[Algorithm] C++ 백준 27046번: Beauty Contest

1
2
3
4
5

4
0 0
0 1
1 1
1 0

1

2

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110

// 42jerrykim.github.io에서 더 많은 정보를 확인 할 수 있습니다.

#include <bits/stdc++.h>
using namespace std;

struct Point {
    long long x, y;
    bool operator<(const Point& other) const {
        if (x != other.x) return x < other.x;
        return y < other.y;
    }
    bool operator==(const Point& other) const {
        return x == other.x && y == other.y;
    }
};

static inline Point operator-(const Point& a, const Point& b) {
    return {a.x - b.x, a.y - b.y};
}

static inline long long cross(const Point& a, const Point& b) {
    return a.x * b.y - a.y * b.x;
}

static inline long long cross(const Point& a, const Point& b, const Point& c) {
    // (b-a) x (c-a)
    return cross(b - a, c - a);
}

static inline long long dist2(const Point& a, const Point& b) {
    long long dx = a.x - b.x;
    long long dy = a.y - b.y;
    return dx * dx + dy * dy;
}

vector<Point> convexHull(vector<Point> pts) {
    sort(pts.begin(), pts.end());
    pts.erase(unique(pts.begin(), pts.end()), pts.end());

    int n = (int)pts.size();
    if (n <= 1) return pts;

    vector<Point> lower, upper;
    lower.reserve(n);
    upper.reserve(n);

    for (int i = 0; i < n; i++) {
        while ((int)lower.size() >= 2 &&
               cross(lower[(int)lower.size() - 2], lower.back(), pts[i]) <= 0) {
            lower.pop_back();
        }
        lower.push_back(pts[i]);
    }

    for (int i = n - 1; i >= 0; i--) {
        while ((int)upper.size() >= 2 &&
               cross(upper[(int)upper.size() - 2], upper.back(), pts[i]) <= 0) {
            upper.pop_back();
        }
        upper.push_back(pts[i]);
    }

    lower.pop_back();
    upper.pop_back();
    lower.insert(lower.end(), upper.begin(), upper.end()); // CCW hull
    return lower;
}

long long diameterSquared(const vector<Point>& hull) {
    int m = (int)hull.size();
    if (m <= 1) return 0;
    if (m == 2) return dist2(hull[0], hull[1]);

    auto area2 = [&](int i, int ni, int k) -> long long {
        return llabs(cross(hull[i], hull[ni], hull[k]));
    };

    long long ans = 0;
    int j = 1;

    for (int i = 0; i < m; i++) {
        int ni = (i + 1) % m;
        while (area2(i, ni, (j + 1) % m) > area2(i, ni, j)) {
            j = (j + 1) % m;
        }
        ans = max(ans, dist2(hull[i], hull[j]));
        ans = max(ans, dist2(hull[ni], hull[j]));
    }
    return ans;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int N;
    cin >> N;
    vector<Point> pts;
    pts.reserve(N);

    for (int i = 0; i < N; i++) {
        long long x, y;
        cin >> x >> y;
        pts.push_back({x, y});
    }

    vector<Point> hull = convexHull(pts);
    cout << diameterSquared(hull) << '\n';
    return 0;
}