【矩阵快速幂】UVA 10698 G - Yet another Number Sequence

【题目链接】click here~~

【题目大意】

Let's define another number sequence, given by the following function:

f(0) = a 

f(1) = b 

f(n) = f(n-1) + f(n-2), n > 1

When a = 0 and b = 1, this sequence gives the Fibonacci Sequence. Changing the values ofa and b , you can get many different sequences. Given the values ofa, b, you have to find the last m digits of f(n) .

Input

The first line gives the number of test cases, which is less than 10001. Each test case consists of a single line containing the integersa b n m. The values of a and b range in[0,100], value of n ranges in [0, 1000000000] and value ofm ranges in [1, 4].

Input

The first line gives the number of test cases, which is less than 10001. Each test case consists of a single line containing the integersa b n m. The values of a and b range in[0,100], value of n ranges in [0, 1000000000] and value ofm ranges in [1, 4].

Output

For each test case, print the last m digits of f(n). However, you shouldNOT print any leading zero.

4 0 1 11 3 0 1 42 4 0 1 22 4 0 1 21 4

89 4296 7711 946

【解题思路】

类似于fibonacci数列的求法，值得注意的是题目并不是让求简单的F（n）,而是求f(n)%f(m),由题目可知，

m ranges in [1, 4].于是定义一个mod数组 const int mod[5]= {0,10,100,1000,10000};每次取模即可

代码

#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <math.h>
using namespace std;
const int mod[5]= {0,10,100,1000,10000};
const int MOD =1e9+7;
#define LL long long
LL X,Y,N,M,i,j;
struct Matrlc
{
    int  mapp[2][2];
} ans,base;
Matrlc unit= {1,0,0,1};
Matrlc mult(Matrlc a,Matrlc b)
{
    Matrlc c;
    for(int i=0; i<2; i++)
        for(int j=0; j<2; j++)
        {
            c.mapp[i][j]=0;
            for(int k=0; k<2; k++)
                c.mapp[i][j]+=(a.mapp[i][k]*b.mapp[k][j])%mod[M];
            c.mapp[i][j]%=mod[M];
        }
    return c;
}
void  pow1(int  n)
{
    base.mapp[0][0] =base.mapp[0][1]=base.mapp[1][0]=1;
    base.mapp[1][1]=0;
    ans.mapp[0][0] = ans.mapp[1][1] = 1;// ans 初始化为单位矩阵
    ans.mapp[0][1] = ans.mapp[1][0] = 0;
    while(n)
    {
        if(n&1)   ans=mult(ans,base);
        base=mult(base,base);
        n>>=1;
    }
   // return ans.mapp[0][1];
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lld%lld%lld%lld",&X,&Y,&N,&M);
        if(N==0) return X;
        else if(N==1) return Y;
        else
        {
            pow1(N-1);
            LL  result=(ans.mapp[0][0]*Y+ans.mapp[0][1]*X)%mod[M];
                  printf("%lld\n",result);
        }
    }
    return 0;
}