SPOJ 8222 [后缀自动机]

题目

NSUBSTR - Substrings

You are given a string S which consists of 250000 lowercase latin letters at most. We define F(x) as the maximal number of times that some string with length x appears in S. For example for string ‘ababa’ F(3) will be 2 because there is a string ‘aba’ that occurs twice. Your task is to output F(i) for every i so that 1<=i<=|S|.

输入

String S consists of at most 250000 lowercase latin letters.

输出

Output |S| lines. On the i-th line output F(i).

样例输入

ababa

样例输出

3

2

2

1

1

分析

没什么好分析的hh,基本裸的后缀自动机,对parent树进行Tsort(),自底向上维护r[i]的大小,注意开始赋值时每个实节点(即np,而非nq)的r赋为1,其他为0

完整代码

#include<bits/stdc++.h>
#define maxn 500010
//#define DEBUG
using namespace std;
int n;
int sum[maxn],tmp[maxn],f[maxn];
char ch[maxn];

struct SAM
{
int root,tot,last;
int son[maxn][26],fa[maxn],maxl[maxn],r[maxn];
int addnode(int n) {return maxl[++tot]=n,tot;}

void init()
{
root=tot=last=1;
memset(son,0,sizeof(son));
memset(fa,0,sizeof(fa));
memset(maxl,0,sizeof(maxl));
memset(r,0,sizeof(r));
}

void add(int pos)
{
int x=ch[pos]-'a',np=addnode(pos),p=last;
last=np,r[np]=1;
for( ; p&&!son[p][x] ; p=fa[p] ) son[p][x]=np;
if(!p) fa[np]=root;
else
{
int q=son[p][x];
if(maxl[q]==maxl[p]+1) fa[np]=q;
else
{
int nq=addnode(maxl[p]+1);
memcpy(son[nq],son[q],sizeof(son[q]));
fa[nq]=fa[q];
fa[np]=fa[q]=nq;
for( ; son[p][x]==q ; p=fa[p] ) son[p][x]=nq;
}
}
}

void Tsort()
{
for(int i=1;i<=tot;++i) sum[maxl[i]]++;
for(int i=1;i<=n;++i) sum[i]+=sum[i-1];
for(int i=1;i<=tot;++i) tmp[sum[maxl[i]]--]=i;
#ifdef DEBUG
for(int i=1;i<=tot;++i) printf("   tmp[%d]=%d   maxl[tmp[%d]]=%d\n",i,tmp[i],i,maxl[tmp[i]]);
#endif
}

void build()
{
init();
scanf("%s",ch+1);
n=strlen(ch+1);
for(int i=1;i<=n;++i) add(i);
Tsort();
}

void work()
{
build();
#ifdef DEBUG
for(int i=1;i<=tot;++i)
cerr<<"r["<<i<<"]="<<r[i]<<endl;
#endif
for(int i=tot;i;i--) r[fa[tmp[i]]]+=r[tmp[i]];
for(int i=1;i<=tot;++i) f[maxl[i]]=max(f[maxl[i]],r[i]);
for(int i=1;i<=n;++i) printf("%d\n",f[i]);
}

} sam ;

int main()
{
sam.work();
return 0;
}

/*
Input:
ababanoi

Output:
3
2
2
1
1
*/