CF1902E. Collapsing Strings-LCP、字典树

link:https://codeforces.com/contest/1902/problem/E

题意：You are given $n$ strings $s_1,s_2,\dots ,s_n$, consisting of lowercase Latin letters. Let $|x|$ be the length of string $x$. Let a collapse $C(a,b)$ of two strings $a$ and $b$ be the following operation:

• if $a$ is empty, $C(a,b)=b$; - if $b$ is empty, $C(a,b)=a$;
• if the last letter of $a$ is equal to the first letter of $b$, then $C(a,b)=C(a_{1,|a|-1},b_{2,|b|})$, where $s_{l,r}$ is the substring of $s$ from the $l$-th letter to the $r$-th one;
• otherwise, $C(a,b)=a+b$, i. e. the concatenation of two strings.
  Calculate $\sum _{i=1}^n\sum _{j=1}^n|C(s_i,s_j)|$.

$\sum |s_i|\le {10}^6$.

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$C(s,t)=|s|+|t|-2\times LCP(t,s^{\prime })$，其中 $s^{\prime }$ 表示 $s$ 的反串， $LCP$ 表示最长公共前缀。

因此 $$ans=\sum_{i=1}^n\sum_{j=1}n |s_i|+|s_j|-2 LCP(s_j,s_i')=2n\cdot\sum_{i=1}^{n|s_i|-2\sum_{i=1}}n\sum_{j=1}^n LCP(s_i',s_j)$$
对于后者，枚举每个 $s_i^{\prime }$ ，查询其和所有其他串最长公共前缀，将所有串插入到字典树上，做一个子树查询即可。

#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define fastio ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
using namespace std;
typedef long long ll;
const int N=1e6+5;
const int C=26;
int n,tr[N][C+1],tag[N],cnt;
string s[N];
void insert(const string &s){
    int len=s.length(),k=0;
    for(int i=0;i<len;i++){
        int ch=s[i]-'a';
        if(!tr[k][ch])tr[k][ch]=++cnt;
        k=tr[k][ch];
        tag[k]++;
    }
}
ll work(const string &s){
    int len=s.length(),k=0;
    ll ret=0;
    for(int i=len-1;i>=0;i--){
        int ch=s[i]-'a';
        k=tr[k][ch];
        if(!k)break;
        ret+=tag[k];
    }
    return ret;
}
int main(){
    fastio;
    cin>>n;
    ll ans=0;
    rep(i,1,n){
        cin>>s[i];
        insert(s[i]);
        ans+=(ll)2*n*s[i].length();
    }
    rep(i,1,n)ans-=2*work(s[i]);
    cout<<ans;
    return 0;
}