HDU ------ (1757) A simple math problem (simple matrix fast power)

A simple math problem

Time Limit: 3000/1000 MS (Java/others) memory limit: 32768/32768 K (Java/Others)
Total submission (s): 2791 accepted submission (s): 1659

Problem descriptionlele now is thinking about a simple function f (x ).

If x <10 f (x) = x.
If X> = 10 f (x) = A0 * F (x-1) + A1 * F (X-2) + A2 * F (X-3) + ...... + A9 * F (X-10 );
And AI (0 <= I <= 9) can only be 0 or 1.

Now, I will give a0 ~ A9 and two positive integers K and M, and cocould you help Lele to caculate F (k) % m.

 

Inputthe problem contains mutiple test cases. Please process to the end of file.
In each case, there will be two lines.
In the first line, there are two positive integers K and M. (K <2*10 ^ 9, m <10 ^ 5)
In the second line, there are ten integers represent a0 ~ A9.

 

Outputfor each case, Output F (k) % m in one line.

 

Sample input10 99991 1 1 1 1 1 1 1 120 5001 0 1 0 1 0 1 0 1 0 0

 

Sample output45104

 

Authorlinle

 

Source 2007 provincial training team exercise session (6) _ linle session code:

 1 //#define LOCAL 2 #include<cstdio> 3 #include<cstring> 4 #define LL __int64 5 using namespace std; 6 const int maxn=10; 7 LL k,m; 8 int aa[maxn],mat[maxn][maxn]; 9 int ans[maxn][maxn];10 11 void init()12 {13     for(int i=0;i<10;i++)14     {15      for(int j=0;j<10;j++)16      {17        if(i==0)18          mat[i][j]=aa[j];19        else20           if(i==j+1)mat[i][j]=1;21        else mat[i][j]=0;22        if(i==j)23            ans[i][j]=1;24        else ans[i][j]=0;25      }26     }27 }28 29 void Matrix(int a[][10],int b[][10])30 {31 32      int c[10][10];33      for(int i=0;i<10;i++)34      {35          for(int j=0;j<10;j++)36         {37             c[i][j]=0;38           for(int k=0;k<10;k++)39            {40             c[i][j]=(c[i][j]+a[i][k]*b[k][j])%m;41           }42         }43      }44     for(int i=0;i<10;i++)45     {46       for(int j=0;j<10;j++)47       {48         a[i][j]=c[i][j];49       }50     }51 }52 53 void pow(LL n)54 {55     while(n>0)56     {57         if(n&1) Matrix(ans,mat);58         n>>=1L;59         if(n==0)break;60         Matrix(mat,mat);61     }62 }63 64 int main()65 {66     #ifdef LOCAL67      freopen("test.in","r",stdin);68     #endif69 70   while(scanf("%I64d%I64d",&k,&m)!=EOF)71   {72        for(int i=0;i<10;i++)73        scanf("%d",aa+i);74      if(k<10) printf("%I64d\n",k%m);75      else76      {77        init();78        pow(k-9);79        int res=0;80        for(int i=0;i<10;i++)81         res=(res+(10-i-1)*ans[0][i])%m;82        printf("%d\n",res);83     }84   }85   return 0;86 }

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HDU ------ (1757) A simple math problem (simple matrix fast power)