hdu 4291 矩阵幂循环节

来源：互联网发布：淘宝刷单兼职 360 编辑：程序博客网时间：2024/06/03 18:05

http://acm.hdu.edu.cn/showproblem.php?pid=4291

凡是取模的都有循环节-----常数有，矩阵也有，而且矩阵的更神奇：
g(g(g(n))) mod 10⁹ + 7 最外层MOD=1e9+7 可以算出g(g(n))的循环节222222224，进而算出g(n)的循环节183120LL，然后由内而外计算即可

注释掉的是求循环节的代码

//#pragma comment(linker, "/STACK:102400000,102400000")#include <cstdio>#include <cstring>#include <algorithm>#include <string>#include <iostream>#include <iomanip>#include <cmath>#include <map>#include <set>#include <queue>using namespace std;#define ls(rt) rt*2#define rs(rt) rt*2+1#define ll long long#define ull unsigned long long#define rep(i,s,e) for(int i=s;i<e;i++)#define repe(i,s,e) for(int i=s;i<=e;i++)#define CL(a,b) memset(a,b,sizeof(a))#define IN(s) freopen(s,"r",stdin)#define OUT(s) freopen(s,"w",stdout)const ll ll_INF = ((ull)(-1))>>1;const double EPS = 1e-8;const double pi = acos(-1.0);const int INF = 100000000;const ll MOD[3] = {183120LL,222222224LL,1000000007LL};const int N = 2;struct Matrix{    ll m[N][N];    //int sz;//矩阵的大小};Matrix I= {3LL,1LL,//要幂乘的矩阵           1LL,0LL,          };Matrix unin={1LL,0LL,//单位矩阵             0LL,1LL,            };Matrix matrixmul(Matrix a,Matrix b,long long  mod)//矩阵a乘矩阵b{    Matrix c;    for(int i=0; i<N; i++)        for(int j=0; j<N; j++)        {            c.m[i][j]=0LL;            for(int k=0; k<N; k++)                c.m[i][j]+=(a.m[i][k]*b.m[k][j])%mod;            c.m[i][j]%=mod;        }    return c;}Matrix quickpow(long long n,long long  mod){    Matrix m=I,b=unin;//求矩阵I的n阶矩阵    while(n>=1)    {        if(n&1)            b=matrixmul(b,m,mod);        n=n>>1;        m=matrixmul(m,m,mod);    }    return b;}ll solve(ll n){    ll ans;    Matrix ret;    ret.m[0][0]=n;    for(int i=0;i<3;i++)    {        if(ret.m[0][0]!=0 && ret.m[0][0]!=1)ret=quickpow(ret.m[0][0]-1,MOD[i]);    }    return ret.m[0][0];}int main(){    //precal();    ll n;    while(~scanf("%I64d",&n))    {        if(n==0){puts("0");continue;}        if(n==1){puts("1");continue;}        //printf("%I64d\n",solve(n));        cout << solve(n)%1000000007LL << endl;    }    return 0;}

hdu 4291 矩阵幂循环节

0 0

hdu 4291 矩阵幂 循环节

hdu 4291 矩阵幂循环节