h>
  2 using namespace std;
  3 #define MAXN 100010
  4 struct node
  5 {
  6     int begin,end,next;
  7 }edge[MAXN*2];
  8 struct NODE
  9 {
 10     int left,right;
 11 }tree[MAXN*20];
 12 int cnt,Head[MAXN],SIZE,deep[MAXN],P[MAXN][17],tot,root[MAXN],n,sum[MAXN*20],val[MAXN],cc[MAXN],pos[MAXN],value[MAXN];
 13 bool vis[MAXN];
 14 void addedge(int bb,int ee)
 15 {
 16     edge[++cnt].begin=bb;edge[cnt].end=ee;edge[cnt].next=Head[bb];Head[bb]=cnt;
 17 }
 18 void addedge1(int bb,int ee)
 19 {
 20     addedge(bb,ee);addedge(ee,bb);
 21 }
 22 int read()
 23 {
 24     int s=0,fh=1;char ch=getchar();
 25     while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)fh=-1;ch=getchar();}
 26     while(ch>=‘0‘&&ch<=‘9‘){s=s*10+(ch-‘0‘);ch=getchar();}
 27     return s*fh;
 28 }
 29 void dfs(int u)
 30 {
 31     int i,v;
 32     vis[u]=true;
 33     SIZE++;pos[u]=SIZE;value[SIZE]=u;
 34     for(i=Head[u];i!=-1;i=edge[i].next)
 35     {
 36         v=edge[i].end;
 37         if(vis[v]==false)
 38         {
 39             deep[v]=deep[u]+1;
 40             P[v][0]=u;
 41             dfs(v);
 42         }
 43     }
 44 }
 45 void Ycl()
 46 {
 47     int i,j;
 48     for(j=1;(1<<j)<=n;j++)
 49     {
 50         for(i=1;i<=n;i++)
 51         {
 52             if(P[i][j-1]!=-1)P[i][j]=P[P[i][j-1]][j-1];
 53         }
 54     }
 55 }
 56 int LCA(int x,int y)
 57 {
 58     if(deep[x]<deep[y])swap(x,y);
 59     int i,j;
 60     for(i=0;(1<<i)<=deep[x];i++);i--;
 61     for(j=i;j>=0;j--)if(deep[x]-(1<<j)>=deep[y])x=P[x][j];
 62     if(x==y)return x;
 63     for(j=i;j>=0;j--)
 64     {
 65         if(P[x][j]!=-1&&P[x][j]!=P[y][j])
 66         {
 67             x=P[x][j];
 68             y=P[y][j];
 69         }
 70     }
 71     return P[x][0];
 72 }
 73 void Build(int x,int &y,int l,int r,int B)
 74 {
 75     y=++SIZE;
 76     sum[y]=sum[x]+1;
 77     if(l==r)return;
 78     tree[y].left=tree[x].left;tree[y].right=tree[x].right;
 79     int mid=(l+r)/2;
 80     if(B<=mid)Build(tree[x].left,tree[y].left,l,mid,B);
 81     else Build(tree[x].right,tree[y].right,mid+1,r,B);
 82 }
 83 int Query(int l,int r,int A,int B,int C,int D,int Q)
 84 {
 85     if(l==r)return l;
 86     int mid,delta=sum[tree[A].left]+sum[tree[B].left]-sum[tree[C].left]-sum[tree[D].left];
 87     mid=(l+r)/2;
 88     if(Q<=delta)return Query(l,mid,tree[A].left,tree[B].left,tree[C].left,tree[D].left,Q);
 89     else return Query(mid+1,r,tree[A].right,tree[B].right,tree[C].right,tree[D].right,Q-delta);
 90 }
 91 int query(int u,int v,int lca,int k)
 92 {
 93     int A=pos[u],B=pos[v],C=pos[lca],D=pos[P[lca][0]];
 94     return Query(1,tot,root[A],root[B],root[C],root[D],k);
 95 }
 96 int main()
 97 {
 98     int m,i,wz,s1,s2,s3,lca,k,bb,ee;
 99     n=read();m=read();
100     for(i=1;i<=n;i++)val[i]=read(),cc[i]=val[i];
101     sort(cc+1,cc+n+1);
102     tot=unique(cc+1,cc+n+1)-(cc+1);
103     memset(Head,-1,sizeof(Head));cnt=1;
104     for(i=1;i<n;i++){bb=read();ee=read();addedge1(bb,ee);}
105     memset(P,-1,sizeof(P));
106     SIZE=0;
107     dfs(1);Ycl();
108     SIZE=0;
109     for(i=1;i<=n;i++)//按树上顺序插入.
110     {
111         k=value[i];
112         wz=lower_bound(cc+1,cc+tot+1,val[k])-cc;
113         Build(root[pos[P[k][0]]],root[i],1,tot,wz);
114     }
115     SIZE=0;
116     for(i=1;i<=m;i++)
117     {
118         s1=read();s2=read();s3=read();
119         if(s1==1){lca=LCA(s2,s3);printf("%d\n",cc[query(s2,s3,lca,1)]);}
120         else if(s1==2){lca=LCA(s2,s3);k=deep[s2]+deep[s3]-2*deep[lca]+1;printf("%d\n",cc[query(s2,s3,lca,k)]);}
121         else {lca=LCA(s2,s3);k=(deep[s2]+deep[s3]-2*deep[lca]+3)/2;printf("%d\n",cc[query(s2,s3,lca,k)]);}
122     }
123     fclose(stdin);
124     fclose(stdout);
125     return 0;
126 }