UVa 11468

方法：ac自动机 dp
方法比较明显，dp[cur][left] 表示在cur结点，能走left步的期望。在ac自动机上记忆化搜索即可。注意，判断下一个结点nxt是否可行，要看val[nxt] 和 last[nxt]。所以在get fail 的时候，也可省去last，直接 val[nxt] |= val[f[nxt]]。（val[i] = 1 代表 i结点为某个禁止串的终点，＝0则不是）。
code:
  1 #include <cstdio>
  2 #include <cstring>
  3 #include <algorithm>
  4 #include <iostream>
  5 #include <string>
  6 #include <vector>
  7 #include <stack>
  8 #include <bitset>
  9 #include <cstdlib>
 10 #include <cmath>
 11 #include <set>
 12 #include <list>
 13 #include <deque>
 14 #include <map>
 15 #include <queue>
 16 #include <fstream>
 17 #include <cassert>
 18 #include <unordered_map>
 19 #include <unordered_set>
 20 #include <cmath>
 21 #include <sstream>
 22 #include <time.h>
 23 #include <complex>
 24 #include <iomanip>
 25 #define Max(a,b) ((a)>(b)?(a):(b))
 26 #define Min(a,b) ((a)<(b)?(a):(b))
 27 #define FOR(a,b,c) for (ll (a)=(b);(a)<(c);++(a))
 28 #define FORN(a,b,c) for (ll (a)=(b);(a)<=(c);++(a))
 29 #define DFOR(a,b,c) for (ll (a)=(b);(a)>=(c);--(a))
 30 #define FORSQ(a,b,c) for (ll (a)=(b);(a)*(a)<=(c);++(a))
 31 #define FORC(a,b,c) for (char (a)=(b);(a)<=(c);++(a))
 32 #define FOREACH(a,b) for (auto &(a) : (b))
 33 #define rep(i,n) FOR(i,0,n)
 34 #define repn(i,n) FORN(i,1,n)
 35 #define drep(i,n) DFOR(i,n-1,0)
 36 #define drepn(i,n) DFOR(i,n,1)
 37 #define MAX(a,b) a = Max(a,b)
 38 #define MIN(a,b) a = Min(a,b)
 39 #define SQR(x) ((LL)(x) * (x))
 40 #define Reset(a,b) memset(a,b,sizeof(a))
 41 #define fi first
 42 #define se second
 43 #define mp make_pair
 44 #define pb push_back
 45 #define all(v) v.begin(),v.end()
 46 #define ALLA(arr,sz) arr,arr+sz
 47 #define SIZE(v) (int)v.size()
 48 #define SORT(v) sort(all(v))
 49 #define REVERSE(v) reverse(ALL(v))
 50 #define SORTA(arr,sz) sort(ALLA(arr,sz))
 51 #define REVERSEA(arr,sz) reverse(ALLA(arr,sz))
 52 #define PERMUTE next_permutation
 53 #define TC(t) while(t--)
 54 #define forever for(;;)
 55 #define PINF 1000000000000
 56 #define newline '
'
 57 
 58 #define test if(1)if(0)cerr
 59 using namespace std;
 60 using namespace std;
 61 typedef vector<int> vi;
 62 typedef vector<vi> vvi;
 63 typedef pair<int,int> ii;
 64 typedef pair<double,double> dd;
 65 typedef pair<char,char> cc;
 66 typedef vector<ii> vii;
 67 typedef long long ll;
 68 typedef unsigned long long ull;
 69 typedef pair<ll, ll> l4;
 70 const double pi = acos(-1.0);
 71 
 72 const int MAXNODE = 20*20+5;
 73 const int SIGMA_SIZE = 130;
 74 const int MAXL = 105;
 75 inline int idx(char c)
 76 {
 77     return c;
 78 }
 79 
 80 struct AC
 81 {
 82     int g[MAXNODE][SIGMA_SIZE], val[MAXNODE], last[MAXNODE], f[MAXNODE];
 83     int sz;
 84     int newnode()
 85     {
 86         Reset(g[sz], 0);
 87         val[sz] = last[sz] = 0;
 88         return sz++;
 89     }
 90     void init()
 91     {
 92         sz = 0; newnode();
 93     }
 94     void insert(const string &str, int v)
 95     {
 96         int u = 0, n = str.length();
 97         rep(i, n)
 98         {
 99             int c = idx(str[i]);
100             if (!g[u][c]) g[u][c] = newnode();
101             u = g[u][c];
102         }
103         val[u] = v;
104     }
105     void get_fail()
106     {
107         queue<int> q;   f[0] = 0;
108         rep(i, SIGMA_SIZE)
109         {
110             int u = g[0][i];
111             if (u)
112             {
113                 f[u] = last[u] = 0; q.push(u);
114             }
115         }
116         while (!q.empty())
117         {
118             int r = q.front();  q.pop();
119             rep(c, SIGMA_SIZE)
120             {
121                 int u = g[r][c];
122                 if (!u)
123                 {
124                     g[r][c] = g[f[r]][c]; continue;
125                 }
126                 q.push(u);
127                 int v = f[r];
128                 while (v && !g[v][c]) v = f[v];
129                 f[u] = g[v][c];
130                 last[u] = val[f[u]]?f[u]:last[f[u]];
131             }
132         }
133     }
134     void valid(int j)
135     {
136         if (j)
137         {
138             valid(last[j]);
139         }
140     }
141     void find(const string &str)
142     {
143         int n = str.length(), j = 0;
144         rep(i, n)
145         {
146             int c = idx(str[i]);
147             j = g[j][c];
148             if (val[j]) valid(j);
149             else if (last[j]) valid(last[j]);
150         }
151     }
152 };
153 AC ac;
154 
155 map<int, double> p;
156 string str;
157 int k, l, N;
158 double d[MAXNODE][MAXL];
159 bool vis[MAXNODE][MAXL];
160 double dp(int cur, int left)
161 {
162     if (!left) return 1.0;
163     if (!vis[cur][left])
164     {
165         vis[cur][left] = true;
166         double &ans = d[cur][left];
167         ans = 0;
168         for (auto &pr : p) if (!ac.val[ac.g[cur][pr.first]] && !ac.last[ac.g[cur][pr.first]])
169         {
170             ans += pr.second*dp(ac.g[cur][pr.first], left-1);
171         }
172     }
173     return d[cur][left];
174 }
175 int main()
176 {
177     ios::sync_with_stdio(false);
178     cin.tie(0);
179     int T;  cin >> T;
180     repn(kase, T)
181     {
182         ac.init();
183         p.clear();
184         cin >> k;
185         rep(i, k)
186         {
187             string line;    cin >> line;
188             ac.insert(line, 1);
189         }
190         ac.get_fail();
191         cin >> N;
192         rep(i, N)
193         {
194             char c; cin >> c;
195             double temp;    cin >> temp;
196             p[idx(c)] = temp;
197         }
198         cin >> l;
199         Reset(vis, 0);
200         printf("Case #%d: %.6lf
", kase, dp(0, l));
201     }
202 }
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