[HAOI2008]圆上的整点

Posted 2020-10-04 Elder_Giang

1041: [HAOI2008]圆上的整点

Time Limit: 10 Sec  Memory Limit: 162 MB Submit: 4319  Solved: 1955 [Submit][Status][Discuss]

Description

求一个给定的圆(x^2+y^2=r^2)，在圆周上有多少个点的坐标是整数。

Input

只有一个正整数n,n<=2000 000 000

Output

整点个数

Sample Input

4

Sample Output

4

HINT

 科普视频

太神了，看这个

#include <cmath>
#include <iostream>
using namespace std;
typedef long long ll;
ll Gcd(ll x, ll y){
    ll t;
    if(x > y){
        t = x;
        x = y;
        y = t;
    }
    while(x){
        t = x;
        x = y % x;
        y = t;
    }
    return y;
}
inline bool Judge(ll a, ll b){
    double t = sqrt(b);
    if(t != floor(t)) return false;
    if(Gcd(a, b) == 1 && a != b) return true;
    return false;
}
int main(){
    ll r, ans = 0;
    cin >> r;
    for(ll d = 1; d * d <= r * 2; d++)
        if(2 * r % d == 0){
            for(ll i = 1; i * i * d <= r; i++)
                if(Judge(i * i, 2 * r / d - i * i)) ans++;
            if(d * d != 2 * r)
                for(ll i = 1; i * i * 2 <= d; i++)
                    if(Judge(i * i, d - i * i)) ans++;    
        }
    cout << (ans + 1) * 4 << endl;
    return 0;
}