[HNOI2011][BZOJ2326] 数学作业|动态规划|矩阵乘法|快速乘

2326: [HNOI2011]数学作业

Time Limit: 10 Sec  Memory Limit: 128 MB
Submit: 1388  Solved: 799
[Submit][Status][Discuss]

Description

Input

 

Output

 

Sample Input

 

Sample Output

 

HINT

 

Source

矩阵乘法

 

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#define ll long long
using namespace std;
ll n,m,a[4][4],b[4][4];
ll mu(ll x,ll y)
{
    ll s=0;
    while (y)
    {
        if (y&1) s=(s+x)%m;
        x=(x<<1)%m;
        y>>=1;
    }
    return s;
}
void mul(ll a[4][4],ll b[4][4],ll ans[4][4])
{
    ll t[4][4];
    for (int i=1;i<=3;i++)
        for (int j=1;j<=3;j++)
        {
            t[i][j]=0;
            for (int k=1;k<=3;k++)
                t[i][j]=(t[i][j]+mu(a[i][k],b[k][j]))%m;
        }
    for (int i=1;i<=3;i++)
        for (int j=1;j<=3;j++)
            ans[i][j]=t[i][j];
}
void cal(ll t,ll last)
{
    memset(b,0,sizeof(b));
    b[1][1]=t;
    b[2][1]=b[2][2]=b[3][1]=b[3][2]=b[3][3]=1;
    ll y=last-t/10+1;
    while (y)
    {
        if (y&1) mul(a,b,a);
        mul(b,b,b);
        y>>=1;
    }
}
int main()
{
    scanf("%lld%lld",&n,&m);
    for (int i=1;i<=3;i++) a[i][i]=1;
    ll t=10;
    while (n>=t)
    {
        cal(t,t-1);
        t*=10;
    }
    cal(t,n);
    printf("%lld",a[3][1]);
    return 0;
}