poj3358 Period of an Infinite Binary Expansion

The first step is to define the binary representation of the fraction:

1 // supposing the fraction is a/b, (a < b && (A, b)) 2 // Its binary expression is denoted as:0.bit[1]bit[2] ... 3 seed[0] = A;
4  for (int1;; i++) {5     1)/b; 6     Seed[i] = (Seed[i-1] << 1)% B;
7 }

You may wish to set one of the cycle sections to Bit[r]. Bit[s], apparently seed[r-1] = Seed[s] and bit[r] = bit[s + 1], where the cyclic section length L = (s-r + 1).

by seed[i] = 2i+1% B, then there is 2r% B = 2s+1% B, i.e. 2r (2s-r+1-1) ≡0 (MODB),

Note B = 2t*b1, where (b1,2), and r = T, then 2l≡1 (MODB1).

L|φ (B1), which enumerates the approximate b1 of a period L.

and has the initial position P = t + 1.

http://poj.org/problem?id=3358

1#include <cstdio>2#include <cstring>3#include <algorithm>4#include <cmath>5 using namespacestd;6 typedef __int64 LL;7 Const intMAXN = 1e2 +Ten;8 intPRIME[MAXN], K;9 intFAC[MAXN];Ten intA, B, b; One  A intPowerintAintp) { -A%=B; -     intAns =1; the      while(p) { -         if(P &1) ans = (LL) ans * a%B; -P >>=1; -A = (LL) A * a%B; +     } -     returnans; + } A  at intgcdintAintb) {return!b? A:GCD (b, a%b); } -  - voidsolve () { -A%=b; -     intD =gcd (A, b); -A/= D, b/=D; in     intt =0; -      while(b%2==0) b/=2, ++T; toprintf"%d,", ++t); +     if(b = =1) {printf ("%d\n",1);return; } -K =0; theB =b; *     intPhi =b; $     intMID = (int) sqrt (b);Panax Notoginseng      for(inti =3; I <= mid; i + =2){ -         if(b% i = =0){ theprime[k++] =i; +              while(b% i = =0) b/=i; A          } the     } +     if(b! =1) prime[k++] =b; -      for(inti =0; I < K; i++) Phi/=Prime[i]; $      for(inti =0; I < K; i++) Phi *= (Prime[i]-1); $K =0; -      for(inti =1; I * I <= phi; i++){ -         if(phi% i = =0) fac[k++] = i, fac[k++] = phi/i; the     } -Sort (FAC, FAC +k);Wuyi      for(inti =0; I < K; i++)if(Power (2, fac[i]) = =1){ theprintf"%d\n", Fac[i]); -          Break; Wu     } - } About  $ intMain () { -     //freopen ("In.txt", "R", stdin); -     intKase =0; -      while(~SCANF ("%d/%d", &a, &b)) { Aprintf"Case #%d:", ++Kase); + solve (); the     } -     return 0; $}

View Code

poj3358 Period of an Infinite Binary Expansion