POJ 3641 Prime number playing table + fast power simple problem

Give 2 numbers, p and a,2<p<=1e9,1<a<p

If p satisfies the following 2 conditions, the output is yes, otherwise the output no

1.P is not a prime number

2. A^p=a (mod p)

First condition is judged first:

Originally wanted to use an array is_prime[i] means I is not prime, obviously, here p is too large, the array cannot be opened

If P is not a prime number,

Then P must have p=b*c, of which b<=c,

(sqrt (p)) ^2=b*c, then B<=sqrt (p) <=10^4.5<10^5

So if there is a number B in 10^5 to satisfy b<p&&p%b==0, p is not prime

Further, as long as the validation 10^5 existence prime B1 satisfies b1<p&&p%b1==0, stating that P is not a prime number, that is, satisfies the first condition

So as long as all the prime numbers inside the 10^5 are found, placed in the array prime, for p, traversing one side can, note: Prime[i]>=p, to break

If the first condition is satisfied, the second condition is validated, and a fast power can be done.

1#include <cstdio>2#include <cstring>3#include <cmath>4 5 using namespacestd;6 7 #defineLL Long Long8 9 Const intmaxn=1e5;Ten BOOLIS_PRIME[MAXN]; One intPrime[maxn>>1]; A  - intinit_prime () - { the     inti; -     inttot=1; -     intE= (int) (sqrt (0.0+MAXN) +1); -memset (Is_prime,true,sizeofis_prime); +is_prime[1]=false; -is_prime[2]=true; +prime[tot++]=2; A      for(i=4; i<maxn;i+=2) atis_prime[i]=false; -      for(i=3; i<e;i+=2) -     { -         if(Is_prime[i]) -         { -prime[tot++]=i; in             ints; -              for(intj=i*i,s=2*i;j<maxn;j+=s) tois_prime[j]=false; +         } -     } the      for(; i<maxn;i+=2) *     { $         if(Is_prime[i])Panax Notoginsengprime[tot++]=i; -     } the     returntot; + } A  the ll Quick_pow (ll A,ll p) + { -LL mod=p; $LL ret=1; $      while(p>0) -     { -         if(p&1) theret=ret*a%MoD; -a=a*a%MoD;Wuyip>>=1; the     } -     returnret; Wu } -  About voidSolveinttot,ll p,ll a) $ { -     BOOLflag=false; -      for(intI=1; i<tot;i++) -     { A         if(prime[i]>=p) +              Break; the         if(p%prime[i]==0) -         { $flag=true; the              Break; the         } the     } the     if(!flag) -     { inprintf"no\n"); the         return ; the     } AboutLL ret=Quick_pow (a,p); the     if(ret%p==a%p) the     { theprintf"yes\n"); +     } -     Else the     {Bayiprintf"no\n"); the     } the     return ; - } -  the intMain () the { the LL p,a; the     inttot=init_prime (); -      while(SCANF ("%lld%lld",&p,&a)) the     { the         if(!p&&!a) the              Break;94 solve (tot,p,a); the     } the     return 0; the}

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POJ 3641 Prime number playing table + fast power simple problem