2389번: 세상의 중심에서... ↗

#include <bits/stdc++.h>

#define for1(s,n) for(int i = s; i < n; i++)
#define for1j(s,n) for(int j = s; j < n; j++)
#define foreach(k) for(auto i : k)
#define foreachj(k) for(auto j : k)
#define pb(a) push_back(a)
#define sz(a) a.size()

using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef vector <int> iv1;
typedef vector <vector<int>> iv2;
typedef vector <ll> llv1;
typedef unsigned int uint;
typedef vector <ull> ullv1;
typedef vector <vector <ull>> ullv2;

struct Point {
    double x, y;
    Point() : x(0), y(0) {}
    Point(double x, double y) : x(x), y(y) {}
};

Point getAveragePoint(Point* array, ll len) {
    Point ret = Point(0, 0);
    for1(0, len) {
        ret.x += array[i].x;
        ret.y += array[i].y;
    }
    ret.x/=len;
    ret.y/=len;
    return ret;
}

double getDistance(Point a, Point b) {
    return (a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y);
}

Point getFarestPoint(Point* array, ll len, Point crt) {
    Point ret = Point(crt.x, crt.y);
    for1(0, len) {
        if(getDistance(array[i], crt) > getDistance(ret, crt)) {
            ret = Point(array[i].x , array[i].y);
        }
    }
    return ret;
}

ll N;
Point ar[110];
ll gen = 500000;
double learning_rate = 1;

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    cin >> N;
    for1(0, N) {
        cin >> ar[i].x >> ar[i].y;
    }   

    Point current = getAveragePoint(ar, N);

    for1(0, gen) {
        Point farPoint = getFarestPoint(ar, N, current);
        current.x = current.x + (farPoint.x - current.x) * learning_rate;
        current.y = current.y + (farPoint.y - current.y) * learning_rate;
        learning_rate *= 0.999;
    }

    Point farPoint = getFarestPoint(ar, N, current);
    cout << current.x << " " << current.y << " " << sqrt(getDistance(current, farPoint));
}