HNOI2011 BZOJ2326 数学作业

传送门
看到这道题后应该很容易想到矩阵加速递推， 但是构造矩阵时发现有一个lg，不知道怎么办，就只好每翻十倍做一次，结果竟然是正解，汗(⊙﹏⊙)b。（但是我不知道第一页的那些0ms怎么跑的……）

/**************************************************************
    Problem: 2326
    User: geng4512
    Language: C++
    Result: Accepted
    Time:20 ms
    Memory:808 kb
****************************************************************/

#include<cstdio>
#include<cstring>
#define min(a,b) (a)<(b)?(a):(b)
typedef long long LL;
const int MAXN = 18;
LL mod, n, P[MAXN+10];
struct Mat
{
    LL a[3][3];
    void init(int x)
    {
        memset(a, 0, sizeof a);
        if(x == 1)
            a[0][0] = a[1][1] = a[2][2] = 1;
    }
    Mat operator * (const Mat &t)
    {
        Mat ans; ans.init(0);
        for(int k = 0; k < 3; k++)
            for(int i = 0; i < 3; i++)
                for(int j = 0; j < 3; j++)
                {
                    ans.a[i][j] += a[i][k] * t.a[k][j] % mod;
                    ans.a[i][j] %= mod;
                }
        return ans;
    }
};
Mat ksm(Mat a, LL k)
{
    Mat ans;
    ans.init(1);
    while(k)
    {
        if(k & 1) ans = ans * a;
        a = a * a;
        k >>= 1;
    }
    return ans;
}
Mat solve(LL x, LL k)
{
    Mat a;
    a.init(0);
    a.a[0][0] = k; a.a[1][0] = a.a[1][1] = a.a[2][0] = a.a[2][1] = a.a[2][2] = 1;
    return ksm(a, x);
}
int main()
{
    scanf("%lld%lld", &n, & mod);
    P[0] = 1;
    for(int i = 1; i <= 18; i++)
        P[i] = P[i-1] * 10;
    Mat a;
    a.init(1);
    for(int i = 1; ; i++)
    {
        LL L = P[i-1], R = min(P[i]-1, n);
        a = a * solve(R - L + 1, P[i] % mod);
        if(R == n) break;
    }
    printf("%lld", a.a[2][0]);
}