HDU 2650 - A math problem (高斯素数扩展)
题意
判断一个高斯整数是不是高斯素数。
思路
对于一个高斯整数$a+bi$。
-
如果$a = 0 b = 0$，判断另一个数是不是形为$4n+3$或者$-(4n+3)$的素数 - 判断$a^2 + b^2$是不是素数。如果是就是。
这题把$i^2$变成了$\sqrt {2}$，所以可以扩(Y)展(Y)一下，判断$a^2 + 2b^2$是不是素数。
代码
#include <stack>
#include <cstdio>
#include <list>
#include <cassert>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <functional>
#include <cstring>
#include <algorithm>
#include <cctype>
#include <string>
#include <map>
#include <cmath>
using namespace std;
#define LL long long
#define ULL unsigned long long
#define SZ(x) (int)x.size()
#define Lowbit(x) ((x) & (-x))
#define MP(a, b) make_pair(a, b)
#define MS(arr, num) memset(arr, num, sizeof(arr))
#define PB push_back
#define X first
#define Y second
#define ROP freopen("input.txt", "r", stdin);
#define MID(a, b) (a + ((b - a) >> 1))
#define LC rt << 1, l, mid
#define RC rt << 1|1, mid + 1, r
#define LRT rt << 1
#define RRT rt << 1|1
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const double eps = 1e-8;
const int MAXN = 2e3 + 10;
const int MOD = 1e9 + 7;
const int dir[][2] = { {-1, 0}, {0, -1}, { 1, 0 }, { 0, 1 } };
const int hash_size = 4e5 + 10;
int cases = 0;
typedef pair<int, int> pii;
int main()
{
LL n, m;
while (cin >> n >> m)
{
bool flag = false;
if (n == 0)
{
if ((m+3) % 4 == 0 || (m-3) % 4 == 0) flag = true;
}
else
{
flag = true;
LL num = n*n + 2*m*m;
int k = sqrt(num + 0.5);
for (int i = 2; i <= k; i++)
if (num % i == 0)
{
flag = false;
break;
}
}
printf("%s\n", flag ? "Yes" : "No");
}
return 0;
}