BOJ 1708: 볼록 껍질

https://www.acmicpc.net/problem/1708

  • 3월동안 210문제 풀기 (5/210)
  • Graham Scan 배워보기
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#include <bits/stdc++.h>
using namespace std;

const double EPS = 1e-9;
struct Vector {
  double x, y;

  Vector() { this->x = 0, this->y = 0; }
  Vector(int x, int y) { this->x = x, this->y = y; }
  Vector(const Vector& v1) { x = v1.x, y =v1.y; }

  Vector& operator+=(const Vector &other) {
    x += other.x;
    y += other.y;
    return *this;
  }

  Vector& operator-=(const Vector &other) {
    x -= other.x;
    y -= other.y;
    return *this;
  }

  Vector& operator*=(const double C) {
    x *= C;
    y *= C;
    return *this;
  }

  Vector& operator/=(const double C) {
    x /= C;
    y /= C;
    return *this;
  }
  Vector operator+(const Vector &other) const { return Vector(*this) += other; }
  Vector operator-(const Vector &other) const { return Vector(*this) -= other; }
  Vector operator*(const double C) const { return Vector(*this) *= C; }
  Vector operator/(const double C) const { return Vector(*this) /= C; }
};

double cross(Vector v1, Vector v2) {
  return v1.x * v2.y - v1.y * v2.x;
}

double ccw(Vector va, Vector vb) {
  double v = cross(va, vb);
  if(abs(v) < EPS) return 0;
  if(v > 0) return 1;
  if(v < 0) return -1;
}

double ccw(Vector vr, Vector va, Vector vb) {
  return ccw(va - vr, vb - vr);
}

typedef array<Vector, 2> Segment;

bool segmentInter(Vector v1, Vector v2, Vector v3, Vector v4) {
  double v1Root = ccw(v1, v2, v3) * ccw(v1, v2, v4);
  double v3Root = ccw(v3, v4, v1) * ccw(v3, v4, v2);

  auto project = [](double x1, double x2, double x3, double x4) {
    if(x1 > x2) swap(x1,x2);
    if(x3 > x4) swap(x3,x4);
    return max(x1,x3) <= min(x2, x4);
  };

  if (v1Root == 0 && v3Root == 0)
    return project(v1.x, v2.x, v3.x, v4.x) && project(v1.y, v2.y, v3.y, v4.y);
  return v1Root <= 0 && v3Root <= 0;
}

bool segmentInter(Segment& s1, Segment& s2) {
  return segmentInter(s1[0], s1[1], s2[0], s2[1]);
}


void grahamScan(vector<Vector>& arr, vector<int>& hull) {
  sort(arr.begin(), arr.end(), [](Vector& v1, Vector& v2) {
    return v1.y < v2.y || (v1.y == v2.y && v1.x < v2.x);
  });

  Vector origin = arr[0];
  for(Vector& v : arr)
    v -= origin;

  sort(arr.begin()+1, arr.end(), [](Vector& v1, Vector& v2) {
    if(ccw(v1, v2) > 0) return true;
    if(ccw(v1, v2) < 0) return false;
    return v1.y < v2.y || (v1.y == v2.y && v1.x < v2.x);
  });

  int next = 2;
  hull = {0,1};
  while(next < arr.size()) {
    while(hull.size() >= 2) {
      int center = hull.back();
      hull.pop_back();
      int prev = hull.back();

      if(ccw(arr[center], arr[next], arr[prev]) > 0) {
        hull.push_back(center);
        break;
      }
    }
    hull.push_back(next++);
  }
}


int main() {
  int N, x, y;
  scanf("%d", &N);
  vector<Vector> arr;
  vector<int> hull;
  arr.resize(N);
  for (int i = 0; i < N; i++) {
    scanf("%d %d", &x, &y);
    arr[i] = Vector(x,y);
  }
  grahamScan(arr, hull);
  printf("%d", hull.size());
}