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

2326: [HNOI2011]数学作业

Description

Input

Output

Sample Input

Sample Output

HINT

Source

#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;
}