CF504E Misha and LCP on Tree 后缀自动机+树链剖分+倍增

求树上两条路径的 LCP （树上每个节点代表一个字符）

总共写+调了6个多小时，终于过了~

绝对是我写过的最复杂的数据结构了

我们对这棵树进行轻重链剖分，然后把所有的重链分正串，反串插入到广义后缀自动机中.

求 LCP 的话就是后缀树中两点 $LCA$ 的深度.

如果 $LCP$ 的长度小于两个重链的长度，就直接输出答案，否则还要继续爬重链.

这道题恶心之处在于将所有重链不重不漏存起来，无法形容有多恶心.

code:

#include <cstdio>
#include <cstring>
#include <vector>
#include <queue>
#include <algorithm>
#include <stack>
#include <string>
using namespace std;
void setIO(string s)
{
    string in=s+".in";
    string out=s+".out";
    freopen(in.c_str(),"r",stdin);
    freopen(out.c_str(),"w",stdout);
}
namespace sam
{
    #define N 1200004
    int last,tot;
    int ch[N][27],pre[N],mx[N];
    inline int extend(int c)
    {
        if(ch[last][c])
        {
            int p=last;
            int q=ch[p][c];
            if(mx[q]==mx[p]+1) last=q;
            else
            {
                int nq=++tot;
                mx[nq]=mx[p]+1;
                memcpy(ch[nq],ch[q],sizeof(ch[q]));
                pre[nq]=pre[q],pre[q]=nq;
                for(;p&&ch[p][c]==q;p=pre[p]) ch[p][c]=nq;
                last=nq;
            }
        }
        else
        {
            int np=++tot,p=last;
            mx[np]=mx[p]+1,last=np;
            for(;p&&!ch[p][c];p=pre[p]) ch[p][c]=np;
            if(!p) pre[np]=1;
            else
            {
                int q=ch[p][c];
                if(mx[q]==mx[p]+1) pre[np]=q;
                else
                {
                    int nq=++tot;
                    mx[nq]=mx[p]+1;
                    memcpy(ch[nq],ch[q],sizeof(ch[q]));
                    pre[nq]=pre[q],pre[np]=pre[q]=nq;
                    for(;p&&ch[p][c]==q;p=pre[p]) ch[p][c]=nq;
                }
            }
            last=np;
        }
        return last;
    }
    #undef N
};

// 优美的后缀自动机

namespace suffix_tree
{
    #define LOG 21
    #define N 1200006
    vector<int>G[N];
    int fa[LOG][N],dis[N];
    void dfs(int u)
    {
        int i,j;
        dis[u]=dis[sam::pre[u]]+1;
        fa[0][u]=sam::pre[u];
        for(i=1;i<LOG;++i) fa[i][u]=fa[i-1][fa[i-1][u]];
        for(i=0;i<(int)G[u].size();++i) dfs(G[u][i]);
    }
    inline void build()
    {
        int i,j;
        for(i=2;i<=sam::tot;++i)
            G[sam::pre[i]].push_back(i);
        dfs(1);
    }
    inline int jump(int x,int len)
    {
        for(int i=LOG-1;i>=0;--i) if(sam::mx[fa[i][x]]>=len) x=fa[i][x];
        return x;
    }
    inline int LCA(int x,int y)
    {
        if(dis[x]!=dis[y])
        {
            if(dis[x]>dis[y]) swap(x,y);
            for(int i=LOG-1;i>=0;--i) if(dis[fa[i][y]]>=dis[x]) y=fa[i][y];
        }
        if(x==y) return x;
        for(int i=LOG-1;i>=0;--i)  if(fa[i][x]!=fa[i][y]) x=fa[i][x], y=fa[i][y];
        return fa[0][x];
    }
    #undef N
    #undef LOG
};     

// 优美的后缀树

namespace tree
{
    #define N 600003
    int tot,iii;
    int son[N],size[N],dep[N],dfn[N],top[N],fa[N],up[N],down[N],val[N],idx[N],pp[N];
    vector<int>G[N];
    struct node
    {
        int u,c;
        node(int u=0,int c=0):u(u),c(c){}
    };
    vector<node>A[N];
    inline void add(int u,int v)
    {
        G[u].push_back(v);
        G[v].push_back(u);
    }
    void dfs1(int u,int ff)
    {
        fa[u]=ff,dep[u]=dep[ff]+1,size[u]=1;
        for(int i=0;i<G[u].size();++i)
        {
            if(G[u][i]==ff) continue;
            dfs1(G[u][i],u);
            size[u]+=size[G[u][i]];
            if(size[G[u][i]]>size[son[u]]) son[u]=G[u][i];
        }
    }
    void dfs2(int u,int tp)
    {
        idx[u]=++iii;
        pp[iii]=u;
        top[u]=tp;
        if(tp==u) dfn[tp]=++tot;
        A[dfn[tp]].push_back(node(u,val[u]));
        if(son[u]) dfs2(son[u],tp);
        for(int i=0;i<G[u].size();++i)
            if(G[u][i]!=son[u]&&G[u][i]!=fa[u])
                dfs2(G[u][i], G[u][i]);
    }
    inline void build()
    {
        int i,j;
        dfs1(1,0);
        dfs2(1,1);
        for(i=1;i<=tot;++i)
        {
            sam::last=1;
            // 从上到下 （实际是从下到上）
            for(j=0;j<A[i].size();++j)
            {
                int u=A[i][j].u;
                int c=A[i][j].c;
                up[u]=sam::extend(c);
            }
            // 从下到上 （实际上是从上到下）
            sam::last=1;
            for(j=A[i].size()-1;j>=0;--j)
            {
                int u=A[i][j].u;
                int c=A[i][j].c;
                down[u]=sam::extend(c);
            }
        }
    }
    int LCA(int x,int y)
    {
        while(top[x]!=top[y]) dep[top[x]]>dep[top[y]]?x=fa[top[x]]:y=fa[top[y]];
        return dep[x]<dep[y]?x:y;
    }
    #undef N
};

// 优美的树链剖分

struct node
{
    int u,len,ty,tt;
    node(int u=0,int len=0,int ty=0,int tt=0):u(u),len(len),ty(ty),tt(tt){}
};
#define N 300003
char S[N];
int ty;
vector<node>A[2];
stack<node>ss;
void insert(int a,int b,int id)
{
    int lca=tree::LCA(a,b);
    // 向上走
    while(tree::dep[a]>tree::dep[lca])
    {
        int pp=tree::dep[tree::top[a]]<tree::dep[lca]?lca:tree::top[a];
        A[id].push_back(node(tree::up[a], tree::dep[a]-max(tree::dep[lca],tree::dep[tree::top[a]])+1,0,a));
        a=tree::fa[tree::top[a]];
    }
    // 向下走
    if(a==lca)
    {
        // 未计算 lca
        while(tree::dep[b]>=tree::dep[lca])
        {
            int pp=tree::dep[tree::top[b]]<tree::dep[lca]?lca:tree::top[b];
            ss.push(node(tree::down[pp], tree::dep[b]-max(tree::dep[lca],tree::dep[pp])+1,1,pp));
            b=tree::fa[tree::top[b]];
        }
    }
    else
    {
        while(tree::dep[b]>tree::dep[lca])
        {
            int pp=tree::dep[tree::top[b]]<tree::dep[lca]?lca:tree::top[b];
            ss.push(node(tree::down[pp], tree::dep[b]-max(tree::dep[lca],tree::dep[pp])+1,1,pp));
            b=tree::fa[tree::top[b]];
        }
    }
    while(!ss.empty()) A[id].push_back(ss.top()),ss.pop();
}
int main()
{
    // setIO("input");
    int i,j,n,m;
    scanf("%d%s",&n,S+1);
    for(i=1;i<=n;++i) tree::val[i]=S[i]-'a';
    for(i=1;i<n;++i)
    {
        int u,v;
        scanf("%d%d",&u,&v);
        tree::add(u,v);
    }
    sam::tot=1;
    tree::build();              // 建完树剖  +  上/下走定位到后缀自动机的位置
    suffix_tree::build();       // 建完后缀树
    scanf("%d",&m);
    for(i=1;i<=m;++i)
    {
        int a,b,c,d;
        scanf("%d%d%d%d",&a,&b,&c,&d);
        insert(a,b,0);
        insert(c,d,1);
        int t1=0,t2=0,lcp=0;
        while(t1<A[0].size()&&t2<A[1].size())
        {
            node a1=A[0][t1], a2=A[1][t2];
            int lca;
            int uu=a1.u;
            int vv=a2.u;
            int u=a1.tt;
            int v=a2.tt;
            int tmp=min(sam::mx[lca=suffix_tree::LCA(uu,vv)], min(a1.len,a2.len));
            lcp+=tmp;
            if(tmp<min(a1.len,a2.len)) break;
            else
            {
                if(tmp==a1.len) ++t1;
                else
                {
                    A[0][t1].u=(A[0][t1].ty==1)?(tree::down[tree::pp[tree::idx[u]+tmp]]):(tree::up[tree::pp[tree::idx[u]-tmp]]);
                    A[0][t1].tt=(A[0][t1].ty==1)?(tree::pp[tree::idx[u]+tmp]):(tree::pp[tree::idx[u]-tmp]);
                    A[0][t1].len=A[0][t1].len-tmp;
                }
                if(tmp==a2.len) ++t2;
                else
                {
                    A[1][t2].u=(A[1][t2].ty==1)?(tree::down[tree::pp[tree::idx[v]+tmp]]):(tree::up[tree::pp[tree::idx[v]-tmp]]);
                    A[1][t2].tt=(A[1][t2].ty==1)?(tree::pp[tree::idx[v]+tmp]):(tree::pp[tree::idx[v]-tmp]);
                    A[1][t2].len=A[1][t2].len-tmp;
                }
            }
        }
        A[0].clear(),A[1].clear();
        printf("%d\n",lcp);
    }
    return 0;
}