Censored!
| Time Limit: 5000MS | Memory Limit: 10000K |
| Total Submissions: 8623 | Accepted: 2341 |
Description
The alphabet of Freeland consists of exactly N letters. Each sentence of Freeland language (also known as Freish) consists of exactly M letters without word breaks. So, there exist exactly N^M different Freish sentences.
But after recent election of Mr. Grass Jr. as Freeland president some words offending him were declared unprintable and all sentences containing at least one of them were forbidden. The sentence S contains a word W if W is a substring of S i.e. exists such k >= 1 that S[k] = W[1], S[k+1] = W[2], ...,S[k+len(W)-1] = W[len(W)], where k+len(W)-1 <= M and len(W) denotes length of W. Everyone who uses a forbidden sentence is to be put to jail for 10 years.
Find out how many different sentences can be used now by freelanders without risk to be put to jail for using it.
Input
The first line of the input file contains three integer numbers: N -- the number of letters in Freish alphabet, M -- the length of all Freish sentences and P -- the number of forbidden words (1 <= N <= 50, 1 <= M <= 50, 0 <= P <= 10).
The second line contains exactly N different characters -- the letters of the Freish alphabet (all with ASCII code greater than 32).
The following P lines contain forbidden words, each not longer than min(M, 10) characters, all containing only letters of Freish alphabet.
Output
Output the only integer number -- the number of different sentences freelanders can safely use.
Sample Input
2 3 1
ab
bb
Sample Output
5
Source
Northeastern Europe 2001, Northern Subregion
Kuang神說:
"AC自動機+DP+高精度
好題"
最近在啃AC自動機，代碼了解上尚可，但是似乎有很多變型，多看多了解才是最重要的。
轉載用意：DP學習+AC自動機（含矩陣加速）學習備看 & 大資料模闆記錄
Code By Kuangbin:
#include <queue>
#include <cstdio>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#include <map>
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");
}
}
};
/*
* 高精度，支援乘法和加法
*/
struct BigInt
{
const static int mod = 10000;
const static int DLEN = 4; //per 4 digit for a section
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,
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()
{
// freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
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();
// ac.debug();
Matrix a= ac.getMatrix();
// for(int i = 0;i <a.n;i++)
// {
// for(int j=0;j<a.n;j++)printf("%d ",a.mat[i][j]);
// cout<<endl;
// }
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];
// for(int j = 0;j < a.n;j++)
// dp[now][j].output();
}
BigInt ans = 0;
for(int i = 0;i < a.n;i++)
ans = ans + dp[now][i];
ans.output();
}
return 0;
}
![Count ways to reach the n’th stair Count ways to reach the n’th stair[圖]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACwAAAAAAQABAAACAkQBADs=)