BZOJ 1444 [Jsoi2009]有趣的游戏 (AC自动机 + 概率DP + Gauss)

1444: [Jsoi2009]有趣的游戏

Time Limit: 10 Sec  Memory Limit: 64 MB
Submit: 1382  Solved: 498
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Description

Input

注意 是0<=P

Output

Sample Input

Sample Output

HINT

 30%的数据保证, n ≤ 2. 50%的数据保证, n ≤ 5. 100%的数据保证, n , l, m≤ 10.

Source

析：很容易列出方程，dp[i] = ∑dp[j] * pj ，所以要处理出来就需要AC自动机，然后再用Gauss 消元即可。

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <cctype>
#include <cmath>
#include <stack>
#include <sstream>
#include <list>
#include <assert.h>
#include <bitset>
#include <numeric>
#define debug() puts("++++")
#define gcd(a, b) __gcd(a, b)
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define fi first
#define se second
#define pb push_back
#define sqr(x) ((x)*(x))
#define ms(a,b) memset(a, b, sizeof a)
//#define sz size()
#define pu push_up
#define pd push_down
#define cl clear()
#define all 1,n,1
#define FOR(i,x,n)  for(int i = (x); i < (n); ++i)
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;

typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const LL LNF = 1e17;
const double inf = 1e20;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int maxn = 150000 + 10;
const int maxm = 3e5 + 10;
const int mod = 10007;
const int dr[] = {-1, 0, 1, 0};
const int dc[] = {0, -1, 0, 1};
const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};
int n, m;
const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
inline bool is_in(int r, int c) {
  return r >= 0 && r < n && c >= 0 && c < m;
}
const int maxnode = 10 * 10 + 50;
int sigma;
double A[maxnode][maxnode];
double p[15];
int pos[15];

struct Aho{
  int ch[maxnode][11], f[maxnode];
  bool val[maxnode];
  int sz;

  void init(){ sz = 1;  ms(ch[0], 0); }
  inline int idx(char ch){ return ch - 'A'; }

  int insert(const char *s){
    int u = 0;
    for(int i = 0; s[i]; ++i){
      int c = idx(s[i]);
      if(!ch[u][c]){
        ms(ch[sz], 0);
        val[sz] = 0;
        ch[u][c] = sz++;
      }
      u = ch[u][c];
    }
    val[u] = 1;
    return u;
  }

  void getFail(){
    queue<int> q;  f[0] = 0;
    for(int c = 0; c < sigma; ++c){
      int u = ch[0][c];
      if(u){ q.push(u);  f[u] = 0; }
    }

    while(!q.empty()){
      int r = q.front();  q.pop();
      for(int c = 0; c < sigma; ++c){
        int u = ch[r][c];
        if(!u){ ch[r][c] = ch[f[r]][c];  continue; }
        q.push(u);
        int v = f[r];
        while(v && !ch[v][c])  v = f[v];
        f[u] = ch[v][c];
      }
    }
  }

  int solve(){
    for(int i = 0; i < sz; ++i){
      A[i][i] += 1.;
      if(val[i])  continue;
      for(int j = 0; j < sigma; ++j){
        int nxt = ch[i][j];
        A[nxt][i] -= p[j];
      }
    }
    return sz;
  }
};
Aho aho;
char s[20];

void Gauss(int n){
  for(int i = 0; i < n; ++i){
    int r = i;
    for(int j = i+1; j < n; ++j)
      if(fabs(A[j][i] > fabs(A[r][i]))) r = j;
    if(r != i)  for(int j = 0; j <= n; ++j)  swap(A[r][j], A[i][j]);

    for(int k = i+1; k < n; ++k){
      double f = A[k][i] / A[i][i];
      for(int j = i; j <= n; ++j)  A[k][j] -= f * A[i][j];
    }
  }
  for(int i = n-1; i >= 0; --i){
    for(int j = i+1; j < n; ++j)
      A[i][n] -= A[j][n] * A[i][j];
    A[i][n] /= A[i][i];
  }
}

int main(){
  scanf("%d %d %d", &n, &m, &sigma);
  for(int i = 0; i < sigma; ++i){
    int x, y;  scanf("%d %d", &x, &y);
    p[i] = x * 1. / y;
  }
  aho.init();
  for(int i = 1; i <= n; ++i){
    scanf("%s", s);
    pos[i] = aho.insert(s);
  }
  aho.getFail();
  int len = aho.solve();
  A[0][len] = 1.;
  Gauss(len);
  for(int i = 1; i <= n; ++i)  printf("%.2f\n", A[pos[i]][len] / A[pos[i]][pos[i]]);
  return 0;
}