【HDU 5015】233 Matrix

【题目链接】

http://acm.hdu.edu.cn/showproblem.php?pid=5015

【算法】

矩阵乘法

【代码】

#include<bits/stdc++.h>
using namespace std;
const int P = ;

int i,j,n,m,ans;
int a[],val[];

struct Matrix
{
        int mat[][];
} b;

inline void multipy(Matrix &a,Matrix b)
{
        int i,j,k;
        Matrix res;
        memset(res.mat,,sizeof(res.mat));
        for (i = ; i <= n + ; i++)
        {
                for (j = ; j <= n + ; j++)
                {
                        for (k = ; k <= n + ; k++)
                        {
                                res.mat[i][j] = (res.mat[i][j] + 1ll * a.mat[i][k] * b.mat[k][j]) % P;
                        }
                }
        }
        a = res;
}
inline Matrix power(Matrix a,int n)
{
        Matrix res;
        memcpy(res.mat,a.mat,sizeof(a.mat));
        n--;
        while (n > )
        {
                if (n & ) multipy(res,a);
                multipy(a,a);
                n >>= ;
        }
        return res;
}

int main()
{

        while (scanf("%d%d",&n,&m) != EOF)
        {
                ans = ;
                a[] = ;
                for (i = ; i <= n; i++) scanf("%d",&a[i]);
                val[] = ;
                for (i = ; i <= n; i++) val[i] = (val[i-] % P + a[i] % P) % P;
                val[n+] = ;
                if (m == )
                {
                        printf("%d\n",val[n]);
                        continue;
                }
                memset(b.mat,,sizeof(b.mat));
                for (i = ; i <= n; i++)
                {
                        b.mat[i][] = ;
                        b.mat[i][n+] = ;
                        for (j = ; j <= n; j++)
                        {
                                b.mat[i][j] = (i >= j);
                        }
                }
                b.mat[n+][n+] = ;
                b = power(b,m-);
                for (i = ; i <= n + ; i++) ans = (ans + 1ll * b.mat[n][i] * val[i]) % P;
                printf("%d\n",ans);

        }

        return ;

}