POJ 2778 DNA Sequence (ac automata + Matrix fast Power)

Title Link: http://poj.org/problem?id=2778

Test instructions: There is a disease in the M DNA sequence, asking how many DNA sequences of length n do not contain any kind of disease-containing DNA sequences. (A,t,c,g four characters only)

Idea: Trie diagram of the state transfer, with the Matrix Mat[i][j] to represent from the node I to J only walk one step there are several ways, then the n power of the mat from the node I to J Walk N steps there are several ways to solve the problem is to go from the head node N step and do not contain dangerous nodes of the walk method.

Mat = mat^n ans = (mat[0][0] + mat[0][1] + ... + mat[0][num]) num is the number of nodes

Code

1#include <cstdio>2#include <cstring>3#include <queue>4#include <map>5 using namespacestd;6 Const intKIND =4;7 Const intMAXN = the;8 Const intMOD =100000;9typedefLong LongLL;Ten  One structTrie A { -     intNext[maxn][kind], FAIL[MAXN]; -     BOOLISEXIT[MAXN]; the     introot, L; -map<Char,int>MP; - LL MAT[MAXN][MAXN]; - LL RET[MAXN][MAXN]; + LL TMP[MAXN][MAXN]; -     intCreate () +     { A          for(inti =0; i < KIND; ++i) atNext[l][i] =-1; -isexit[l++] =false; -         returnL1; -     } -     voidInit () -     { inL =0; -Root =Create (); tomp['A'] =0; +mp['C'] =1; -mp['G'] =2; themp['T'] =3; *Memset (Mat,0,sizeof(MAT)); $memset (ret,0,sizeof(ret));Panax Notoginseng     } -     voidInsertCharstr[]) the     { +         intnow =Root; A         intLen =strlen (str); the          for(inti =0; i < Len; ++i) +         { -             if(-1==Next[now][mp[str[i]]) $Next[now][mp[str[i]] =Create (); $now =Next[now][mp[str[i]]; -         } -Isexit[now] =true; the     } -     voidbuild ()Wuyi     { thequeue<int>Q; -          for(inti =0; i < KIND; ++i) Wu         { -             if(-1==Next[root][i]) AboutNext[root][i] =Root; $             Else -             { -Fail[next[root][i]] =Root; - Q.push (Next[root][i]); A             } +         } the          while(!q.empty ()) -         { $             intnow =Q.front (); the Q.pop (); the             if(Isexit[fail[now]]) theIsexit[now] =true; the              for(inti =0; i < KIND; ++i) -             { in                 if(-1==Next[now][i]) theNext[now][i] =Next[fail[now]][i]; the                 Else About                 { theFail[next[now][i]] =Next[fail[now]][i]; the Q.push (Next[now][i]); the                 } +             } -         } the     }Bayi     voidGetmatrix () the     { the          for(inti =0; i < L; ++i) -         { -              for(intj =0; J < KIND; ++j) the             { the                 if(!Isexit[next[i][j]]) the++Mat[i][next[i][j]]; the             } -         } the     } the     voidMatrixmul (ll MAT1[MAXN][MAXN], LL MAT2[MAXN][MAXN]) the     {94 LL MAT3[MAXN][MAXN]; the          for(inti =0; i < L; ++i) the         { the              for(intj =0; J < L; ++j)98             { AboutMAT3[I][J] =0; -                  for(intK =0; K < L; ++k)101MAT3[I][J] = (Mat3[i][j] + mat1[i][k] * mat2[k][j])%MOD;102             }103         }104memcpy (MAT1, MAT3,sizeof(MAT3)); the     }106     voidMatrixquickmod (LL N)107     {108 Getmatrix ();109          for(inti =0; i < L; ++i) the         {111Ret[i][i] =1; the              for(intj =0; J < L; ++j)113TMP[I][J] =Mat[i][j]; the         } the          while(n) the         {117             if(N &1) Matrixmul (ret, TMP);118 Matrixmul (TMP, TMP);119N >>=1; -         }121     }122 };123 Trie ac;124 Charstr[ the]; the intMain ()126 {127     intm; - LL N;129      while(SCANF ("%d%lld", &m, &n)! =EOF) the     {131 ac.init (); the          for(inti =0; I < m; ++i)133         {134scanf"%s", str);135 Ac.insert (str);136         }137 ac.build ();138 ac.matrixquickmod (n);139         intAns =0; $          for(inti =0; I < AC. L ++i)141Ans = (ans + ac.ret[0][i])%MOD;142printf"%d\n", ans);143     }144     return 0;145}

POJ 2778 DNA Sequence (ac automata + Matrix fast Power)