题解 | 优雅的点

#include <iostream>
#include <cmath>
using namespace std;

class Solution {
public:
    int countPoints(int n) {
        int count = 0;
        
        // 处理坐标轴上的点
        int r = (int)sqrt(n);
        if (r * r == n) {
            count += 4;  // 如果r是整数，(±r,0)和(0,±r)是整点
            --r;
        }
        
        // 遍历可能的y坐标
        for (int y = r; y > 0; y--) {
            int x = (int)sqrt(n - y * y);
            if (x * x + y * y == n) {
                count += 4;  // 每找到一对(x,y)，由对称性可得4个点
            }
        }
        
        return count;
    }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    
    int n;
    while (cin >> n) {
        Solution solution;
        cout << solution.countPoints(n) << endl;
    }
    
    return 0;
}

import java.util.*;

public class Main {
    static class Solution {
        public int countPoints(int n) {
            int count = 0;
            
            // 处理坐标轴上的点
            int r = (int)Math.sqrt(n);
            if (r * r == n) {
                count += 4;
                --r;
            }
            
            // 遍历可能的y坐标
            for (int y = r; y > 0; y--) {
                int x = (int)Math.sqrt(n - y * y);
                if (x * x + y * y == n) {
                    count += 4;
                }
            }
            
            return count;
        }
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        while (sc.hasNext()) {
            int n = sc.nextInt();
            Solution solution = new Solution();
            System.out.println(solution.countPoints(n));
        }
        sc.close();
    }
}

from math import sqrt

class Solution:
    def count_points(self, n: int) -> int:
        count = 0
        
        # 处理坐标轴上的点
        r = int(sqrt(n))
        if r * r == n:
            count += 4  # 坐标轴上的四个点
            r -= 1
        
        # 遍历可能的y坐标
        for y in range(r, 0, -1):
            x = int(sqrt(n - y * y))
            if x * x + y * y == n:
                count += 4  # 每组解可以得到四个对称点
        
        return count

def main():
    while True:
        try:
            n = int(input())
            solution = Solution()
            print(solution.count_points(n))
        except EOFError:
            break

if __name__ == "__main__":
    main()