【BZOJ 1146】【CTSC 2008】网络管理network

来源：互联网发布：mac电脑免费翻墙编辑：程序博客网时间：2024/06/05 17:28

一句话题意，树链上带修改区间第k大
感觉可以dfs+主席树O(nlog2n)过掉，但我不会写= =
于是写的线段树套平衡树+链剖+二分（修改O(nlog3n),查询O(nlog4n)慢了好多啊QAQ）
这里简单介绍一下区间第K大做法，对于每个线段树所”管辖“的范围，建一棵相应范围内的平衡树（我用的Treap）；修改时，修改每个包含被修改节点的线段树节点所对应的Treap；查询时，二分
答案，统计每个区间内比当前答案小的数即可（为了保证是序列里的数，我们可以二分答案在原序列中排名）
PS：这题真的是第K大，不是排名第K的，被坑WA了一次= =
code：

#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#define mid (l+r)/2#define lch i<<1,l,mid#define rch i<<1|1,mid+1,rusing namespace std;struct treap_node{    treap_node *left,*right;    int val,fix,size,wgt;    treap_node(int val): val(val) {size=1; wgt=1; left=right=NULL; fix=rand();}    int lsize()      {if (left) return left->size; else return 0;}    int rsize()      {if (right) return right->size; else return 0;}    void Maintain()      {size=wgt; size+=lsize()+rsize();}};treap_node *seg[320001];int f[80001],plc[80001];int point[80001],next[200001];struct hp{    int u,v;}ai[200001];struct hq{    int dep,fat,top,size,wson;}tree[80001];int n,a[80001],ans,m,totw,e=0;void tlr(treap_node *&a){    treap_node *b=a->right;    a->right=b->left; b->left=a;    a->Maintain(); b->Maintain(); a=b;}void trr(treap_node *&a){    treap_node *b=a->left;    a->left=b->right; b->right=a;    a->Maintain(); b->Maintain(); a=b;}void add(int u,int v){    e++; ai[e].u=u; ai[e].v=v; next[e]=point[u]; point[u]=e;    e++; ai[e].v=u; ai[e].v=u; next[e]=point[v]; point[v]=e;}void insert(treap_node *&p,int value)  {      if (!p)        p=new treap_node(value);      else        {          if (value==p->val)            p->wgt++;          if (value<p->val)            {              insert(p->left,value);              if (p->left->fix<p->fix)                trr(p);            }          if (value>p->val)            {              insert(p->right,value);              if (p->right->fix<p->fix)                tlr(p);            }        }      p->Maintain();  }void make_node(int i,int l,int r){    int j;    for (j=l;j<=r;++j)      insert(seg[i],a[f[j]]);}void build(int i,int l,int r){    make_node(i,l,r);    if (l==r) return;    build(lch); build(rch);}void build_tree(int now,int last,int depth){    int i;    tree[now].fat=last;    tree[now].dep=depth;    tree[now].size=1;    tree[now].wson=0;    for (i=point[now];i;i=next[i])      if (ai[i].v!=last)        {          build_tree(ai[i].v,now,depth+1);          tree[now].size+=tree[ai[i].v].size;          if (tree[ai[i].v].size>tree[tree[now].wson].size)            tree[now].wson=ai[i].v;        }}void build_seg(int now,int tp){    int i;    tree[now].top=tp;    plc[now]=++totw; f[totw]=now;    if (tree[now].wson!=0)      build_seg(tree[now].wson,tp);    for (i=point[now];i;i=next[i])      if (ai[i].v!=tree[now].wson&&ai[i].v!=tree[now].fat)        build_seg(ai[i].v,ai[i].v);}void del(treap_node *&p,int val){    if (val==p->val)      {        if (p->wgt==1)          {            if (!p->left||!p->right)              {                if (!p->left) p=p->right;                else p=p->left;              }            else              {                if (p->left->fix<p->right->fix)                  {trr(p); del(p->right,val);}                else                  {tlr(p); del(p->left,val);}              }          }        else          p->wgt--;      }    else      {        if (val<p->val) del(p->left,val);        else del(p->right,val);      }    if (p!=NULL) p->Maintain(); }int kth(treap_node *p,int k){    if (k<=p->lsize()) return kth(p->left,k);    if (k>p->lsize()+p->wgt) return kth(p->right,k-p->lsize()-p->wgt);    if (k<=p->lsize()+p->wgt) return p->val;}int rank(treap_node *p,int val,int cur){    if (val==p->val) return cur+p->lsize();    if (val>p->val&&!p->right) return cur+p->lsize()+p->wgt;    if (val<p->val&&!p->left) return cur;    if (val<p->val) return rank(p->left,val,cur);    if (val>p->val) return rank(p->right,val,cur+p->lsize()+p->wgt);}void query(int i,int l,int r,int x,int y,int val){    if (x<=l&&y>=r)      {        ans+=rank(seg[i],val,0);        return;        }    if (x<=mid) query(lch,x,y,val);    if (y>mid) query(rch,x,y,val);}void delt(int i,int l,int r,int x,int num){    if (l==x&&l==r)      {        del(seg[i],num);        return;      }    del(seg[i],num);    if (x<=mid) delt(lch,x,num);    else delt(rch,x,num);}void ins(int i,int l,int r,int x,int num){    if (l==x&&l==r)      {        insert(seg[i],num);        return;      }    insert(seg[i],num);    if (x<=mid) ins(lch,x,num);    else ins(rch,x,num);}int Qsum(int x,int y){    int t=0,f1=tree[x].top,f2=tree[y].top;    while (f1!=f2)      {        //cout<<x<<' '<<y<<' '<<f1<<' '<<f2<<endl;        if (tree[f1].dep<tree[f2].dep) {swap(x,y); swap(f1,f2);}        t+=plc[x]-plc[f1]+1;        x=tree[f1].fat; f1=tree[x].top;      }    if (tree[x].dep>tree[y].dep) swap(x,y);    t+=plc[y]-plc[x]+1;    return t;}void Q(int x,int y,int num){    int f1=tree[x].top,f2=tree[y].top;    while (f1!=f2)      {        if (tree[f1].dep<tree[f2].dep) {swap(x,y); swap(f1,f2);}        query(1,1,n,plc[f1],plc[x],num);        x=tree[f1].fat; f1=tree[x].top;      }     if (tree[x].dep>tree[y].dep) swap(x,y);    query(1,1,n,plc[x],plc[y],num);}void work(int x,int y,int k){    int l,r,t,midx,len;    l=1; r=n;    len=Qsum(x,y);    if (k>len) {printf("invalid request!\n"); return;}    k=len-k+1;    while (l<r)      {        midx=(l+r+1)/2;        t=kth(seg[1],midx);        ans=0; Q(x,y,t);        if (ans<=k-1) l=midx;        else r=midx-1;      }    printf("%d\n",kth(seg[1],l));}int main(){    int i,x,y,k;    scanf("%d%d",&n,&m);    for (i=1;i<=n;++i)      scanf("%d",&a[i]);    for (i=1;i<n;++i)      {        scanf("%d%d",&x,&y);        add(x,y);      }    build_tree(1,0,0);    build_seg(1,1);    build(1,1,n);    for (i=1;i<=m;++i)      {        scanf("%d%d%d",&k,&x,&y);        if (k==0)          {            delt(1,1,n,plc[x],a[x]);            ins(1,1,n,plc[x],y);            a[x]=y;           }        if (k>0)          work(x,y,k);      }}

1 0