Censored! POJ - 1625 AC自动机+大数DP

题意：

给出一n种字符的字典，有p个禁用的单词，

问能组成多少个不同的长度为m的合法字符串。(m<=50)

题解：

是不是个我们之前做的题目非常非常像，题意都一样。

直接将上次写的AC自动机+矩阵快速幂的代码交上去。

然后突然发现没有取模，好像直接炸了。即便只有50，但是方案数还是爆__int128了

处理不了，这题还是必须用大数的。

p<=10 我们可以考虑状压实现。

这题还是和之前的题目有点关系的，需要求出可达矩阵，然后根据这个去DP

dp[i][j] 表示第 i 步 在AC自动机 j 这个节点 的方案数目，

然后第 i 步只跟 第 i - 1步的状态有关，然后可以滚动掉这一维。

不用试不滚动的了，会mle的。 别问我怎么知道的！！！！

 #include <set>
 #include <map>
 #include <stack>
 #include <queue>
 #include <cmath>
 #include <cstdio>
 #include <string>
 #include <vector>
 #include <time.h>
 #include <cstring>
 #include <iostream>
 #include <algorithm>

 #define  pi acos(-1.0)
 #define  eps 1e-9
 #define  fi first
 #define  se second
 #define  rtl   rt<<1
 #define  rtr   rt<<1|1
 #define  bug               printf("******\n")
 #define  mem(a, b)         memset(a,b,sizeof(a))
 #define  name2str(x)       #x
 #define  fuck(x)           cout<<#x" = "<<x<<endl
 #define  sf(n)             scanf("%d", &n)
 #define  sff(a, b)         scanf("%d %d", &a, &b)
 #define  sfff(a, b, c)     scanf("%d %d %d", &a, &b, &c)
 #define  sffff(a, b, c, d) scanf("%d %d %d %d", &a, &b, &c, &d)
 #define  pf                printf
 #define  FIN               freopen("../date.txt","r",stdin)
 #define  gcd(a, b)         __gcd(a,b)
 #define  lowbit(x)         x&-x
 #define  IO                iOS::sync_with_stdio(false)

 using namespace std;
 typedef long long LL;
 typedef unsigned long long ULL;
 const int maxn = 1e6 + ;
 const int maxm = 8e6 + ;
 const int INF = 0x3f3f3f3f;
 const int mod = 1e9 + ;

 struct Matrix {
     int mat[][], n;

     Matrix() {}

     Matrix(int _n) {
         n = _n;
         for (int i = ; i < n; i++)
             for (int j = ; j < n; j++)
                 mat[i][j] = ;
     }

     Matrix operator*(const Matrix &b) const {
         Matrix ret = Matrix(n);
         for (int i = ; i < n; i++)
             for (int j = ; j < n; j++)
                 for (int k = ; k < n; k++) {
                     int tmp = (long long) mat[i][k] * b.mat[k][j] % mod;
                     ret.mat[i][j] = (ret.mat[i][j] + tmp) % mod;
                 }
         return ret;
     }
 };

 char buf[];
 int n, m, p;
 map<char, int> mp;

 struct Aho_Corasick {
     int next[][], fail[], End[];
     int root, cnt;

     int newnode() {
         for (int i = ; i < ; i++) next[cnt][i] = -;
         End[cnt++] = ;
         return cnt - ;
     }

     void init() {
         cnt = ;
         root = newnode();
     }

     void insert(char buf[]) {
         int len = strlen(buf);
         int now = root;
         for (int i = ; i < len; i++) {
             if (next[now][mp[buf[i]]] == -) next[now][mp[buf[i]]] = newnode();
             now = next[now][mp[buf[i]]];
         }
         End[now]++;
     }

     void build() {
         queue<int> Q;
         fail[root] = root;
         for (int i = ; i < ; i++)
             if (next[root][i] == -) next[root][i] = root;
             else {
                 fail[next[root][i]] = root;
                 Q.push(next[root][i]);
             }
         while (!Q.empty()) {
             int now = Q.front();
             Q.pop();
             if (End[fail[now]]) End[now] = ;
             for (int i = ; i < ; i++)
                 if (next[now][i] == -) next[now][i] = next[fail[now]][i];
                 else {
                     fail[next[now][i]] = next[fail[now]][i];
                     Q.push(next[now][i]);
                 }
         }
     }

     Matrix get_Matrix() {
         Matrix ret = Matrix(cnt);
         for (int i = ; i < cnt; ++i) {
             for (int j = ; j < n; ++j) {
                 if (!End[next[i][j]]) ret.mat[i][next[i][j]]++;
             }
         }
         return ret;
     }

     void debug() {
         for (int i = ; i < cnt; i++) {
             printf("id = %3d,fail = %3d,end = %3d,chi = [", i, fail[i], End[i]);
             for (int j = ; j < ; j++) printf("%2d", next[i][j]);
             printf("]\n");
         }
     }
 } ac;

 const int MAXL = ;
 const int MAXN = ;
 const int DLEN = ;

 class Big {
 public:
     int a[], len;

     Big(const int b = ) {
         int c, d = b;
         len = ;
         memset(a, , sizeof(a));
         while (d > MAXN) {
             c = d - (d / (MAXN + )) * (MAXN + );
             d = d / (MAXN + );
             a[len++] = c;
         }
         a[len++] = d;
     }

     Big(const char *s) {
         int t, k, index, L;
         memset(a, , sizeof(a));
         L = strlen(s);
         len = L / DLEN;
         if (L % DLEN) len++;
         index = ;
         for (int i = L - ; i >= ; i -= DLEN) {
             t = ;
             k = i - DLEN + ;
             if (k < ) k = ;
             for (int j = k; j <= i; j++) t = t *  + s[j] - '';
             a[index++] = t;
         }
     }

     Big operator/(const LL &b) const {
         Big ret;
         LL down = ;
         for (int i = len - ; i >= ; i--) {
             ret.a[i] = (a[i] + down * (MAXN + )) / b;
             down = a[i] + down * (MAXN + ) - ret.a[i] * b;
         }
         ret.len = len;
         while (ret.a[ret.len - ] ==  && ret.len > ) ret.len--;
         return ret;
     }

     bool operator>(const Big &T) const {
         int ln;
         if (len > T.len) return true;
         else if (len == T.len) {
             ln = len - ;
             while (a[ln] == T.a[ln] && ln >= ) ln--;
             if (ln >=  && a[ln] > T.a[ln]) return true;
             else return false;
         } else return false;
     }

     Big operator+(const Big &T) const {
         Big t(*this);
         int big = T.len > len ? T.len : len;
         for (int i = ; i < big; i++) {
             t.a[i] += T.a[i];
             if (t.a[i] > MAXN) {
                 t.a[i + ]++;
                 t.a[i] -= MAXN + ;
             }
         }
         if (t.a[big] != ) t.len = big + ;
         else t.len = big;
         return t;
     }

     Big operator-(const Big &T) const {
         int big;
         bool flag;
         Big t1, t2;
         if (*this > T) {
             t1 = *this;
             t2 = T;
             flag = ;
         } else {
             t1 = T;
             t2 = *this;
             flag = ;
         }
         big = t1.len;
         for (int i = ; i < big; i++) {
             if (t1.a[i] < t2.a[i]) {
                 int j = i + ;
                 while (t1.a[j] == ) j++;
                 t1.a[j--]--;
                 while (j > i) t1.a[j--] += MAXN;
                 t1.a[i] += MAXN +  - t2.a[i];
             } else t1.a[i] -= t2.a[i];
         }
         t1.len = big;
         while (t1.a[t1.len - ] ==  && t1.len > ) {
             t1.len--;
             big--;
         }
         if (flag) t1.a[big - ] =  - t1.a[big - ];
         return t1;
     }

     LL operator%(const int &b) const {
         LL d = ;
         for (int i = len - ; i >= ; i--) d = ((d * (MAXN + )) % b + a[i]) % b;
         return d;
     }

     Big operator*(const Big &T) const {
         Big ret;
         int i, j, up, temp, temp1;
         for (i = ; i < len; i++) {
             up = ;
             for (j = ; j < T.len; j++) {
                 temp = a[i] * T.a[j] + ret.a[i + j] + up;
                 if (temp > MAXN) {
                     temp1 = temp - temp / (MAXN + ) * (MAXN + );
                     up = temp / (MAXN + );
                     ret.a[i + j] = temp1;
                 } else {
                     up = ;
                     ret.a[i + j] = temp;
                 }
             }
             if (up != ) ret.a[i + j] = up;
         }
         ret.len = i + j;
         while (ret.a[ret.len - ] ==  && ret.len > ) ret.len--;
         return ret;
     }

     void print() {
         printf("%d", a[len - ]);
         for (int i = len - ; i >= ; i--) printf("%04d", a[i]);
     }
 };

 Big dp[][];

 int main() {
        //FIN;
     while (~scanf("%d%d%d", &n, &m, &p)) {
         mp.clear();
         scanf("%s", buf);
         int len = strlen(buf);
         for (int i = ; i < len; ++i) mp[buf[i]] = i;
         ac.init();
         for (int i = ; i < p; ++i) {
             scanf("%s", buf);
             ac.insert(buf);
         }
         ac.build();
         Matrix mat = ac.get_Matrix();
 //        for (int i = 0; i < mat.n; ++i) {
 //            for (int j = 0; j < mat.n; ++j) {
 //                printf("%d ",mat.mat[i][j]);
 //            }
 //            printf("\n");
 //        }
         int now=;
         dp[now][] = ;
         for (int i = ; i < mat.n; ++i) dp[now][i] = ;
         for (int i = ; i <= m; ++i) {
             now^=;
             for (int j = ; j < mat.n; ++j) dp[now][j]=;
             for (int j = ; j < mat.n; ++j) {
                 for (int k = ; k < mat.n; ++k) {
                     if (mat.mat[j][k]) dp[now][k] = dp[now][k] + dp[now^][j] * mat.mat[j][k];
                 }
             }
         }
         Big ans = ;
         for (int i = ; i < mat.n; ++i) ans = ans + dp[now][i];
         ans.print();
         printf("\n");
     }
     return ;
 }