hdu 1757 A Simple Math Problem 矩阵基础题

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
using namespace std;
#define LL __int64
//const LL mod=9973;
LL n,mod;
struct matrix{
    LL f[10][10];
};
matrix mul(matrix a,matrix b)
{
    LL i,j,k;
    matrix c;
    memset(c.f,0,sizeof(c.f));
    for(k=0;k<10;k++)
    {
        for(i=0;i<10;i++)
        {
            if(!a.f[i][k])continue;
            for(j=0;j<10;j++)
            {
                if(!b.f[k][j])continue;
                c.f[i][j]=(c.f[i][j]+a.f[i][k]*b.f[k][j])%mod;//mod<1e5，a.f[i][k]*b.f[k][j]<1e10,会超int。可int就过了，数据有点水
            }
        }
    }
    return c;
}
matrix pow_mod(matrix a,LL b)
{
    matrix s;
    memset(s.f,0,sizeof(s.f));
    for(LL i=0;i<10;i++)
        s.f[i][i]=1;
    while(b)
    {
        if(b&1)
            s=mul(s,a);
        a=mul(a,a);
        b=b>>1;
    }
    return s;
}
int main()
{
    while(cin>>n>>mod)
    {
        LL i,j,k;
        matrix e;
        memset(e.f,0,sizeof(e.f));
        for(i=0;i<10;i++)
            cin>>e.f[i][0];
        if(n<10)
        {
            cout<<n<<endl;
            continue;
        }
        for(i=1;i<10;i++)
            e.f[i-1][i]=1;
        e=pow_mod(e,n-9);
        LL ans=0;
        for(i=0;i<10;i++)
            ans=(ans+(9-i)*e.f[i][0])%mod;
        cout<<ans<<endl;
    }
    return 0;
}
/*
    矩阵:
    |a0 1 0 0 0 0 0 0 0 0|
    |a1 0 1 0 0 0 0 0 0 0|
    |a2 0 0 1 0 0 0 0 0 0|
    |a3 0 0 0 1 0 0 0 0 0|
    |a4 0 0 0 0 1 0 0 0 0|*|f[x-1]...f[x-10]|=|f[x] f[x-1] ... f[x-9]|
    |a5 0 0 0 0 0 1 0 0 0|
    |a6 0 0 0 0 0 0 1 0 0|
    |a7 0 0 0 0 0 0 0 1 0|
    |a8 0 0 0 0 0 0 0 0 1|
    |a9 0 0 0 0 0 0 0 0 0|
*/