Sha 1069 always an integer (Mathematics)

 

Sha 1069 always an integer (Mathematics)

 

 

#include <cstdio>#include <cstring>#include <algorithm>#include <cctype>using namespace std;typedef long long LL;#define MAXN 105#define CLR( a, b ) memset( a, b, sizeof(a) )LL c[ MAXN ], d;char str[ MAXN * MAXN ];void init(){    CLR( c, 0 );    LL k, a, key, sign = 1;    d = k = a = key = 0;    int len = strlen( str );    for( int i = 0; i <= len; ++i )    {        if( isdigit( str[i] ) )        {            if( key == 0 )        a = a * 10 + str[i] - ‘0‘;            else if( key == 1 ) k = k * 10 + str[i] - ‘0‘;            else if( key == 2 ) d = d * 10 + str[i] - ‘0‘;        }        else if( str[i] == ‘/‘ )    key = 2;        else if( str[i] == ‘n‘ )    key = 1;        else if( str[i] == ‘-‘ || str[i] == ‘+‘ || str[i] == ‘)‘ )        {            if( key >= 1 )            {                if( k == 0 )    k = 1;                if( a == 0 )    a = 1;            }            c[k] = a * sign;            if( str[i] == ‘-‘ )    sign = -1;            else sign = 1;                        key = a = k = 0;        }    }}LL fast_mod( LL a, int b, LL MOD ){    LL ans = 1;    while( b )    {        if( b & 1 )    ans = ans * a % MOD;        a = a * a % MOD;        b >>= 1;    }    return ans;}bool judge(){    int n = MAXN - 1;    while( c[n] == 0 ) n--;    for( LL i = 1; i <= n + 1; ++i )    {        LL ans = 0;        for( int j = 0; j <= n; ++j )        {            if( c[j] )                ans = ( ans + c[j] * fast_mod( i, j, d ) ) % d;            ans = ( ans + d ) % d;        }        if( ans )            return false;    }    return true;}int main(){    int cas = 1;    while(     ~scanf( "%s", str) && strcmp( ".", str ) != 0 )    {        init();        printf( "Case %d: %s\n", cas++, judge() ? "Always an integer" : "Not always an integer" );    }    return 0;            }

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Sha 1069 always an integer (Mathematics)