HDU 6055

题意略。

思路：要你找出所有正多边形，其实是唬人的，整点的正多边形只有正方形，具体证明可以参考     2017国家队论文集-《正多边形》-杨景钦

详见代码：

#include<bits/stdc++.h>
#define maxn 505
//#define LOCAL
using namespace std;

struct Point{
    int x,y;
    Point(int a = 0,int b = 0){
        x = a,y = b;
    }
    Point operator+ (const Point& p){
        return Point(x + p.x,y + p.y);
    }
    Point operator- (const Point& p){
        return Point(x - p.x,y - p.y);
    }
    bool operator== (const Point& p) const{
        return x == p.x && y == p.y;
    }
    bool operator< (const Point& p) const{
        if(x != p.x) return x < p.x;
        return y < p.y;
    }
};

struct line{
    Point s,t;
    line(){}
    line(Point a,Point b){
        s = a,t = b;
    }
    bool operator< (const line& l) const{
        if(!(s == l.s)) return s < l.s;
        return t < l.t;
    }
};

set<line> st;
Point store[maxn * maxn];

int main(){
    #ifdef LOCAL
    freopen("kkk.txt","r",stdin);
    freopen("kkkout.txt","w",stdout);
    #endif
    int n;
    while(scanf("%d",&n) == 1){
        st.clear();
        for(int i = 0;i < n;++i)
            scanf("%d%d",&store[i].x,&store[i].y);
        sort(store,store + n);
        for(int i = 0;i < n;++i){
            for(int j = i + 1;j < n;++j){
                st.insert(line(store[i],store[j]));
            }
        }
        int ans = 0;
        for(int i = 0;i < n;++i){
            for(int j = i + 1;j < n;++j){
                Point d = store[j] - store[i];
                Point temp(d.y,-d.x);
                Point s = store[i] + temp;
                Point t = s + d;
                if(st.count(line(s,t))) ++ans;
            }
        }
        printf("%d
",ans / 2);
    }
    return 0;
}