[Codeforces 204E] Little Elephant and Strings

[题目链接]

https://codeforces.com/contest/204/problem/E

[算法]

首先构建广义后缀自动机

对于自动机上的每个节点 ， 维护一棵平衡树存储所有它所匹配的字符串编号

可以通过启发式合并得到

计算答案时 ， 我们枚举每个右端点 ， 当当前集合大小 < K时 ， 不断走向link节点

时间复杂度 ： O(NlogN)

[代码]

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
const int N = 2e5 + ;
const int ALPHA = ;
#define rint register int

int n , k;
string st[N];

struct Suffix_Automaton
{
        int sz , last;
        int father[N] , depth[N] , child[N][ALPHA] , cnt[N];
        set< int > s[N];
        vector< int > a[N];
        Suffix_Automaton()
        {
                sz = ;
                last = ;
        }
        inline int new_node(int dep)
        {
                depth[++sz] = dep;
                father[sz] = ;
                memset(child[sz] ,  , sizeof(child[sz]));
                return sz;
        }
        inline void extend(int ch , int col)
        {
                int np = child[last][ch];
                if (np)
                {
                        if (depth[np] == depth[last] + )
                        {
                                s[np].insert(col);
                                last = np;
                                return;
                        } else
                        {
                                int nq = new_node(depth[last] + );
                                father[nq] = father[np];
                                father[np] = nq;
                                memcpy(child[nq] , child[np] , sizeof(child[nq]));
                                for (int p = last; child[p][ch] == np; p = father[p])
                                        child[p][ch] = nq;
                                s[nq].insert(col);
                                last = nq;
                                return;
                        }
                } else
                {
                        np = new_node(depth[last] + );
                        int p = last;
                        for (; child[p][ch] == ; p = father[p])
                                child[p][ch] = np;
                        if (child[p][ch] == np)
                        {
                                father[np] = ;
                                s[np].insert(col);
                                last = np;
                                return;
                        } else
                        {
                                int q = child[p][ch];
                                if (depth[q] == depth[p] + )
                                {
                                        father[np] = q;
                                        s[np].insert(col);
                                        last = np;
                                        return;
                                } else
                                {
                                        int nq = new_node(depth[p] + );
                                        father[nq] = father[q];
                                        father[np] = father[q] = nq;
                                        memcpy(child[nq] , child[q] , sizeof(child[nq]));
                                        for (; child[p][ch] == q; p = father[p])
                                                child[p][ch] = nq;
                                        s[np].insert(col);
                                        last = np;
                                }
                        }
                }
        }
        inline void insert(string s , int col)
        {
                last = ;
                for (rint i = ; i < (int)s.size(); ++i)
                        extend(s[i] - 'a' , col);
        }
        inline void dfs(int u)
        {
                for (unsigned i = ; i < a[u].size(); ++i)
                {
                        int v = a[u][i];
                        dfs(v);
                        if ((int)s[u].size() < (int)s[v].size())
                                swap(s[u] , s[v]);
                        for (set< int > :: iterator it = s[v].begin(); it != s[v].end(); ++it)
                                s[u].insert(*it);
                }
                cnt[u] = (int)s[u].size();
        }
        inline void work()
        {
                for (rint i = ; i <= sz; ++i)
                        a[father[i]].push_back(i);
                dfs();
        }
} SAM;

template <typename T> inline void chkmax(T &x,T y) { x = max(x,y); }
template <typename T> inline void chkmin(T &x,T y) { x = min(x,y); }
template <typename T> inline void read(T &x)
{
    T f = ; x = ;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
    for (; isdigit(c); c = getchar()) x = (x << ) + (x << ) + c - '';
    x *= f;
}

int main()
{

        read(n); read(k);
        for (rint i = ; i <= n; ++i)
        {
                cin >> st[i];
                SAM.insert(st[i] , i);
        }
        SAM.work();
        for (rint i = ; i <= n; ++i)
        {
                int now = ;
                ll ans = ;
                for (rint j = ; j < st[i].size(); ++j)
                {
                        now = SAM.child[now][st[i][j] - 'a'];
                        while (now !=  && SAM.cnt[now] < k) now = SAM.father[now];
                        ans += (ll)SAM.depth[now];
                }
                printf("%lld " , ans);
        }
        printf("\n");

        return ;

}