Topic 1081: Recursive sequence (Matrix fast-power-recursive)

Topic 1081: Recursive sequence

time limit:1 seconds

Memory limit:32 MB

Special question: No

submitted:5885

Resolution:800

Title Description:

Given A0,A1, and n-2 in An=p*a (n-1) + q*a (p,q). Here n >= 2. The modulus of the number of K to 10000 is obtained.

Input:

The input consists of 5 integers: A0, A1, P, Q, K.

Output:

The number of k a (k) to 10000 modulo.

Sample input:

20 1 1) 14 5

Sample output:

8359

Source:

2009, Tsinghua University computer Research Life Test real problem

1#include <stdio.h>2#include <cstring>3#include <iostream>4#include <algorithm>5#include <cstdlib>6#include <cmath>7#include <vector>8#include <queue>9#include <map>Ten#include <Set> One  A using namespacestd; -  -typedefLong Longll; the  - Constll mod =10000; -  -  + structMatrix - { +ll mat[2][2]; A Matrix () at     { -Memset (Mat,0,sizeof(MAT)); -     } -Matrixoperator*(ConstMatrix A)Const -     { - Matrix ret; in          for(intI=0;i<2; i++) -         { to              for(intj=0;j<2; j + +) +             { -                  for(intk=0;k<2; k++) theRET.MAT[I][J] = (ret.mat[i][j]+ (mat[i][k]*a.mat[k][j])%mod)%MoD; *             } $         }Panax Notoginseng         returnret; -     } the }; +  AMatrix Quickmul (Matrix X,intk) the { + Matrix ret; -      for(intI=0;i<2; i++) $Ret.mat[i][i] =1; $      while(k>0) -     { -         if(k&1) ret=ret*x; thek>>=1; -x=x*x;Wuyi     } the     returnret; - } Wu  - intMain () About { $ ll A0,a1,p,q,k; -      while(~SCANF ("%lld%lld%lld%lld%lld",&a0,&a1,&p,&q,&k)) -     { - Matrix St; Ast.mat[0][0] = p,st.mat[0][1] =Q; +st.mat[1][0] =1, st.mat[1][1] =0; theMatrix A =Quickmul (st,k); - Matrix B; $b.mat[0][0] =A1; theb.mat[1][0] =A0; theA = A *b; theprintf"%lld\n", a.mat[1][0]%MoD); the     } -     return 0; in}

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Topic 1081: Recursive sequence (Matrix fast-power-recursive)