1. 程式人生 > >hdu 5950 Recursive sequence(矩陣快速冪,構造)

hdu 5950 Recursive sequence(矩陣快速冪,構造)

N較大,直接遞推會超時,可以用矩陣快速冪

也是的函式,且

所以在構造的矩陣中維護

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>

using namespace std;

#define FOR(i,k,n) for(int i=k;i<n;i++)
#define FORR(i,k,n) for(int i=k;i<=n;i++)
#define scan(a) scanf("%d",&a)
#define scann(a,b) scanf("%d%d",&a,&b)
#define scannn(a,b,c) scanf("%d%d%d",&a,&b,&c)
#define mst(a,n)  memset(a,n,sizeof(a))
#define ll long long
#define N 20
#define Mod 2147493647
#define INF 0x3f3f3f3f

const double eps=1e-8;
const double pi=acos(-1.0);



struct Matrix
{
    ll val[N][N];
    int row, col;

    Matrix(){}

    Matrix(int row, int col) : row(row), col(col)
    {
        zero();
    }

    void zero()
    {
        memset(val, 0, sizeof(val));
    }

    void unit()
    {
        zero();
        row = col = max(row, col);
        for (int i = 0; i < row; ++i)
        {
            val[i][i] = 1;
        }
    }

    Matrix operator*(const Matrix &m)
    {
        Matrix ret(this->row, m.col);

        for (int i = 0; i < this->row; ++i)
        {
            for (int k = 0; k < this->col; ++k)
            {
                if (this->val[i][k]) // 應付稀疏矩陣
                {
                    for (int j = 0; j < m.col; ++j)
                    {
                        ret.val[i][j] += (this->val[i][k] * m.val[k][j]) % Mod;
                        ret.val[i][j] %= Mod;
                    }
                }
            }
        }

        return ret;
    }

    Matrix operator^(const ll k)
    {
        Matrix ret((*this).col, (*this).col);
        ret.unit();
//        for (int i = 0; i < (*this).col; ++i)
//        {
//            ret.val[i][i] = 1;
//        }

        Matrix base = (*this);

        for (ll e = k; e; e >>= 1)
        {
            if (e & 1)
            {
                ret = ret * base;
            }
            base = base * base;
        }

        return ret;
    }

    void resize(int row, int col)
    {
        this->row = row;
        this->col = col;
    }

};


int main()
{
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);

    int t;
    scan(t);
    while(t--)
    {
        int n,a,b;
        scan(n);
        scann(a,b);
        a%=Mod; b%=Mod;
        if(n==1)
        {
            cout<<a<<endl;
            continue;
        }
        if(n==2)
        {
            cout<<b<<endl;
            continue;
        }
        Matrix m(7,7);
        m.val[0][0]=1; m.val[0][1]=2; m.val[0][2]=1;
        m.val[1][0]=1;
        m.val[2][2]=1; m.val[2][3]=4; m.val[2][4]=6; m.val[2][5]=4; m.val[2][6]=1;
        m.val[3][3]=1; m.val[3][4]=3; m.val[3][5]=3; m.val[3][6]=1;
        m.val[4][4]=1; m.val[4][5]=2; m.val[4][6]=1;
        m.val[5][5]=1; m.val[5][6]=1;
        m.val[6][6]=1;
        m=m^(n-2);
        Matrix x(7,1);
        x.val[0][0]=b; x.val[1][0]=a; x.val[2][0]=81; x.val[3][0]=27; x.val[4][0]=9; x.val[5][0]=3; x.val[6][0]=1;
        x=m*x;
        cout<<x.val[0][0]<<endl;
    }
    return 0;
}