UVa10870 - Recurrences(矩阵)

题目链接

分析：
矩阵快速幂求递推式
练模板

//这里写代码片
#include<cstdio>
#include<cstring>
#include<cstdio>
#define ll long long

using namespace std;

ll n,p,f[20],a[20];
int d;
struct node{
    ll H[20][20];
    node operator *(const node &a) const
    {
        node ans;
        for (int i=1;i<=d;i++)
            for (int j=1;j<=d;j++)
            {
                ans.H[i][j]=0;
                for (int k=1;k<=d;k++)
                    ans.H[i][j]=(ans.H[i][j]+H[i][k]*a.H[k][j]%p)%p;
            }
        return ans;
    }
    void clear()
    {
        memset(H,0,sizeof(H));
    }
    node KSM(ll b)
    {
        node ans=(*this),a=(*this);
        b--;
        while (b)
        {
            if (b&1)
               ans=ans*a;
            b>>=1;
            a=a*a;
        }
        return ans;
    }
};
node ans,H;

int main()
{
    scanf("%d%lld%lld",&d,&n,&p);
    while (d&&n&&p)
    {
        H.clear();
        for (int i=1;i<=d;i++)
            scanf("%lld",&a[i]),
            H.H[i][1]=a[i]%p;
        for (int i=1;i<=d;i++)
            scanf("%lld",&f[i]);
        if (n<=d) 
        {
            printf("%lld\n",f[n]%p);
            scanf("%d%lld%lld",&d,&n,&p);
            continue;
        }
        for (int i=1;i<d;i++)
            H.H[i][i+1]=1;
        ans=H.KSM(n-d);
        ll sum=0;
        for (int i=1;i<=d;i++)
            sum=(sum+(ans.H[i][1]%p*f[d-i+1]%p)%p)%p;  
        printf("%lld\n",sum%p);
        scanf("%d%lld%lld",&d,&n,&p); 
    }
}