HDU_3609 Up-up

http://acm.hdu.edu.cn/showproblem.php?pid=3609

題意：

定義：a↑↑1 = a , a↑↑(k+1) = a ^(a↑↑k)  

^{求 a↑↑k mod 100000000 .}

^思路：

^{A^x = A^( x % phi(C) + phi(C) ) ( mod C )  , x>= phi(C)  ;}

^代碼：

 

#include <stdio.h>
#include <string.h>

typedef __int64 LL ;
const LL Mod = 100000000 ;
const LL PP = 10002 ;
LL a, k ;
LL prime[1225] , cnt ;
bool is_p[PP] ;
LL phi[30] , pnum ;

LL get_phi(LL n){
    LL res = n ;
    for( int i=0;i<cnt && prime[i]*prime[i]<=n ; i++){
        if( n % prime[i] == 0 ){
            res = res / prime[i] * (prime[i] - 1)  ;
            while( n%prime[i] == 0) n /= prime[i] ;
        }
    }
    if( n > 1 ) res = res / n * (n - 1) ;
    return res ;
}

void calc(){
    for(int i=1;i<PP;i++)   is_p[i] = 1 ;
    cnt = 0 ;
    for(LL i=2;i<PP;i++){
        if( is_p[i] ){
            prime[ cnt++ ] = i ;
            for( LL j=2;i*j<PP;j++)
                is_p[i*j] = 0 ;
        }
    }
    pnum = 0 ;
    LL now = Mod , pre = Mod ;
    phi[0] = now ; pnum ++ ;
    while( true ){
        phi[ pnum ] = get_phi( now ) ;
        if( phi[pnum] == now )  break;
        pre = now ;
        now = phi[ pnum++ ] ;
    }
}

LL pow( LL a, LL b , LL n){
    LL res = 1 , add = a % n ;
    while( b ){
        if( b&1 )   res = res * add % n  ;
        add = add * add % n ;
        b >>= 1;
    }
    return res ;
}

int large(LL a , LL b , LL p ){
    LL res = a ;
    for(int i=0;i<b && res<p ; i++ )
        res = res * a ;
    return res >= p ;
}
/*
make函數的作用是求 a↑↑k % p
如果 a↑↑k >= p ,返回  ( a↑↑k ) % p + p ;
如果 a↑↑k < p  ,返回  ( a↑↑k ) % p ;
*/
LL make(LL a ,LL k ,LL num){ //a||k % p
    if( num == pnum ) num -- ;
    LL p = phi[num]  ;
    if( k==1 ){
        if( a < p ) return a ;
        else{
            a %= p ; return a + p ;
        }
    }
    LL bk = make( a , k-1 , num + 1 )  ;
    LL ans = pow( a , bk ,  p ) ;
    ans += large( a , bk , p )* p ;
    return ans ;
}
int main(){
    calc() ;
    while( scanf("%I64d %I64d",&a,&k) == 2){
        printf("%I64d\n", make(a, k ,0)%phi[0] ) ;
    }
    return 0 ;
}