BOJ 2162: 선분 그룹

작성일

https://www.acmicpc.net/problem/2162

  • 3월동안 210문제 풀기 (4/210)
  • Union-Find + 선분 교차
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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);
}

bool 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);
}

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);
  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;
}

typedef array<Vector, 2> Segment;

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

class DisjointSet {
public:
  int N, num;
  vector<int> parent, rank, count;
  DisjointSet(int n): N(n), num(n), parent(n), rank(n), count(n,1) {
    iota(parent.begin(), parent.end(), 0);
  }

  int find(int x) {
    return parent[x] = (parent[x] == x ? x : find(parent[x]));
  }

  void uni(int a, int b) {
    a = find(a);
    b = find(b);
    if(a == b) return;
    if(rank[a] > rank[b]) swap(a,b);
    parent[a] = b;
    if(rank[a] == rank[b]) rank[b]++;
    count[b] += count[a];
    count[a] = 0;
    num--;
  }
};

int main() {
  int N, x1, y1, x2, y2;
  scanf("%d", &N);
  vector<Segment> arr;
  arr.reserve(N);
  for(int i = 0; i < N; i++) {
    scanf("%d %d %d %d", &x1, &y1, &x2, &y2);
    Vector v1 = {x1,y1}, v2 = {x2,y2};
    arr.push_back({v1, v2});
  }

  DisjointSet dset(N);
  for(int i = 0; i < N; i++) {
    for(int j = i+1; j < N; j++) {
      if(segmentInter(arr[i], arr[j]))
        dset.uni(i,j);
    }
  }
  printf("%d\n", dset.num);
  int ans = 0;
  for(int x : dset.count)
    ans = max(ans, x);
  printf("%d\n", ans);
}