oj.uz

Submission #220597

# Submission time Handle Problem Language Result Execution time Memory
220597 2020-04-08T06:49:02 Z rama_pang Fences (JOI18_fences) C++14
100 / 100
 32 ms 4100 KB 
#include <bits/stdc++.h>
using namespace std;
using type_t = double;
const type_t EPS = 1e-9;

struct Point {
  type_t x, y;
  Point() {}
  Point(type_t a, type_t b) : x(a), y(b) {}

  Point operator + (const Point &o) const {
    return Point(x + o.x, y + o.y);
  }

  Point operator - (const Point &o) const {
    return Point(x - o.x, y - o.y);
  }

  friend ostream& operator << (ostream &stream, const Point &p) {
    stream << "(" << p.x << ", " << p.y << ")";
  }
};

struct Line {
  Point a, b;
  Line() {}
  Line(Point a, Point b) : a(a), b(b) {}

  friend ostream& operator << (ostream &stream, const Line &l) {
    stream << "(" << l.a << ", " << l.b << ")";
  }
};

bool Clockwise(Point a, Point b, Point c) { // cross product of vector ab and ac
  Point v1 = b - a, v2 = c - a;
  return (v1.x * v2.y - v1.y * v2.x) > 0;
}

bool CounterClockwise(Point a, Point b, Point c) { // cross product of vector ab and ac
  Point v1 = b - a, v2 = c - a;
  return (v1.x * v2.y - v1.y * v2.x) < 0;
}

bool IntersectLine(Line a, Line b, bool IsTouchIntersect) {
  bool o1 = false, o2 = false;
  o1 |= Clockwise(a.a, a.b, b.a) && CounterClockwise(a.a, a.b, b.b);
  o1 |= CounterClockwise(a.a, a.b, b.a) && Clockwise(a.a, a.b, b.b);
  
  o2 |= Clockwise(b.a, b.b, a.a) && CounterClockwise(b.a, b.b, a.b);
  o2 |= CounterClockwise(b.a, b.b, a.a) && Clockwise(b.a, b.b, a.b);
  
  if (IsTouchIntersect) {
    o1 |= Clockwise(a.a, a.b, b.a) && !Clockwise(a.a, a.b, b.b);
    o1 |= !Clockwise(a.a, a.b, b.a) && Clockwise(a.a, a.b, b.b);
    o2 |= Clockwise(b.a, b.b, a.a) && !Clockwise(b.a, b.b, a.b);
    o2 |= !Clockwise(b.a, b.b, a.a) && Clockwise(b.a, b.b, a.b);
  }

  return o1 && o2;
}

Line PointPointDistance(Point p, Point q) {
  return Line(p, q);
}

Line PointLineDistance(Point p, Line l) {
  Point a = l.a, b = l.b;
  Point vl = b - a;
  Point vp = p - a;

  type_t dot = (vl.x * vp.x + vl.y * vp.y);
  type_t sqr = vl.x * vl.x + vl.y * vl.y;
  type_t partial = dot / sqr;
  
  if (partial > 1 || partial < 0 || sqr == 0) {
    Point d1 = p - l.a;
    Point d2 = p - l.b;
    if (d1.x * d1.x + d1.y * d1.y < d2.x * d2.x + d2.y * d2.y) {
      return PointPointDistance(l.a, p);
    } else {
      return PointPointDistance(l.b, p);
    }
  }

  vl.x *= partial;
  vl.y *= partial;

  return PointPointDistance(vl + a, p);
}

int N, S;
vector<Line> L;
const Line HALFLINE = Line(Point(0, 0), Point(1, 400));

bool IntersectSquare(Line line) {
  bool res = false;
  res |= IntersectLine(line, Line(Point(S, S), Point(-S, S)), false); // top side
  res |= IntersectLine(line, Line(Point(S, S), Point(S, -S)), false); // right side
  res |= IntersectLine(line, Line(Point(-S, -S), Point(-S, S)), false); // left side
  res |= IntersectLine(line, Line(Point(-S, -S), Point(S, -S)), false); // bottom side
  res |= IntersectLine(line, Line(Point(-S, S), Point(S, -S)), false); // diagonal 1
  res |= IntersectLine(line, Line(Point(S, S), Point(-S, -S)), false); // diagonal 2
  return res;
}

void Read() {
  ios::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);

  cin >> N >> S;

  for (int i = 0; i < N; i++) {
    int A, B, C, D;
    cin >> A >> B >> C >> D;
    L.emplace_back(Point(A, B), Point(C, D));
  }

  // Square Corners
  L.emplace_back(Point(S, S), Point(S, S));
  L.emplace_back(Point(S, -S), Point(S, -S));
  L.emplace_back(Point(-S, -S), Point(-S, -S));
  L.emplace_back(Point(-S, S), Point(-S, S)); 
}

struct Edge {
  int u, v;
  Line l;
  bool CrossLine;
  type_t Distance;
  Edge() {}
  Edge(int u, int v, Line l) : u(u), v(v), l(l) {}
};

vector<Edge> edges;

void AddEdge(int u, int v) {
  if (!IntersectSquare(PointPointDistance(L[u].a, L[v].a))) {
    edges.emplace_back(u, v, PointPointDistance(L[u].a, L[v].a));
  }
  if (!IntersectSquare(PointPointDistance(L[u].a, L[v].b))) {
    edges.emplace_back(u, v, PointPointDistance(L[u].a, L[v].b));
  }
  if (!IntersectSquare(PointPointDistance(L[u].b, L[v].a))) {
    edges.emplace_back(u, v, PointPointDistance(L[u].b, L[v].a));
  }
  if (!IntersectSquare(PointPointDistance(L[u].b, L[v].b))) {
    edges.emplace_back(u, v, PointPointDistance(L[u].b, L[v].b));
  }

  if (!IntersectSquare(PointLineDistance(L[u].a, L[v]))) {
    edges.emplace_back(u, v, PointLineDistance(L[u].a, L[v]));
  }
  if (!IntersectSquare(PointLineDistance(L[u].b, L[v]))) {
    edges.emplace_back(u, v, PointLineDistance(L[u].b, L[v]));
  }
  if (!IntersectSquare(PointLineDistance(L[v].a, L[u]))) {
    edges.emplace_back(u, v, PointLineDistance(L[v].a, L[u]));
  }
  if (!IntersectSquare(PointLineDistance(L[v].b, L[u]))) {
    edges.emplace_back(u, v, PointLineDistance(L[v].b, L[u]));
  }
} 

void BuildGraph() {
  int n = L.size();

  { // Split segments that intersecti with HALFLINE into 2 so there are no segments that intersect with HALFLINE
    vector<Line> newL;
    for (int i = 0; i < n; i++) {
      if (IntersectLine(L[i], HALFLINE, true)) { 
        Point Vector = L[i].b - L[i].a;
        type_t l = 0, r = 1;
        for (int it = 0; it < 30; it++) {
          type_t m = (l + r) / 2;
          Point mp = L[i].a + Point(Vector.x * m, Vector.y * m);
          Line p = Line(L[i].a, mp);
          if (IntersectLine(p, HALFLINE, true)) {
            r = m;
          } else {
            l = m;
          }
        }
        Point m;
        m = L[i].a + Point(Vector.x * (r - EPS), Vector.y * (r - EPS));
        newL.emplace_back(L[i].a, m);
        m = L[i].a + Point(Vector.x * (r + EPS), Vector.y * (r + EPS));
        newL.emplace_back(m, L[i].b);
      } else {
        newL.emplace_back(L[i]);
      }
    }
    L = newL;
  }

  n = L.size();

  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      AddEdge(i, j);
    }
  }

  for (auto &e : edges) {
    e.Distance = sqrt((e.l.a.x - e.l.b.x) * (e.l.a.x - e.l.b.x) + (e.l.a.y - e.l.b.y) * (e.l.a.y - e.l.b.y));
    e.CrossLine = IntersectLine(e.l, HALFLINE, true);
  }
}

type_t Solve() {
  int n = L.size();
  vector<vector<type_t>> dist(n * 2, vector<type_t>(n * 2, 1e9));

  for (auto &e : edges) {
    if (e.CrossLine) {
      dist[e.u][e.v + n] = min(dist[e.u][e.v + n], e.Distance);
      dist[e.u + n][e.v] = min(dist[e.u + n][e.v], e.Distance);
      dist[e.v][e.u + n] = min(dist[e.v][e.u + n], e.Distance);
      dist[e.v + n][e.u] = min(dist[e.v + n][e.u], e.Distance);
    } else {
      dist[e.u][e.v] = min(dist[e.u][e.v], e.Distance);
      dist[e.u + n][e.v + n] = min(dist[e.u + n][e.v + n], e.Distance);
      dist[e.v][e.u] = min(dist[e.v][e.u], e.Distance);
      dist[e.v + n][e.u + n] = min(dist[e.v + n][e.u + n], e.Distance);
    } 
  }
  
  for (int i = 0; i < 2 * n; i++) {
    dist[i][i] = 0;
  }

  for (int k = 0; k < 2 * n; k++) {
    for (int i = 0; i < 2 * n; i++) {
      for (int j = 0; j < 2 * n; j++) {
        dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
      }
    }
  }

  type_t cycle = 1e9;
  for (int i = 0; i < n; i++) {
    cycle = min(cycle, dist[i][i + n]);
  }

  return cycle;
}

int main() {
  Read();
  BuildGraph();
  cout << fixed << setprecision(10) << Solve() << "\n";
  return 0;
}

Compilation message

fences.cpp: In function 'std::ostream& operator<<(std::ostream&, const Point&)':
fences.cpp:21:3: warning: no return statement in function returning non-void [-Wreturn-type]
   }
   ^
fences.cpp: In function 'std::ostream& operator<<(std::ostream&, const Line&)':
fences.cpp:31:3: warning: no return statement in function returning non-void [-Wreturn-type]
   }
   ^

Subtask #1
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 4 ms 384 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 512 KB Output is correct
19 Correct 5 ms 384 KB Output is correct
20 Correct 5 ms 384 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 4 ms 384 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 512 KB Output is correct
19 Correct 5 ms 384 KB Output is correct
20 Correct 5 ms 384 KB Output is correct
21 Correct 5 ms 384 KB Output is correct
22 Correct 5 ms 384 KB Output is correct
23 Correct 5 ms 384 KB Output is correct
24 Correct 5 ms 384 KB Output is correct
25 Correct 5 ms 384 KB Output is correct
26 Correct 5 ms 384 KB Output is correct
27 Correct 5 ms 384 KB Output is correct
28 Correct 5 ms 384 KB Output is correct
29 Correct 5 ms 384 KB Output is correct
30 Correct 5 ms 384 KB Output is correct
31 Correct 5 ms 384 KB Output is correct
32 Correct 5 ms 384 KB Output is correct
33 Correct 5 ms 384 KB Output is correct
34 Correct 5 ms 384 KB Output is correct
35 Correct 5 ms 384 KB Output is correct
36 Correct 5 ms 384 KB Output is correct
37 Correct 5 ms 384 KB Output is correct
38 Correct 7 ms 384 KB Output is correct
39 Correct 5 ms 384 KB Output is correct
40 Correct 5 ms 384 KB Output is correct
41 Correct 5 ms 384 KB Output is correct
42 Correct 5 ms 384 KB Output is correct
43 Correct 5 ms 384 KB Output is correct

Subtask #3
49.0 / 49.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 4 ms 384 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 512 KB Output is correct
19 Correct 5 ms 384 KB Output is correct
20 Correct 5 ms 384 KB Output is correct
21 Correct 5 ms 384 KB Output is correct
22 Correct 5 ms 384 KB Output is correct
23 Correct 5 ms 384 KB Output is correct
24 Correct 5 ms 384 KB Output is correct
25 Correct 5 ms 384 KB Output is correct
26 Correct 5 ms 384 KB Output is correct
27 Correct 5 ms 384 KB Output is correct
28 Correct 5 ms 384 KB Output is correct
29 Correct 5 ms 384 KB Output is correct
30 Correct 5 ms 384 KB Output is correct
31 Correct 5 ms 384 KB Output is correct
32 Correct 5 ms 384 KB Output is correct
33 Correct 5 ms 384 KB Output is correct
34 Correct 5 ms 384 KB Output is correct
35 Correct 5 ms 384 KB Output is correct
36 Correct 5 ms 384 KB Output is correct
37 Correct 5 ms 384 KB Output is correct
38 Correct 7 ms 384 KB Output is correct
39 Correct 5 ms 384 KB Output is correct
40 Correct 5 ms 384 KB Output is correct
41 Correct 5 ms 384 KB Output is correct
42 Correct 5 ms 384 KB Output is correct
43 Correct 5 ms 384 KB Output is correct
44 Correct 32 ms 4100 KB Output is correct
45 Correct 25 ms 4100 KB Output is correct
46 Correct 23 ms 2308 KB Output is correct
47 Correct 25 ms 2308 KB Output is correct
48 Correct 31 ms 4100 KB Output is correct
49 Correct 30 ms 4100 KB Output is correct
50 Correct 23 ms 2308 KB Output is correct
51 Correct 24 ms 2308 KB Output is correct
52 Correct 28 ms 2308 KB Output is correct
53 Correct 29 ms 2232 KB Output is correct
54 Correct 24 ms 2308 KB Output is correct
55 Correct 31 ms 2564 KB Output is correct
56 Correct 31 ms 4100 KB Output is correct
57 Correct 20 ms 2308 KB Output is correct
58 Correct 25 ms 2308 KB Output is correct
59 Correct 27 ms 2308 KB Output is correct
60 Correct 30 ms 2436 KB Output is correct
61 Correct 32 ms 2564 KB Output is correct
62 Correct 5 ms 384 KB Output is correct
63 Correct 6 ms 384 KB Output is correct
64 Correct 21 ms 2308 KB Output is correct
65 Correct 21 ms 2308 KB Output is correct
66 Correct 19 ms 1540 KB Output is correct
67 Correct 30 ms 4100 KB Output is correct
68 Correct 29 ms 4100 KB Output is correct
69 Correct 21 ms 2308 KB Output is correct
70 Correct 21 ms 2308 KB Output is correct
71 Correct 22 ms 2308 KB Output is correct
72 Correct 21 ms 2308 KB Output is correct