"Matrix multiplication + fast multiplication" bzoj2875-[noi2012] random number generator

"The main topic"

Knownx + = (a xn +c) mod m, ask Xn mod g.

Ideas

Get to the correct method of longlong multiplication, fast multiply. What is a fast ride?

Simply put, the fast power is the vertical multiplication that simulates the binary. Such as:

10101x1011 = 10101*1+10101*2^1*1+10101*2^2*0+10101*2^3*1

The code is as follows:

Long LongMultiLong LongALong LongBLong Longm) {Long Longans=0;  while(b) {if(b&1) (Ans+=a)%=m; (A=a*2) %=m; b/=2; }    returnans;}

The next method of the subject is the fast power of matrix multiplication.

(A 0

C 1) squared n times

Notice in the function also don't forget to open longlong. At first, the N in my function was written as a int,wa.

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <algorithm>5 using namespacestd;6typedefLong Longll;7ll matrix[2][2],ans_matrix[2][2];8 ll m,n,a,c,g,x0;9 Ten ll KSC (ll A,ll b) One { All ans=0;  -      while(b) -     { the         if(b&1) ans= (ans+a)%m; -A= (a<<1)%m; -b>>=1; -     } +     returnans; - } +  A voidKSM (ll N) at { -ans_matrix[0][0]=ans_matrix[1][1]=1; -ans_matrix[0][1]=ans_matrix[1][0]=0; -      while(n) -     { -         if(n&1) in         { -ans_matrix[0][0]=KSC (ans_matrix[0][0],matrix[0][0]); toans_matrix[1][0]= (KSC (ans_matrix[1][0],matrix[0][0]) +matrix[1][0])%m; +         } -n>>=1; thell TMP1=KSC (matrix[0][0],matrix[0][0]); *ll tmp2= (KSC (matrix[1][0],matrix[0][0]) +matrix[1][0])%m; $matrix[0][0]=tmp1,matrix[1][0]=TMP2;Panax Notoginseng     } - } the  + voidInit () A { thescanf"%lld%lld%lld%lld%lld%lld",&m,&a,&c,&x0,&n,&g);  +matrix[0][0]=a%m,matrix[0][1]=0, matrix[1][0]=c%m,matrix[1][1]=1; - } $  $ voidGet_ans () - { -ll ans= (KSC (ans_matrix[0][0],x0) +ans_matrix[1][0])%m; theans%=G; -printf"%lld", ans);Wuyi } the  - intMain () Wu { -     //freopen ("randoma.in", "R", stdin); About     //freopen ("Randoma.out", "w", stdout); $ init (); - KSM (n); - Get_ans (); -     return 0; A}

"Matrix multiplication + fast multiplication" bzoj2875-[noi2012] random number generator