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hdoj4990Reading comprehension【矩阵快速幂】

2015-11-11 21:01 435 查看

Reading comprehension

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 1128    Accepted Submission(s): 444


Problem Description

Read the program below carefully then answer the question.

#pragma comment(linker, "/STACK:1024000000,1024000000")

#include <cstdio>

#include<iostream>

#include <cstring>

#include <cmath>

#include <algorithm>

#include<vector>

const int MAX=100000*2;

const int INF=1e9;

int main()

{

  int n,m,ans,i;

  while(scanf("%d%d",&n,&m)!=EOF)

  {

    ans=0;

    for(i=1;i<=n;i++)

    {

      if(i&1)ans=(ans*2+1)%m;

      else ans=ans*2%m;

    }

    printf("%d\n",ans);

  }

  return 0;

}
 

Input

Multi test cases，each line will contain two integers n and m. Process to end of file.
[Technical Specification]

1<=n, m <= 1000000000
 

Output

For each case，output an integer，represents the output of above program.
 

Sample Input

1 10
3 100

 

Sample Output

1
5

 

Source

BestCoder Round #8
 

递推公式 f
=f[n-1]+2*f[n-2]+1;

初始矩阵 1     1     0

                 2    0     0

                1    0     1

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
long long a[3][3];
long long ans[3][3];
long long N,M;
void Mulit(long long A[3][3],long long B[3][3]){
long long D[3][3]={0};
for(int i=0;i<3;++i){
for(int k=0;k<3;++k){
if(A[i][k]){
for(int j=0;j<3;++j){
D[i][j]=(D[i][j]+A[i][k]*B[k][j])%M;
}
}
}
}
for(int i=0;i<3;++i){
for(int j=0;j<3;++j){
A[i][j]=D[i][j];
}
}
}
void Martix(long long A[3][3]){
for(int i=0;i<3;++i){
for(int j=0;j<3;++j){
ans[i][j]=(i==j);
}
}
while(N){
if(N&1)Mulit(ans,A);
Mulit(A,A);
N>>=1;
}
}
int main()
{
int num[3]={1,1,2},i,j;
while(scanf("%lld%lld",&N,&M)!=EOF){
if(N<=2){
printf("%d\n",num
%M);
continue;
}
a[0][0]=1;a[0][1]=1;a[0][2]=0;
a[1][0]=2;a[1][1]=0;a[1][2]=0;
a[2][0]=1;a[2][1]=0;a[2][2]=1;
N-=2;
Martix(a);
printf("%lld\n",(2*ans[0][0]+ans[1][0]+ans[2][0])%M);
}
return 0;
}

                                            

                                        

                        
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                         标签： 
                                                hdoj4990Reading
                                                comp
                                                

                        

                    


                

            


            

                
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