- UVA12716
- UVA11582
UVA12716 GCD XOR
題解
參考
這題用到2個結論
a ^ b = c -----> a ^ c = b
a ^ b = gcd( a, b )----->a - b = gcd( a, b ),打表發現。。
設a - b = gcd( a, b ) = c, 枚舉c。然后判斷 a ^ c == a - c即可
代碼
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn = 30000000;
int cnt[ maxn + 10 ], sum[ maxn + 10 ];
int n, Cas, T;
void pre()
{
for( int i = 1; i <= maxn / 2; i ++ )
{
for( int j = i + i; j <= maxn; j += i )
{
if( ( j ^ i ) == j - i ) cnt[ j ] ++;
}
}
for( int i = 1; i <= maxn; i ++ ) sum[ i ] = sum[ i - 1 ] + cnt[ i ];
}
int main()
{
memset( cnt, 0, sizeof( cnt ) );
memset( sum, 0, sizeof( sum ) );
pre();
Cas = 0;
scanf( "%d", &T );
while( T -- )
{
scanf( "%d", &n );
printf( "Case %d: %d\n", ++Cas, sum[ n ] );
}
return 0;
}
