[BZOJ4698][Sdoi2008]Sandy的卡片（后缀数组+st表||后缀自动机）

题目描述

传送门

题目大意：给出n个长度为mi的串，求趋势相同的最长公共子串

题解

将前后两个数差分之后就是一个裸的最长公共子串问题了
将所有的串怼在一起求sa和height，然后用一个指针扫出来至少含有n个串的最短区间，然后用st表求区间min就行了
好久不写sa各种傻逼，比如说st表求max而不是求min啦，，，还有先枚举i再枚举j啦…

同时这道题也是一道sam的裸题，求多个串的最长公共子串
对第一个串建sam，然后其它的串在上面匹配，对每一个点每一次求Max，总体求Min，然后在Min中选一个max
连map都不用

代码

#include<algorithm>#include<iostream>#include<cstring>#include<cstdio>#include<cmath>using namespace std;#define N 200005#define sz 18#define base 2000int cnt,n,m,ans;int s[N],*x,*y,X[N],Y[N],c[N],sa[N],height[N],rank[N];int st[N][sz+3],lg[N],tot[N],id[N],ed[N];void build_sa(){    m=4000;    x=X,y=Y;    for (int i=0;i<n;++i) ++c[x[i]=s[i]];    for (int i=1;i<m;++i) c[i]+=c[i-1];    for (int i=n-1;i>=0;--i) sa[--c[x[i]]]=i;    for (int k=1;k<=n;k<<=1)    {        int p=0;        for (int i=n-k;i<n;++i) y[p++]=i;        for (int i=0;i<n;++i) if (sa[i]>=k) y[p++]=sa[i]-k;        for (int i=0;i<m;++i) c[i]=0;        for (int i=0;i<n;++i) ++c[x[y[i]]];        for (int i=1;i<m;++i) c[i]+=c[i-1];        for (int i=n-1;i>=0;--i) sa[--c[x[y[i]]]]=y[i];        swap(x,y);        p=1;x[sa[0]]=0;        for (int i=1;i<n;++i)            x[sa[i]]=y[sa[i-1]]==y[sa[i]]&&(sa[i-1]+k<n?y[sa[i-1]+k]:-1)==(sa[i]+k<n?y[sa[i]+k]:-1)?p-1:p++;        if (p>=n) break;        m=p;    }}void build_height(){    for (int i=0;i<n;++i) rank[sa[i]]=i;    int k=0;    for (int i=0;i<n;++i)    {        if (!rank[i]) continue;        int j=sa[rank[i]-1];        if (k) --k;        while (s[i+k]==s[j+k]&&i+k<n&&j+k<n) ++k;        height[rank[i]]=k;    }}void rmq(){    for (int i=1,p=0;i<=n;++i)    {        while ((1<<p)<=i) ++p;        lg[i]=p-1;    }    for (int i=0;i<n;++i) st[i+1][0]=height[i];    for (int j=1;j<sz;++j)        for (int i=1;i<=n;++i)            if (i+(1<<j)-1<=n)                st[i][j]=min(st[i][j-1],st[i+(1<<(j-1))][j-1]);}int query(int l,int r){    l+=2,++r;    if (l>r) return 0;    int k=lg[r-l+1];    return min(st[l][k],st[r-(1<<k)+1][k]);}int main(){    scanf("%d",&cnt);    for (int i=1;i<=cnt;++i)    {        int m,x,y;scanf("%d%d",&m,&x);        for (int j=1;j<m;++j)        {            scanf("%d",&y);            s[n++]=y-x+base;id[n-1]=i;            x=y;        }        s[n++]=0;id[n-1]=i;        ed[i]=n-1;    }    build_sa();    build_height();    for (int i=1;i<n;++i)        height[i]=min(height[i],min(ed[id[sa[i-1]]]-sa[i-1],ed[id[sa[i]]]-sa[i]));    rmq();    int pt=0,now=0;    while (!s[sa[now]]) ++now,++pt;    ++tot[id[sa[pt]]];    int sum=1;    while (now<n)    {        while (pt<n&&tot[id[sa[pt]]]-1)        {            --tot[id[sa[pt]]];            ++pt;        }        if (sum==cnt)            ans=max(ans,query(pt,now));        ++now;        if (!tot[id[sa[now]]]) ++sum;        ++tot[id[sa[now]]];    }    printf("%d\n",ans+1);}

#include<algorithm>#include<iostream>#include<cstring>#include<cstdio>#include<cmath>using namespace std;#define N 205#define base 2000int cnt,n,root,last,sz,p,np,q,nq,ans;int s[N],ch[N][4005],pre[N],step[N],Max[N],Min[N],pt[N],c[N];void extend(){    root=last=++sz;    for (int i=0;i<n;++i)    {        int x=s[i];        p=last;np=++sz;last=np;        step[np]=step[p]+1;        while (p&&!ch[p][x])        {            ch[p][x]=np;            p=pre[p];        }        if (!p) pre[np]=root;        else        {            q=ch[p][x];            if (step[q]==step[p]+1) pre[np]=q;            else            {                nq=++sz;                step[nq]=step[p]+1;                pre[nq]=pre[q];                memcpy(ch[nq],ch[q],sizeof(ch[q]));                while (ch[p][x]==q)                {                    ch[p][x]=nq;                    p=pre[p];                }                pre[np]=pre[q]=nq;            }        }    }}void sam(){    memset(Max,0,sizeof(Max));    int p=root,len=0;    for (int i=0;i<n;++i)    {        int x=s[i];        if (ch[p][x]) p=ch[p][x],++len;        else        {            while (p&&!ch[p][x]) p=pre[p];            if (!p) p=root,len=0;            else len=step[p]+1,p=ch[p][x];        }        Max[p]=max(Max[p],len);    }    for (int i=sz;i>=1;--i)    {        p=pt[i];        if (Max[p])            Max[pre[p]]=step[pre[p]];    }    for (int i=1;i<=sz;++i) Min[i]=min(Min[i],Max[i]);}int main(){    scanf("%d",&cnt);    memset(Min,127,sizeof(Min));    for (int i=1;i<=cnt;++i)    {        int m,x,y;scanf("%d%d",&m,&x);        n=0;        for (int j=1;j<m;++j)        {            scanf("%d",&y);            s[n++]=y-x+base;            x=y;        }        if (i==1)        {            extend();            for (int i=1;i<=sz;++i) ++c[step[i]];            for (int i=2;i<=sz;++i) c[i]+=c[i-1];            for (int i=sz;i>=1;--i) pt[c[step[i]]--]=i;        }        else sam();    }    for (int i=1;i<=sz;++i) ans=max(ans,Min[i]);    printf("%d\n",ans+1);}