Chinese Rings hdu 2842 矩阵快速幂

Chinese Rings

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 623    Accepted Submission(s): 370

Problem Description

Dumbear likes to play the Chinese Rings (Baguenaudier). It’s a game played with nine rings on a bar. The rules of this game are very simple: At first, the nine rings are all on the bar.
The first ring can be taken off or taken on with one step.
If the first k rings are all off and the (k + 1)th ring is on, then the (k + 2)th ring can be taken off or taken on with one step. (0 ≤ k ≤ 7)

Now consider a game with N (N ≤ 1,000,000,000) rings on a bar, Dumbear wants to make all the rings off the bar with least steps. But Dumbear is very dumb, so he wants you to help him.

 

Input

Each line of the input file contains a number N indicates the number of the rings on the bar. The last line of the input file contains a number "0".

 

Output

For each line, output an integer S indicates the least steps. For the integers may be very large, output S mod 200907.

 

Sample Input

1

4

0

 

Sample Output

1

10

 

 

#include <iostream>
#include <stdio.h>
#include <algorithm>
#include <math.h>
#include <string.h>
#include <set>
#include <queue>
using namespace std;
#define ll long long
typedef struct matrix
{
    ll a[5][5];
} matrix;
matrix origin,res;
matrix multiply(matrix x,matrix y)
{
    matrix temp;
    memset(temp.a,0,sizeof(temp.a));
    for(int k=0; k<3; k++)
        for(int i=0; i<3; i++)
        if(x.a[i][k])
            for(int j=0; j<3; j++)
            {
                temp.a[i][j]+=x.a[i][k]*y.a[k][j]%200907;
                temp.a[i][j]%=200907;
            }
    return temp;
}
void calc(int n)
{
    memset(res.a,0,sizeof(res.a));
    for(int i=0; i<3; i++)res.a[i][i]=1;
    while(n)
    {
        if(n&1)res=multiply(res,origin);
        n>>=1;
        origin=multiply(origin,origin);
    }
}
void init()
{
    memset(origin.a,0,sizeof(origin.a));
    origin.a[0][0]=origin.a[0][2]=origin.a[1][0]=origin.a[2][2]=1;
    origin.a[0][1]=2;
}
int main()
{
    int n;
    while(scanf("%d",&n),n)
    {
        if(n<=2)
        {
            printf("%d
",n);
            continue;
        }
        init();
        calc(n-2);
        int ans=0;
        ans=res.a[0][0]*2%200907+res.a[0][1]%200907+res.a[0][2]%200907;
        printf("%d
",ans%200907);
    }
}