"Matrix fast Power" codeforces 450b-jzzhu and sequences (formula conversion)

"topic link"Click here~~

"The main topic"

Jzzhu have invented a kind of sequences, they meet the following property:

You is given x and y, please calculate f_n modulo1000000007 (Ten^9?+?7).

"problem-solving ideas"

/*a-jzzhu and sequencescodeforces 450b-jzzhu and sequences (Matrix fast power)given F1 and F2, ask for FNAnalysis:Special Award F1,f2when n>=3 is used, the matrix is quickly idempotent .convert the formula to get a transformation matrixby F (i) =f (i-1) +f (i+1);move the left-hand side to the right.f (i+i) =f (i)-f (i-1);the subscript is also reduced by onef (i) =f (i-1)-F (i-2);thus constructing the matrix(f (i-1), F (i-2)) *[1-1]= (f (i), F (i-1) )[1 0]brought into the i=3to be(f (2) =y,f (1) =x) *[1-1]^ (i-2) = (f (3), F (2))[1 0]The code is as follows * /

#include <stdio.h> #include <string.h> #include <iostream> #include <algorithm> #include < Math.h>using namespace Std;const long long mod=1e9+7; #define LL long longstruct matrlc{long Long 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;        C.mapp[i][j]%=mod; } return C;}    void Pow1 (LL n) {base.mapp[0][0] = 1;    BASE.MAPP[0][1] =-1;    Base.mapp[1][0] = 1;    BASE.MAPP[1][1] = 0;    Ans.mapp[0][0] = ans.mapp[1][1] = 1;//ans initialized to the unit matrix ans.mapp[0][1] = ans.mapp[1][0] = 0;        while (n) {if (n&1) Ans=mult (ans,base);        Base=mult (base,base);    n>>=1;    }}int Main () {LL x,y,n,i,j;    scanf ("%lld%lld%lld", &x,&y,&n); if (n==1) printf ("%lld\n", (x%mod+mod)%mod);    else if (n==2) printf ("%lld\n", (y%mod+mod)%mod);        else {pow1 (N-2);        LL result= (((ans.mapp[0][0]*y+ans.mapp[0][1]*x)%mod) +mod)%mod;    printf ("%lld\n", result); } return 0;}

"Matrix fast Power" codeforces 450b-jzzhu and sequences (formula conversion)