GCD XOR UVA - 12716 ——筛法建立约数表+xor运算+数学规律

1. a ⊕ a = 0
2. a ⊕ b = b ⊕ a
3. a ⊕b ⊕ c = a ⊕ (b ⊕ c) = (a ⊕ b) ⊕ c;
4. d = a ⊕ b ⊕ c 可以推出 a = d ⊕ b ⊕ c.((a^b) == c <=> a(a^c) == b)
5. a ⊕ b ⊕ a = b.
6.若x是二进制数0101，y是二进制数1011；
则x⊕y=1110
只有在两个比较的位不同时其结果是1，否则结果为0
即“两个输入相同时为0，不同则为1”！

/*
1打表发现数学规律gcd(a, b) == (a^b) => (a-b) == (a^b)
2筛法思想建立约数表
3xor运算:(a^b) = c <=> (a^c) = b;
*/
#include <cstdio>
#include <cstring>

using namespace std;

int v[30000004] = {0};

int main(){
int a, b, c;
///筛法思想建立约数表
for(c = 1; c <= 15000000; c++){
for(a = c + c; a <= 30000000; a += c){
b = a - c;
if(c == (a^b))
v[a]++;
}
}
///now:v[a]:(a, xi);
for(int i = 2; i <= 30000000; i++){
v[i] += v[i-1];
}
///now:v[a]:(ai, xi);
int T, k, n;
scanf("%d", &T);
for(k = 1; k <= T; k++){
scanf("%d", &n);
printf("Case %d: %d\n", k, v
);
}
return 0;
}