hdu 4990 Reading comprehension （矩阵快速幂）

Posted 2020-09-25 simpleknight

题意：读程序，找规律

思路：我们把程序输出发现序列为1,2,5,10,21,42,85,170,递推式f(n)=2*f(n-2)+f(n-1)+1

代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#define ll long long

using namespace std;

const int N=3,M=3,P=3;
ll mod;

struct Matrix
{
    ll m[N][N];
};

Matrix A={1,2,1,
          1,0,0,
          0,0,1};

Matrix I={1,0,0,
          0,1,0,
          0,0,1};

Matrix multi(Matrix a,Matrix b)
{
    Matrix ans;
    for(int i=0;i<N;i++)
    {
        for(int j=0;j<M;j++)
        {
            ans.m[i][j]=0;
            for(int k=0;k<P;k++)
            {
                ans.m[i][j]+=(a.m[i][k]*b.m[k][j])%mod;
            }
            ans.m[i][j]%=mod;
        }
    }
    return ans;
}

Matrix power(Matrix a,ll b)
{
    Matrix ans=I;
    while(b)
    {
        if(b&1)
        {
            ans=multi(ans,a);
        }
        b=b/2;
        a=multi(a,a);
    }
    return ans;
}

int main()
{
    ll n;
    while(cin>>n>>mod)
    {
        if(n==1)
        {
            cout<<(1)%mod<<endl;continue;
        }
        else if(n==2)
        {
            cout<<(2)%mod<<endl;
            continue;
        }
        Matrix ans=power(A,n-2);
        cout<<(ans.m[0][0]*2+ans.m[0][1]*1+ans.m[0][2])%mod<<endl;
    }
    return 0;
}