"BZOJ-1009" GT test kmp+dp+ Matrix multiplication + fast Power

1009: [HNOI2008]GT exam Time limit:1 Sec Memory limit:162 MB
submit:2745 solved:1694
[Submit] [Status] [Discuss] Description

Ashen ready to enroll in the GT exam, the ticket number is n-digit x1x2 .... Xn (0<=xi<=9), he does not want to appear on the ticket number of unlucky figures.
His unlucky math a1a2 ... AM (0<=ai<=9) has M-bit, does not appear to refer to x1x2 ... The xn does not have exactly a paragraph equal to A1A2 ... Am. A1 and X1 can think
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Input

The first line enters N,m,k. The next line is to enter the number of M bits. n<=10^9,m<=20,k<=1000

Output

Ashen want to know how many kinds of numbers do not appear unlucky numbers, the result of output modulus K redundancy.

Sample Input4 3 100
111Sample OutputBayiHintsourcesolution

This is a very good question.

Start looking at the range, $10^{9}$ obviously O (n) can not do ah, but also like the digital DP, so it must be optimized to optimize to the O (n) only the moment multiplication fast Power optimization dp

Actually and the digital DP very exhausted, F[I][J] represents the number of bits I, and finally matched the number of J-bit scheme, so the answer is obviously $\sum_{i=1}^{n}f[n][i]$

Consider the next array of KMP, sort the discussion, get on the matrix, and then quickly power up the mess.

Code

#include <iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<cmath>using namespacestd;intn,m,p,next[ the],an;Chars[ the];structmatrixnode{intda[ -][ -]; Matrixnode () {memset (DA,0,sizeof(DA));}} A    Matrixnode Mul (Matrixnode a,matrixnode B) {Matrixnode C;  for(intI=0; i<m; i++)         for(intj=0; j<m; J + +)             for(intk=0; k<m; k++) C.da[i][j]= (C.da[i][j]+a.da[i][k]*b.da[k][j])%p; returnC;} Matrixnode Pow (Matrixnode A,intx)    {Matrixnode re;  for(intI=0; i<m; i++) re.da[i][i]=1;  for(intI=x; I i>>=1, a=Mul (a,a))if(i&1) re=Mul (re,a); returnre;}voidkmp_prework () { for(intj=0, i=2; i<=m; i++)        {             while(J && s[i]!=s[j+1]) j=Next[j]; if(s[j+1]==s[i]) J + +; next[i]=J; }     for(intI=0; i<m; i++)         for(intx,j=0; j<Ten; J + +) {x=i;  while(x && s[x+1]-'0'!=J) x=Next[x]; if(j==s[x+1]-'0') a.da[i][x+1]++;Elsea.da[i][0]++; }}intMain () {scanf ("%d%d%d\n", &n,&m,&p); scanf"%s", s+1);    Kmp_prework (); Matrixnode ans; Ans=Pow (a,n);  for(intI=0; i<m; i++) an= (an+ans.da[0][i])%p; printf ("%d\n", an); return 0;}

Matrixnode write why so long, make the code wind ugly dead

"BZOJ-1009" GT test kmp+dp+ Matrix multiplication + fast Power