BZOJ3413 : 匹配

FDUSC前刷刷题吧。。

本题每个询问就是说将询问串与主串每个后缀匹配,若匹配成功则结束,否则加上lcp的长度

对主串建立后缀树,并用主席树维护DFS序

对于每个询问串,找到最后走到的点fin_node(在边上就往下走),

并求出完成匹配的后缀的位置match(若匹配成功则是fin_node子树中的最小值,否则就是n)

然后从fin_node开始一直往上走,

每个节点对答案的贡献为该点子树中小于等于match的后缀的个数乘以这条边的长度,

答案最后再加上match

时间复杂度预处理$O(nlog n)$,询问$O(mlog n)$

#include<cstdio>
#include<cstring>
const int inf=1<<25,S=12,N=100010,M=1800010;
using namespace std;
char tmp[N];
int text[N],root,last,pos,need,remain,acnode,ace,aclen;
int n,m,i,fin_node,fin_len,match,ans;
int dfn,seq[N<<1],st[N<<1],en[N<<1];
int head[N<<1],tot,val[M],l[M],r[M];
int min(int a,int b){return a<b?a:b;}
struct node{int st,en,lk,son[S],f;int len(){return min(en,pos+1)-st;}}tree[N<<1];
int new_node(int st,int en=inf){
  node nd;
  nd.st=st;nd.en=en;
  for(int i=nd.lk=0;i<S;i++)nd.son[i]=0;
  tree[++last]=nd;
  return last;
}
int acedge(){return text[ace];}
void addedge(int node){
  if(need)tree[need].lk=node;
  need=node;
}
bool down(int node){
  if(aclen>=tree[node].len())return ace+=tree[node].len(),aclen-=tree[node].len(),acnode=node,1;
  return 0;
}
void init(){
  need=last=remain=ace=aclen=0;
  root=acnode=new_node(pos=-1,-1);
}
void extend(int c){
  text[++pos]=c;need=0;remain++;
  while(remain){
    if(!aclen)ace=pos;
    if(!tree[acnode].son[acedge()])tree[acnode].son[acedge()]=new_node(pos),addedge(acnode);
    else{
      int nxt=tree[acnode].son[acedge()];
      if(down(nxt))continue;
      if(text[tree[nxt].st+aclen]==c){aclen++;addedge(acnode);break;}
      int split=new_node(tree[nxt].st,tree[nxt].st+aclen);
      tree[acnode].son[acedge()]=split;
      tree[split].son[c]=new_node(pos);
      tree[nxt].st+=aclen;
      tree[split].son[text[tree[nxt].st]]=nxt;
      addedge(split);
    }
    remain--;
    if(acnode==root&&aclen)aclen--,ace=pos-remain+1;
    else acnode=tree[acnode].lk?tree[acnode].lk:root;
  }
}
bool search(){
  int x=fin_node=root,i=1,j;
  fin_len=0;
  while(i<=n){
    if(tree[x].son[tmp[i]-'0'+1]){
      x=fin_node=tree[x].son[tmp[i]-'0'+1];
      fin_len=0;
      j=tree[x].st;
      while(i<=n&&j<min(tree[x].en,pos+1))if(tmp[i]-'0'+1==text[j])i++,j++,fin_len++;else return 0;
    }else return 0;
  }
  return 1;
}
void dfs(int x,int sum,int f){
  tree[x].f=f;
  sum+=tree[x].len();
  seq[st[x]=++dfn]=tree[x].en==inf?pos-sum+1:-1;
  for(int i=0;i<S;i++)if(tree[x].son[i])dfs(tree[x].son[i],sum,x);
  en[x]=dfn;
}
int ins(int x,int a,int b,int c){
  int y=++tot;
  val[y]=val[x]+1;
  if(a==b)return y;
  int mid=(a+b)>>1;
  if(c<=mid)l[y]=ins(l[x],a,mid,c),r[y]=r[x];else l[y]=l[x],r[y]=ins(r[x],mid+1,b,c);
  return y;
}
int ask(int x,int a,int b,int c){
  if(!x)return 0;
  if(b<=c)return val[x];
  int mid=(a+b)>>1,t=ask(l[x],a,mid,c);
  if(c>mid)t+=ask(r[x],mid+1,b,c);
  return t;
}
int askmin(int x,int y){
  int a=0,b=pos,mid;
  while(1){
    if(a==b)return a;
    mid=(a+b)>>1;
    if(val[l[y]]>val[l[x]])x=l[x],y=l[y],b=mid;else x=r[x],y=r[y],a=mid+1;
  }
}
int main(){
  init();
  scanf("%d%s",&n,tmp+1);
  for(i=1;i<=n;i++)extend(tmp[i]-'0'+1);extend(11);
  dfs(root,0,0);
  for(i=1;i<=dfn;i++)head[i]=~seq[i]?ins(head[i-1],0,pos,seq[i]):head[i-1];
  scanf("%d",&m);
  while(m--){
    scanf("%s",tmp+1);n=strlen(tmp+1);
    ans=match=search()?askmin(head[st[fin_node]-1],head[en[fin_node]]):pos;
    if(fin_node!=root){
      ans+=fin_len*(ask(head[en[fin_node]],0,pos,match)-ask(head[st[fin_node]-1],0,pos,match));
      fin_node=tree[fin_node].f;
    }
    while(fin_node!=root){
      ans+=tree[fin_node].len()*(ask(head[en[fin_node]],0,pos,match)-ask(head[st[fin_node]-1],0,pos,match));
      fin_node=tree[fin_node].f;
    }
    printf("%d
",ans);
  }
  return 0;
}

  

原文地址:https://www.cnblogs.com/clrs97/p/4403223.html