P1939 [TEMPLATE] matrix acceleration (series), p1939 Matrix

P1939 [TEMPLATE] matrix acceleration (series), p1939 Matrix
Description

A [1] = a [2] = a [3] = 1

A [x] = a [X-3] + a [x-1] (x> 3)

Returns the remainder value of the nth clause of Series a on 1000000007 (10 ^ 9 + 7.

Input/output format:

 

The first line is an integer T, indicating the number of queries.

The following T rows have a positive integer n in each row.

 

Output Format:

 

Each row outputs a non-negative integer to indicate the answer.

 

Input and Output sample input sample #1:

36810

Output sample #1:

4919

Description

For 30% of Data n <= 100;

For 60% of data, n <= 2*10 ^ 7;

For 100% of data T <= 100, n <= 2*10 ^ 9;

 

 1 #include<cstdio> 2 #include<cstring> 3 #include<iostream> 4 using namespace std; 5 const int MAXN=101; 6 inline void read(int &n){char c='+';bool flag=0;n=0;     7 while(c<'0'||c>'9') c=='-'?flag=1,c=getchar():c=getchar();     8 while(c>='0'&&c<='9') n=n*10+c-48,c=getchar();flag==1?n=-n:n=n;} 9 struct matrix10 {11     long long  m[11][11];12     int h,l;matrix(){memset(m,0,sizeof(m));h=l=0;}13 };14 matrix ma;15 int limit;16 const int mod=1000000007;17 matrix mul(matrix a,matrix b)18 {19     matrix c;c.h=c.l=3;20     for(int k=0;k<a.l;k++)21         for(int i=0;i<a.h;i++)22             for(int j=0;j<b.l;j++)23                 c.m[i][j]=(c.m[i][j]+(a.m[i][k]*b.m[k][j]))%mod;24     return c;25 }26 matrix fast_martix_pow(matrix ma,int p)27 {28     matrix bg;29     for(int i=0;i<3;i++)30         for(int j=0;j<3;j++)31             bg.m[i][j]=(i==j);32     bg.h=bg.l=3;33     while(p)34     {35         if(p&1)    bg=mul(bg,ma);36         ma=mul(ma,ma);37         p>>=1;38     }39     return bg;40 }41 int main()42 {43     int T;read(T);44     while(T--)45     {46         int m;47         read(m);48         if (m<=3&&m>0) {cout<<1<<endl; continue;} else if (m<=0) {cout<<0<<endl; continue;} 49         matrix a,b;50         a.m[0][0]=1;51         a.m[0][2]=1;52         a.m[1][0]=1;53         a.m[2][1]=1;54         b.m[0][0]=1;55         b.m[1][0]=1;56         b.m[2][0]=1;57         a.h=a.l=3;58         b.h=3;b.l=1;59         a=fast_martix_pow(a,m-3);60         a=mul(a,b);61         printf("%d\n",a.m[0][0]%mod);62     }63     return 0;64 }