oj.uz

Submission #223802

# Submission time Handle Problem Language Result Execution time Memory
223802 2020-04-16T13:30:55 Z rama_pang Sky Walking (IOI19_walk) C++14
100 / 100
 3759 ms 251816 KB 
#include <bits/stdc++.h>
using namespace std;

class Graph {
 private:
  struct edge_t {
    int v;
    long long w;
    edge_t() {}
    edge_t(int v, long long w) : v(v), w(w) {}
    bool operator < (const edge_t &o) const { return w > o.w; }
  };

  vector<vector<edge_t>> adj;

 public:
  Graph() {}

  int AddVertex() {
    adj.emplace_back();
    return (int) adj.size() - 1;
  }

  void AddEdge(int u, int v, long long w) {
    adj[u].emplace_back(v, w);
    adj[v].emplace_back(u, w);
  }

  long long Dijkstra(int s, int g) {
    priority_queue<edge_t> pq;
    vector<long long> dist(adj.size(), -1);
    pq.emplace(s, 0);
    dist[s] = 0;

    while (!pq.empty()) {
      int u = pq.top().v;
      long long d = pq.top().w;
      pq.pop();
      if (dist[u] != d) continue;
      for (auto e : adj[u]) {
        if (dist[e.v] == -1 || dist[e.v] > dist[u] + e.w) {
          dist[e.v] = dist[u] + e.w;
          pq.emplace(e.v, dist[e.v]);
        }
      }
    }

    return dist[g];
  }
};

struct Point {
  int x, y;
  Point() {}
  Point(int x, int y) : x(x), y(y) {}
  bool operator < (const Point &o) const { return make_pair(x, y) < make_pair(o.x, o.y); }
  bool operator > (const Point &o) const { return make_pair(x, y) > make_pair(o.x, o.y); }
  bool operator == (const Point &o) const { return x == o.x && y == o.y; }
};

class Planar {
 private:
  Graph G;
  map<Point, int> id;
  set<pair<Point, Point>> edges;

 public:
  Planar() {}

  void AddVertex(Point p) {
    if (!id.count(p)) id.emplace(p, G.AddVertex());
  }

  void AddEdge(Point a, Point b) {
    if (a == b) return;
    if (edges.count({min(a, b), max(a, b)})) return;
    AddVertex(a), AddVertex(b);
    G.AddEdge(id[a], id[b], abs(a.x - b.x) + abs(a.y - b.y));
    edges.emplace(min(a, b), max(a, b));
  }

  long long Dijkstra(Point s, Point g) {
    AddVertex(s), AddVertex(g);
    return G.Dijkstra(id[s], id[g]);
  }
};

long long min_distance(vector<int> x, vector<int> h, vector<int> l, 
                       vector<int> r, vector<int> y, int s, int g) {
  Planar G;

  auto SplitSkywalk = [&](int p) { // Split skywalks that passes over p into separate parts
    struct event_t {
      int t; // type 0 = skywalk, 1 = building
      int id;
      int h, l, r;
      event_t() {}
      event_t(int t, int id, int h, int l, int r) : t(t), id(id), h(h), l(l), r(r) {}
    };

    int n = x.size(), m = y.size();
    vector<int> new_l;
    vector<int> new_r;
    vector<int> new_y;

    vector<event_t> events; 
    for (int i = 0; i < m; i++) {
      events.emplace_back(0, i, y[i], l[i], r[i]);
    }
    for (int i = 0; i < n; i++) {
      events.emplace_back(1, i, h[i], i, i);
    }
    
    set<int> active; // active buildings
    for (int i = 0; i < n; i++) {
      active.emplace(i);
    }

    sort(begin(events), end(events), [&](const event_t &a, const event_t &b) {
      return make_pair(a.h, a.t) < make_pair(b.h, b.t);
    });

    for (auto event : events) {
      if (event.t == 0) { // skywalk
        if (event.r < p || p < event.l) { // doesn't pass over p
          new_y.emplace_back(event.h);
          new_l.emplace_back(event.l);
          new_r.emplace_back(event.r);
          continue;
        }

        auto lb = active.lower_bound(p);
        auto ub = active.upper_bound(p);

        int on_left = (ub == begin(active) ? -1 : *prev(ub));
        int on_right = (lb == end(active) ? -1 : *lb);

        if (event.l <= on_left && on_right <= event.r) {
          new_y.emplace_back(event.h);
          new_l.emplace_back(event.l);
          new_r.emplace_back(on_left);

          new_y.emplace_back(event.h);
          new_l.emplace_back(on_left);
          new_r.emplace_back(on_right);
          
          new_y.emplace_back(event.h);
          new_l.emplace_back(on_right);
          new_r.emplace_back(event.r);
        }
      } else { // building
        active.erase(event.id);
      }
    }

    l = new_l, r = new_r, y = new_y;
  };
  
  auto BuildGraph = [&]() { // For each endpoint of skywalks, add vertices on the skywalk above and below the current one
    l.emplace_back(s);
    r.emplace_back(s);
    y.emplace_back(0);

    l.emplace_back(g);
    r.emplace_back(g);
    y.emplace_back(0);

    int n = x.size(), m = y.size();
    vector<vector<pair<int, int>>> events(n); // (height, id)
    vector<int> last_point(m); // last point added on the i-th skywalk

    for (int i = 0; i < m; i++) {
      events[l[i]].emplace_back(+y[i], i); // add new skywalk starting from at l[i]
      events[r[i]].emplace_back(-y[i], i); // delete skywalks ending at r[i]
      last_point[i] = x[l[i]];
    }

    set<pair<int, int>> ys; // (height, id)
    ys.emplace(-1, -1);

    for (int i = 0; i < n; i++) {
      sort(begin(events[i]), end(events[i]), greater<pair<int, int>>());
      for (auto event : events[i]) {
        int y = abs(event.first), id = event.second;

        auto lb = ys.lower_bound({y, -1});
        auto ub = ys.upper_bound({y, m});
        
        int above = (ub == end(ys) ? -1 : ub->first);
        int id_above = (ub == end(ys) ? -1 : ub->second);
        
        int below = (lb == begin(ys) ? -1 : prev(lb)->first);
        int id_below = (lb == begin(ys) ? -1 : prev(lb)->second);
        
        if (above != -1 && above <= h[i]) {
          G.AddEdge(Point(x[i], y), Point(x[i], above));
          G.AddEdge(Point(last_point[id_above], above), Point(x[i], above));
          last_point[id_above] = x[i];
        }
        
        if (below != -1) {
          G.AddEdge(Point(x[i], y), Point(x[i], below));
          G.AddEdge(Point(last_point[id_below], below), Point(x[i], below));
          last_point[id_below] = x[i];
        }

        if (event.first > 0) {
          ys.emplace(y, id);
        } else if (event.first < 0) {
          G.AddEdge(Point(x[i], y), Point(last_point[id], y));
          ys.erase({y, id});
        }
      }
    }
  };

  SplitSkywalk(s);
  SplitSkywalk(g);
  BuildGraph();

  return G.Dijkstra(Point(x[s], 0), Point(x[g], 0));
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB Output is correct
2 Correct 4 ms 256 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 4 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 6 ms 512 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 5 ms 384 KB Output is correct
15 Correct 4 ms 256 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct

Subtask #2
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 256 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 1166 ms 122568 KB Output is correct
4 Correct 1101 ms 122236 KB Output is correct
5 Correct 792 ms 92236 KB Output is correct
6 Correct 754 ms 84516 KB Output is correct
7 Correct 767 ms 92880 KB Output is correct
8 Correct 1265 ms 132804 KB Output is correct
9 Correct 1006 ms 114068 KB Output is correct
10 Correct 1214 ms 129964 KB Output is correct
11 Correct 876 ms 93832 KB Output is correct
12 Correct 559 ms 50152 KB Output is correct
13 Correct 1160 ms 132544 KB Output is correct
14 Correct 650 ms 59776 KB Output is correct
15 Correct 592 ms 54100 KB Output is correct
16 Correct 482 ms 56592 KB Output is correct
17 Correct 493 ms 54676 KB Output is correct
18 Correct 1185 ms 99420 KB Output is correct
19 Correct 27 ms 3212 KB Output is correct
20 Correct 322 ms 29480 KB Output is correct
21 Correct 541 ms 52324 KB Output is correct
22 Correct 466 ms 50184 KB Output is correct
23 Correct 920 ms 80320 KB Output is correct
24 Correct 460 ms 52900 KB Output is correct
25 Correct 472 ms 54668 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 167 ms 20264 KB Output is correct
2 Correct 1741 ms 160220 KB Output is correct
3 Correct 1898 ms 166708 KB Output is correct
4 Correct 1980 ms 171172 KB Output is correct
5 Correct 2653 ms 181128 KB Output is correct
6 Correct 2365 ms 163448 KB Output is correct
7 Correct 820 ms 86908 KB Output is correct
8 Correct 480 ms 50184 KB Output is correct
9 Correct 2228 ms 155140 KB Output is correct
10 Correct 752 ms 82692 KB Output is correct
11 Correct 50 ms 4508 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 167 ms 20264 KB Output is correct
2 Correct 1741 ms 160220 KB Output is correct
3 Correct 1898 ms 166708 KB Output is correct
4 Correct 1980 ms 171172 KB Output is correct
5 Correct 2653 ms 181128 KB Output is correct
6 Correct 2365 ms 163448 KB Output is correct
7 Correct 820 ms 86908 KB Output is correct
8 Correct 480 ms 50184 KB Output is correct
9 Correct 2228 ms 155140 KB Output is correct
10 Correct 752 ms 82692 KB Output is correct
11 Correct 50 ms 4508 KB Output is correct
12 Correct 1919 ms 165936 KB Output is correct
13 Correct 1847 ms 170736 KB Output is correct
14 Correct 2683 ms 181100 KB Output is correct
15 Correct 1458 ms 126888 KB Output is correct
16 Correct 1606 ms 141200 KB Output is correct
17 Correct 1840 ms 171472 KB Output is correct
18 Correct 1437 ms 127188 KB Output is correct
19 Correct 1575 ms 140940 KB Output is correct
20 Correct 953 ms 84780 KB Output is correct
21 Correct 168 ms 8752 KB Output is correct
22 Correct 1122 ms 128884 KB Output is correct
23 Correct 1074 ms 119480 KB Output is correct
24 Correct 667 ms 72636 KB Output is correct
25 Correct 884 ms 105468 KB Output is correct
26 Correct 487 ms 49332 KB Output is correct
27 Correct 2706 ms 179564 KB Output is correct
28 Correct 1615 ms 167968 KB Output is correct
29 Correct 2423 ms 163252 KB Output is correct
30 Correct 862 ms 86268 KB Output is correct
31 Correct 2371 ms 155124 KB Output is correct
32 Correct 607 ms 65520 KB Output is correct
33 Correct 592 ms 64268 KB Output is correct
34 Correct 792 ms 80248 KB Output is correct
35 Correct 781 ms 83652 KB Output is correct
36 Correct 590 ms 65348 KB Output is correct
37 Correct 537 ms 52452 KB Output is correct
38 Correct 497 ms 50056 KB Output is correct
39 Correct 917 ms 80340 KB Output is correct
40 Correct 467 ms 53032 KB Output is correct
41 Correct 468 ms 54568 KB Output is correct

Subtask #5
43.0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 256 KB Output is correct
2 Correct 4 ms 256 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 4 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 6 ms 512 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 5 ms 384 KB Output is correct
15 Correct 4 ms 256 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 4 ms 256 KB Output is correct
19 Correct 5 ms 384 KB Output is correct
20 Correct 1166 ms 122568 KB Output is correct
21 Correct 1101 ms 122236 KB Output is correct
22 Correct 792 ms 92236 KB Output is correct
23 Correct 754 ms 84516 KB Output is correct
24 Correct 767 ms 92880 KB Output is correct
25 Correct 1265 ms 132804 KB Output is correct
26 Correct 1006 ms 114068 KB Output is correct
27 Correct 1214 ms 129964 KB Output is correct
28 Correct 876 ms 93832 KB Output is correct
29 Correct 559 ms 50152 KB Output is correct
30 Correct 1160 ms 132544 KB Output is correct
31 Correct 650 ms 59776 KB Output is correct
32 Correct 592 ms 54100 KB Output is correct
33 Correct 482 ms 56592 KB Output is correct
34 Correct 493 ms 54676 KB Output is correct
35 Correct 1185 ms 99420 KB Output is correct
36 Correct 27 ms 3212 KB Output is correct
37 Correct 322 ms 29480 KB Output is correct
38 Correct 541 ms 52324 KB Output is correct
39 Correct 466 ms 50184 KB Output is correct
40 Correct 920 ms 80320 KB Output is correct
41 Correct 460 ms 52900 KB Output is correct
42 Correct 472 ms 54668 KB Output is correct
43 Correct 167 ms 20264 KB Output is correct
44 Correct 1741 ms 160220 KB Output is correct
45 Correct 1898 ms 166708 KB Output is correct
46 Correct 1980 ms 171172 KB Output is correct
47 Correct 2653 ms 181128 KB Output is correct
48 Correct 2365 ms 163448 KB Output is correct
49 Correct 820 ms 86908 KB Output is correct
50 Correct 480 ms 50184 KB Output is correct
51 Correct 2228 ms 155140 KB Output is correct
52 Correct 752 ms 82692 KB Output is correct
53 Correct 50 ms 4508 KB Output is correct
54 Correct 1919 ms 165936 KB Output is correct
55 Correct 1847 ms 170736 KB Output is correct
56 Correct 2683 ms 181100 KB Output is correct
57 Correct 1458 ms 126888 KB Output is correct
58 Correct 1606 ms 141200 KB Output is correct
59 Correct 1840 ms 171472 KB Output is correct
60 Correct 1437 ms 127188 KB Output is correct
61 Correct 1575 ms 140940 KB Output is correct
62 Correct 953 ms 84780 KB Output is correct
63 Correct 168 ms 8752 KB Output is correct
64 Correct 1122 ms 128884 KB Output is correct
65 Correct 1074 ms 119480 KB Output is correct
66 Correct 667 ms 72636 KB Output is correct
67 Correct 884 ms 105468 KB Output is correct
68 Correct 487 ms 49332 KB Output is correct
69 Correct 2706 ms 179564 KB Output is correct
70 Correct 1615 ms 167968 KB Output is correct
71 Correct 2423 ms 163252 KB Output is correct
72 Correct 862 ms 86268 KB Output is correct
73 Correct 2371 ms 155124 KB Output is correct
74 Correct 607 ms 65520 KB Output is correct
75 Correct 592 ms 64268 KB Output is correct
76 Correct 792 ms 80248 KB Output is correct
77 Correct 781 ms 83652 KB Output is correct
78 Correct 590 ms 65348 KB Output is correct
79 Correct 537 ms 52452 KB Output is correct
80 Correct 497 ms 50056 KB Output is correct
81 Correct 917 ms 80340 KB Output is correct
82 Correct 467 ms 53032 KB Output is correct
83 Correct 468 ms 54568 KB Output is correct
84 Correct 152 ms 17088 KB Output is correct
85 Correct 1990 ms 171208 KB Output is correct
86 Correct 3156 ms 209696 KB Output is correct
87 Correct 179 ms 14700 KB Output is correct
88 Correct 257 ms 16252 KB Output is correct
89 Correct 172 ms 14440 KB Output is correct
90 Correct 57 ms 7700 KB Output is correct
91 Correct 7 ms 512 KB Output is correct
92 Correct 57 ms 6572 KB Output is correct
93 Correct 671 ms 59356 KB Output is correct
94 Correct 180 ms 9008 KB Output is correct
95 Correct 1205 ms 136848 KB Output is correct
96 Correct 1004 ms 116832 KB Output is correct
97 Correct 727 ms 76836 KB Output is correct
98 Correct 869 ms 105316 KB Output is correct
99 Correct 3759 ms 251816 KB Output is correct
100 Correct 1779 ms 170156 KB Output is correct
101 Correct 2782 ms 186532 KB Output is correct
102 Correct 896 ms 86640 KB Output is correct
103 Correct 607 ms 63980 KB Output is correct
104 Correct 585 ms 62652 KB Output is correct
105 Correct 801 ms 76020 KB Output is correct
106 Correct 653 ms 65060 KB Output is correct
107 Correct 748 ms 64756 KB Output is correct
108 Correct 119 ms 12880 KB Output is correct
109 Correct 1831 ms 128604 KB Output is correct
110 Correct 1594 ms 169012 KB Output is correct
111 Correct 1602 ms 169348 KB Output is correct
112 Correct 723 ms 81084 KB Output is correct
113 Correct 688 ms 79356 KB Output is correct