bzoj 3796: Mushroom追妹纸 AC自动机+后缀自动机+dp

题目大意:

给定三个字符串s1,s2,s3,求一个字符串w满足:

• w是s1的子串
• w是s2的子串
• s3不是w的子串
• w的长度应尽可能大

题解:

首先我们可以用AC自动机找出s3在s1,s2中出现的位置(窝不会kmp)
不完全包括特定区间的最长公共子串了.
我们二分一下答案的长度k
于是我们发现问题变成了:

• 给定两个字符串,有一些点不能选择,问是否存在两个点所代表后缀的LCP >= k

所以我们将两个字符串拼接起来,有后缀自动机建立后缀树
然后在后缀树上O(n)dp一边便可处理

\(O(nlogn)\)

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
inline void read(int &x){
    x=0;char ch;bool flag = false;
    while(ch=getchar(),ch<'!');if(ch == '-') ch=getchar(),flag = true;
    while(x=10*x+ch-'0',ch=getchar(),ch>'!');if(flag) x=-x;
}
inline int cat_max(const int &a,const int &b){return a>b ? a:b;}
inline int cat_min(const int &a,const int &b){return a<b ? a:b;}
namespace ACM{
    const int maxn = 10010;
    int ch[maxn][26],nodecnt;
    bool danger[maxn];
    inline void insert(char *s){
        int nw = 0;
        for(int i=0,c;s[i] != 0;++i){
            c = s[i] - 'a';
            if(ch[nw][c] == 0) ch[nw][c] = ++ nodecnt;
            nw = ch[nw][c];
        }danger[nw] = true;
    }
    int q[maxn],l,r,fail[maxn];
    inline void build(){
        l = 0;r = -1;fail[0] = 0;
        for(int c=0;c<26;++c){
            if(ch[0][c]){
                fail[ch[0][c]] = 0;
                q[++r] = ch[0][c];
            }
        }
        while(l <= r){
            int u = q[l++];
            for(int c=0;c<26;++c){
                int t = ch[fail[u]][c];
                if(ch[u][c] == 0) ch[u][c] = t;
                else{
                    fail[ch[u][c]] = t;
                    q[++r] = ch[u][c];
                }
            }
        }
    }
}
namespace Graph{
    const int maxn = 210010;
    struct Node{
        int to,next;
    }G[maxn];
    int head[maxn],cnt;
    void add(int u,int v){
        G[++cnt].to = v;
        G[cnt].next = head[u];
        head[u] = cnt;
    }
}
namespace SAM{
    const int maxn = 210010;
    struct Node{
        int nx[27];
        int len,fa,x;
    }T[maxn];
    int last,nodecnt;
    inline void init(){
        T[last = nodecnt = 0].fa = -1;
    }
    inline void insert(char cha,int i){
        int c = cha - 'a',cur = ++nodecnt,p;
        T[cur].len = T[last].len + 1;
        for(p = last;p != -1 && T[p].nx[c] == 0;p = T[p].fa) T[p].nx[c] = cur;
        if(p == -1) T[cur].fa = 0;
        else{
            int q = T[p].nx[c];
            if(T[q].len == T[p].len + 1) T[cur].fa = q;
            else{
                int co = ++ nodecnt;
                T[co] = T[q];T[co].len = T[p].len + 1;
                for(;p != -1 && T[p].nx[c] == q;p = T[p].fa) T[p].nx[c] = co;
                T[cur].fa = T[q].fa = co;
            }
        }T[last = cur].x = i;
    }
}
const int maxn = 210010;
char s1[maxn],s2[maxn],s3[maxn];
bool flag1[maxn],flag2[maxn];
int len1,len2,w,mid;
inline void work1(){
    using namespace ACM;
    int nw = 0;
    for(int i=0;s1[i] != 0;++i){
        nw = ch[nw][s1[i] - 'a'];
        if(danger[nw]) flag1[i-w+1] = true;
    }
    nw = 0;
    for(int i=0;s2[i] != 0;++i){
        nw = ch[nw][s2[i] - 'a'];
        if(danger[nw]) flag2[i-w+1] = true;
    }
}
bool vis[maxn];
bool le[maxn],ri[maxn],both[maxn];
#define v G[i].to
inline bool dfs(int u,int f){
    using namespace Graph;
    using namespace SAM;
 
    for(int i = head[u];i;i=G[i].next){
        if(v == f) continue;
        if(dfs(v,u)) return true;
        if(le[v] && ri[v]) both[u] = true;
        else le[u] |= le[v],ri[u] |= ri[v];
    }
    if(!vis[T[u].x]){
        if(T[u].x < len1) le[u] = true;
        if(T[u].x > len1) ri[u] = true;
    }
    if(T[u].len >= mid){
        if(le[u] && ri[u]) return true;
        if(le[u] && both[u]) return true;
        if(ri[u] && both[u]) return true;
    }
    le[u] |= both[u];ri[u] |= both[u];
    return false;
}
#undef v
inline bool check(){
    for(int i=len1-1,c=0;i>=0;--i){
        vis[i] = false;
        if(flag1[i]) c = mid - w + 1;
        if(c != 0) vis[i] = true,-- c;
    }vis[len1] = true;
    for(int i=len2-1,c=0;i>=0;--i){
        vis[i+len1+1] = false;
        if(flag2[i]) c = mid - w + 1;
        if(c != 0) vis[i+len1+1] = true,--c;
    }
    for(int i=0;i<=SAM::nodecnt;++i) le[i] = ri[i] = both[i] = 0;
    if(dfs(0,0)) return true;
    return false;
}
int main(){
    scanf("%s",s1);scanf("%s",s2);scanf("%s",s3);
    ACM::insert(s3);ACM::build();
    len1 = strlen(s1);len2 = strlen(s2);w = strlen(s3);
    work1();SAM::init();
    for(int i=len2-1;i>=0;--i) SAM::insert(s2[i],len1+i+1);SAM::insert('z'+1,len1);
    for(int i=len1-1;i>=0;--i) SAM::insert(s1[i],i);
    for(int i=1;i<=SAM::nodecnt;++i) Graph::add(SAM::T[i].fa,i);
    int l = 0,r = len1,ans = 0;
    while(l <= r){
        mid = (l+r) >> 1;
        if(check()) l = mid+1,ans = mid;
        else r = mid-1;
    }
    printf("%d\n",ans);
    getchar();getchar();
    return 0;
}