#include <iostream> #include <string.h> #include <algorithm> #include <stdio.h> #include <queue> #include <map> using namespace std; map<char,int>mp; int N,M,P; struct Matrix { int mat[110][110]; int n; Matrix(){} Matrix(int _n) { n=_n; for(int i = 0;i < n;i++) for(int j = 0;j < n;j++) mat[i][j] = 0; } }; struct Trie { int next[110][256],fail[110]; bool end[110]; int L,root; int newnode() { for(int i = 0;i < 256;i++) next[L][i] = -1; end[L++] = false; return L-1; } void init() { L = 0; root = newnode(); } void insert(char buf[]) { int len = strlen(buf); int now = root; for(int i = 0;i < len;i++) { if(next[now][mp[buf[i]]] == -1) next[now][mp[buf[i]]] = newnode(); now = next[now][mp[buf[i]]]; } end[now] = true; } void build() { queue<int>Q; fail[root] = root; for(int i = 0;i < 256;i++) if(next[root][i] == -1) 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]]==true)end[now]=true; for(int i = 0;i < 256;i++) if(next[now][i] == -1)next[now][i] = next[fail[now]][i]; else {fail[next[now][i]] = next[fail[now]][i];Q.push(next[now][i]); } } } Matrix getMatrix() { Matrix res = Matrix(L); for(int i = 0;i < L;i++) for(int j = 0;j < N;j++) if(end[next[i][j]]==false)res.mat[i][next[i][j]]++; return res; } void debug() { for(int i = 0;i < L;i++) { printf("id = %3d,fail = %3d,end = %3d,chi = [",i,fail[i],end[i]); for(int j = 0;j < 26;j++) printf("%2d",next[i][j]); printf("]n"); } } }; struct BigInt { const static int mod = 10000; const static int DLEN = 4; int a[600],len; BigInt() { memset(a,0,sizeof(a)); len = 1; } BigInt(int v) { memset(a,0,sizeof(a)); len = 0; do { a[len++] = v%mod; v /= mod; }while(v); } BigInt(const char s[]) { memset(a,0,sizeof(a)); int L = strlen(s); len = L/DLEN; if(L%DLEN)len++; int index = 0; for(int i = L-1;i >= 0;i -= DLEN) { int t = 0; int k = i - DLEN + 1; if(k < 0)k = 0; for(int j = k;j <= i;j++) t = t*10 + s[j] - '0'; a[index++] = t; } } BigInt operator +(const BigInt &b)const { BigInt res; res.len = max(len,b.len); for(int i = 0;i <= res.len;i++) res.a[i] = 0; for(int i = 0;i < res.len;i++) { res.a[i] += ((i < len)?a[i]:0)+((i < b.len)?b.a[i]:0); res.a[i+1] += res.a[i]/mod; res.a[i] %= mod; } if(res.a[res.len] > 0)res.len++; return res; } BigInt operator *(const BigInt &b)const { BigInt res; for(int i = 0; i < len;i++) { int up = 0; for(int j = 0;j < b.len;j++) { int temp = a[i]*b.a[j] + res.a[i+j] + up; res.a[i+j] = temp%mod; up = temp/mod; } if(up != 0) res.a[i + b.len] = up; } res.len = len + b.len; while(res.a[res.len - 1] == 0 &&res.len > 1)res.len--; return res; } void output() { printf("%d",a[len-1]); for(int i = len-2;i >=0 ;i--) printf("%04d",a[i]); printf("n"); } }; char buf[1010]; BigInt dp[2][110]; Trie ac; int main() { while(scanf("%d%d%d",&N,&M,&P)==3) { gets(buf); gets(buf); mp.clear(); int len = strlen(buf); for(int i = 0;i < len;i++) mp[buf[i]]=i; ac.init(); for(int i = 0;i < P;i++) { gets(buf); ac.insert(buf); } ac.build(); Matrix a= ac.getMatrix(); int now = 0; dp[now][0] = 1; for(int i = 1;i < a.n;i++) dp[now][i] = 0; for(int i = 0;i < M;i++) { now^=1; for(int j = 0;j < a.n;j++) dp[now][j] = 0; for(int j = 0;j < a.n;j++) for(int k = 0;k < a.n;k++)if(a.mat[j][k] > 0) dp[now][k] = dp[now][k]+dp[now^1][j]*a.mat[j][k]; } BigInt ans = 0; for(int i = 0;i < a.n;i++) ans = ans + dp[now][i]; ans.output(); } return 0; }
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