【AC自动机+矩阵快速幂】poj2778 DNA Sequence

渐渐开始变难orz
先老老实实建树；
然后建ac自动机，注意两个：
1. 若ch[I][j] ==0 ,某个节点没有某一字符的儿子，考虑将其指向其失配节点的儿子：ch[I][j] = ch[f[I]][j];Tire数就变成Tire图了。

2.若val[f[I]]==1,某节点失配节点是危险节点，则将此节点标为危险节点。

然后构造矩阵mp，如果a,b节点相连且b不是危险节点，mp[a][b]++;

然后把矩阵mp扔去快速幂，求mp[0][i]（I>=0&&I<=sz ）的和，就是答案；

#define _CRT_SECURE_NO_WARNINGS#include<iostream>#include<cstdio>#include<cstring>#include<queue>using namespace std;typedef long long ll;const int maxn = 101;const int mod = 100000;int n, l;struct Matrix{    ll mat[101][101];    int r, c;    Matrix(int x){ memset(mat, 0, sizeof(mat)); r = x; c = x; }    Matrix operator*(const Matrix &b) const{        Matrix res(b.r);        for (int i = 0; i <= b.r; i++){            for (int j = 0; j <= b.r; j++){                for (int k = 0; k <= b.r; k++){                    res.mat[i][j] = (res.mat[i][j] + mat[i][k] * b.mat[k][j]) % mod;                }            }        }        return res;    }};Matrix Qpow(Matrix x, ll n){    Matrix res(x.c), tmp = x;    for (int i = 0; i <= x.c; i++) res.mat[i][i] = 1;    while (n){        if (n & 1) res = res *tmp;        n >>= 1;        tmp = tmp*tmp;    }    return res;}struct Trie{    int ch[maxn][26];    int val[maxn];    int last[maxn];    int f[maxn];    int sz;    int idx(char x){        if (x == 'A') return 0;        if (x == 'T') return 1;        if (x == 'C') return 2;        if (x == 'G') return 3;    }    void insert(char *s){        int u = 0, n = strlen(s);        for (int i = 0; i < n; i++){            int c = idx(s[i]);            if (!ch[u][c]){                ch[u][c] = sz++;            }            u = ch[u][c];        }        val[u] = 1;    }    void init(){        memset(ch, 0, sizeof(ch));        memset(val, 0, sizeof(val));        sz = 1;        for (int i = 0; i < n; i++){            char str[55]; scanf("%s", str);            insert(str);        }    }    void build(){        queue<int> q;        memset(f, 0, sizeof(f));        memset(last, 0, sizeof(last));        for (int i = 0; i < 26; i++){            int u = ch[0][i];            if (u){ q.push(u); }        }        while (!q.empty()){            int r = q.front(); q.pop();            for (int i = 0; i < 26; i++){                int u = ch[r][i];                if (!u) {                    ch[r][i] = ch[f[r]][i];                    continue;                };                q.push(u);                int v = f[r];                while (v && !ch[v][i]) v = f[v];                f[u] = ch[v][i];                last[u] = val[f[u]] ? f[u] : last[f[u]];                if (val[f[u]] == 1) val[u] = 1;            }        }    }    Matrix getM(){        Matrix mp(sz);        for (int i = 0; i < sz; i++){            for (int j = 0; j < 4; j++){                if (!val[i] && !val[ch[i][j]])                    mp.mat[i][ch[i][j]]++;            }        }        return mp;    }};Trie ac;int main(){    while (~scanf("%d%d", &n, &l)){        ac.init();        ac.build();        Matrix m = ac.getM();        m = Qpow(m, l);        ll ans = 0;        for (int i = 0; i < ac.sz; i++){            ans = (ans + m.mat[0][i]) % mod;        }        cout << ans << endl;    }}