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 Description
Lele 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 could you help Lele to caculate f(k)%m.
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 could you help Lele to caculate f(k)%m.
Input
The 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.
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.
Output
For each case, output f(k) % m in one line.
Sample Input
10 9999
1 1 1 1 1 1 1 1 1 1
20 500
1 0 1 0 1 0 1 0 1 0
Sample Output
45
104
Author
linle
Source
代码:
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 else 20 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 LOCAL 67 freopen("test.in","r",stdin); 68 #endif 69 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 ",k%m); 75 else 76 { 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 ",res); 83 } 84 } 85 return 0; 86 }