题目：http://www.lydsy.com/JudgeOnline/problem.php?id=3238

这是我ORZ了网上的题解才知道的555：

首先做一次后缀数组，求出sa[],height[]，然后对于height[2..len(s)]建立Cartesian Tree,那么每个节点对于题目中项lcp()的贡献为(size[left[v]]+1)*(size[right[v]]+1)（很好证明。。。略），然后得出答案。

代码：

速度依旧被虐成渣。。。

b219ebc4b74543a9194daec31c178a82b901146e.jpg.png

#include <cstdio>
#include <algorithm>
#include <cstring>
 
using namespace std;
 
#define MAXN 500010
#define ll long long 
#define F(t) father[t]
#define L(t) left[t]
#define R(t) right[t]
#define K(t) key[t]
#define S(t) size[t]
#define clear(t) memset(t,0,sizeof(t))
 
int getstring(char *s) {
    int ch,len=0;
    for (ch=getchar();!(ch>='a'&&ch<='z');ch=getchar()) ;
    s[++len]=ch;
    for (ch=getchar();ch>='a'&&ch<='z';ch=getchar()) s[++len]=ch;
    return len;
}
 
char s[MAXN];
int n,height[MAXN],sa[MAXN],rank[MAXN],w[MAXN],r[MAXN],x[MAXN],y[MAXN];
 
void make_sa() {
    int N,b=1,M=n;
    s[sa[0]=0]='$';
    for (int i=0;i++<n;) M=max(M,rank[i]=s[i]);
    do {
        for (int i=0;i++<n;) x[i]=rank[i],y[i]=i+b<=n?rank[i+b]:0;
        b<<=1;
        for (int i=0;i<=M;i++) w[i]=0;
        for (int i=0;i++<n;) w[y[i]]++;
        for (int i=0;i++<M;) w[i]+=w[i-1];
        for (int i=0;i++<n;) r[w[y[i]]--]=i;
        for (int i=0;i<=M;i++) w[i]=0;
        for (int i=0;i++<n;) w[x[r[i]]]++;
        for (int i=0;i++<M;) w[i]+=w[i-1];
        for (int i=n;i;i--) sa[w[x[r[i]]]--]=r[i];
        N=0;
        for (int i=0;i++<n;) {
            if (i==1||x[sa[i]]!=x[sa[i-1]]||y[sa[i]]!=y[sa[i-1]]) N++;
            rank[sa[i]]=N;
        }
    } while (N<n);
    int k=0;
    for (int i=0;i++<n;) {
        height[rank[i]]=k;
        for (int j=k;i+j<=n&&sa[rank[i]-1]+j<=n&&s[i+j]==s[sa[rank[i]-1]+j];j++) height[rank[i]]++;
        k=max(height[rank[i]]-1,0);
    }
}
 
int father[MAXN],left[MAXN],right[MAXN],roof=0;
ll size[MAXN],key[MAXN];
 
void dfs(int t) {
    S(t)=1;
    if (L(t)) dfs(L(t)),S(t)+=S(L(t));
    if (R(t)) dfs(R(t)),S(t)+=S(R(t));
}
 
ll Solve() {
    ll rec=0;
    for (int i=0;i++<n;) {
        ll ret=n-i+1;
        rec+=ret;
    }
    rec*=(n-1);
    F(0)=L(0)=R(0)=K(0)=S(0)=0;
    int t=0;
    for (int i=2;i<=n;i++) {
        K(i)=height[i];
        if (!roof) { roof=t=i; continue; }
        for (;t&&K(t)>K(i);t=F(t)) ;
        if (t) {
            L(i)=R(t),R(t)=i,F(i)=t;
        } else if (K(roof)>K(i)) L(i)=roof,roof=i; else L(i)=R(roof),R(roof)=i,F(i)=roof;
        t=i;
    }
    dfs(roof);
    for (int i=2;i<=n;i++) {
        ll ret=(S(L(i))+1)*(S(R(i))+1)*K(i)*2;
        rec-=ret;
    }
    return rec;
}
 
int main() {
    n=getstring(s);
    make_sa();
    printf("%lld\n",Solve());
    return 0;
}