Red Huang

Red Huang

uva 12470

矩阵 + 快速幂模

//====================================================================||  
//                                                                    ||  
//                                                                    ||  
//                         作者 : GCA                               ||  
//                  6AE7EE02212D47DAD26C32C0FE829006                  ||  
//====================================================================||  
#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <cmath>  
#include <climits>  
#include <vector>  
#include <set>  
#include <map>  
#include <queue>  
#include <cctype>  
#include <utility>  
using namespace std;  
#ifdef ONLINE\_JUDGE  
#define ll "%lld"  
#else  
#define ll "%I64d"  
#endif  
typedef unsigned int uint;  
typedef long long int Int;  
#define Set(a,s) memset(a,s,sizeof(a))  
#define Write(w) freopen(w,"w",stdout)  
#define Read(r) freopen(r,"r",stdin)  
#define Pln() printf("\\n")  
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()  
#define De(x)printf(#x"%d\\n",x)  
#define For(i,x)for(int i=0;i<x;i++)  
#define CON(x,y) x##y  
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\  
    printf("%d ",dp\[htx\]\[hty\]);}Pln();}  
#define M 55  
#define PII pair<int,int\>  
#define PB push\_back  
#define oo INT\_MAX  
#define Set\_oo 0x3f  
#define Is\_debug true  
#define debug(...) if(Is\_debug)printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)  
#define FOR(it,c) for(\_\_typeof((c).begin()) it=(c).begin();it!=(c).end();it++)  
#define eps 1e-6  
bool xdy(double x,double y){return x>y+eps;}  
bool xddy(double x,double y){return x>y-eps;}  
bool xcy(double x,double y){return x<y-eps;}  
bool xcdy(double x,double y){return x<y+eps;}  
int min3(int x,int y,int z){  
    int tmp=min(x,y);  
    return min(tmp,z);  
}  
int max3(int x,int y,int z){  
    int tmp=max(x,y);  
    return max(tmp,z);  
}  
Int n;  
Int mod=1000000009;  
struct m{  
    Int x\[3\]\[3\];  
    m(){  
        Set(x,0);  
    }  
}a;  
  
m mul(m a,m b){  
    m ans;  
    for(int i=0;i<3;i++){  
        for(int j=0;j<3;j++){  
            ans.x\[j\]\[i\]=(a.x\[0\]\[i\]\*b.x\[j\]\[0\])%mod;  
            ans.x\[j\]\[i\]=(ans.x\[j\]\[i\]+a.x\[1\]\[i\]\*b.x\[j\]\[1\])%mod;  
            ans.x\[j\]\[i\]=(ans.x\[j\]\[i\]+a.x\[2\]\[i\]\*b.x\[j\]\[2\])%mod;  
        }  
    }  
    return ans;  
}  
void pm(){  
    m ans;  
    for(int i=0;i<3;i++)  
        for(int j=0;j<3;j++)  
            if(i==j)ans.x\[i\]\[j\]=1;  
    while(n>0){  
        if(n&1)  
            ans=mul(ans,a);  
        a=mul(a,a);  
        n>>=1;  
    }  
    Int fans=(2\*ans.x\[0\]\[0\])%mod;  
    fans=(fans+ans.x\[1\]\[0\])%mod;  
    printf("%lld\\n",fans);  
}  
int main() {  
    ios\_base::sync\_with\_stdio(0);  
    while(~scanf("%lld",&n)&&n){  
  
        Set(a.x,0);  
        a.x\[0\]\[0\]=a.x\[1\]\[0\]=a.x\[2\]\[0\]=a.x\[0\]\[1\]=a.x\[1\]\[2\]=1;  
        if(n<=3){  
            printf("%lld\\n",n-1);  
        }else{  
            n-=3;  
            pm();  
        }  
    }  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
}  

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