UVA 10870 Recurrences

矩阵快速幂。

矩阵很容易构造：

#include<cstdio>
#include<cstring>
#include<cmath>
#include<vector>
#include<algorithm>
using namespace std;

int d,n;
long long m;
long  long F[20],D[20];

struct Matrix
{
    long long A[20][20];
    int R, C;
    Matrix operator*(Matrix b);
};

Matrix X, Y, Z;

Matrix Matrix::operator*(Matrix b)
{
    Matrix c;
    memset(c.A, 0, sizeof(c.A));
    int i, j, k;
    for (i = 1; i <= R; i++)
        for (j = 1; j <= C; j++)
            for (k = 1; k <= C; k++)
                c.A[i][j] = (c.A[i][j] + (A[i][k] * b.A[k][j])%m)%m;
    c.R=R; c.C=b.C;
    return c;
}

void init()
{
    n = n - 1;
    memset(X.A,0,sizeof X.A);
    memset(Y.A,0,sizeof Y.A);
    memset(Z.A,0,sizeof Z.A);

    for(int j=1;j<=d;j++) Z.A[1][j]=F[j]; Z.R = 1; Z.C = d;

    for(int i=1;i<=d;i++) Y.A[i][i]=1; Y.R = d; Y.C = d;

    for(int j=1;j<=d-1;j++) X.A[j+1][j]=1;
    for(int i=1;i<=d;i++) X.A[i][d]=D[d-i+1];
     X.R = d; X.C = d;
}

void work()
{
    while (n)
    {
        if (n % 2 == 1) Y = Y*X;
        n = n >> 1;
        X = X*X;
    }
    Z = Z*Y;

    printf("%lld\n", Z.A[1][1]);
}

void read()
{
    for(int i=1;i<=d;i++) scanf("%lld",&D[i]);
    for(int i=1;i<=d;i++) scanf("%lld",&F[i]);
}

int main()
{
    while(~scanf("%d%d%lld",&d,&n,&m))
    {
        if(d==0&&n==0&&m==0) break;
        read();
        init();
        work();
    }
    return 0;
}