GYM 101002 G Symmetry

暴力枚举中心点和对称的线段，注意点在线段上的情况，以及许多点都在一条直线上的情况。

#include<bits/stdc++.h>
#define pb push_back
#define fuck(x) cout<<'['<<#x<<' '<<x<<']'<<endl
using namespace std;
typedef long long ll;
#define mp make_pair
#define pii pair<int,int>
#define debug(x) cout<<#x<<" = "<<x<<endl;
#define fi first
#define se second
#define clr(x,y) memset(x,y,sizeof(x))
const int mod = 175781251;
const int MAXN = 1e6 + 2;
const int MX = 1e3 + 7;

map<pii, int> dot;
map<pair<pii, pii>, int> line;
struct Point {
    int x, y;
    Point() {}
    Point(int x, int y): x(x), y(y) {}
    void read() {
        scanf("%d%d", &x, &y);
    }
} P[MX];

int main() {
#ifdef LOCAL
    freopen("in.txt", "r", stdin);
#endif
    int n;
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) {
        P[i].read();
    }
    for(int i = 1; i <= n; i++) {
        dot[mp(P[i].x*2, P[i].y*2)]++;
        for(int j = i + 1; j <= n; j++) {
            pii d = mp(P[i].x + P[j].x, P[i].y + P[j].y);
            dot[d] += 2;
            int xx = P[i].x - P[j].x, yy = P[i].y - P[j].y;

            int g = __gcd(xx, yy);
            xx /= g;
            yy /= g;
            if(yy < 0) {
                yy = -yy;
                xx = -xx;
            }
            int x = yy, y = -xx;

            pair<pii, pii> Li;
            if(x == 0) {
                Li = mp(mp(d.fi,0), mp(x, y));
            }
            else if(y == 0){
                Li = mp(mp(0,d.se), mp(x, y));
            }
            else {
                int k = d.fi/x + (d.fi%x< 0? 1 : 0);
                Li = mp(mp(d.fi - k*x, d.se - k*y), mp(x, y));
            }
            line[Li] += 2;
        }
    }

    int cnt = 0;
    int ans = 1e9;
    for(auto it = dot.begin(); it != dot.end(); it++) {
        ans = min(ans,n - it->se);
    }
    for(auto it = line.begin(); it != line.end(); it++) {
        int cnt = it->se;
        for(int i = 1; i <= n; i++){
            pii m = it->fi.fi;
            pii v = it->fi.se;
            pii t = mp(P[i].x*2, P[i].y*2);
            if(v.fi == 0){
                cnt += (t.fi == m.fi);
                continue;
            }
            else if(v.se == 0){
                cnt += (t.se == m.se);
                continue;
            }
            t = mp(t.fi - m.fi, t.se - m.se);
            cnt += (t == mp(0,0) || (t.fi/v.fi == t.se/v.se && t.fi%v.fi == 0 && t.se%v.se == 0));
        }
        ans = min(ans,n - cnt);
    }
    for(int i = 1; i <= n; i++){
        for(int j = 1; j < i; j++){
            int A = P[i].x - P[j].x;
            int B = P[i].y - P[j].y;
            int C = P[i].y*(P[i].x-P[j].x) - P[i].x*(P[i].y-P[j].y);
            int cnt = 0;
            for(int k = 1; k <= n; k++) {
                if(-A*P[k].y + B*P[k].x + C == 0) cnt++;
            }
            ans = min(ans,n-cnt);
        }
    }
    cout << ans << endl;
    return 0;
}