oj.uz

Submission #991229

# Submission time Handle Problem Language Result Execution time Memory
991229 2024-06-01T15:30:56 Z model_code Portal (BOI24_portal) C++17
100 / 100
 68 ms 2144 KB 
#include <iostream>
#include <stdexcept>
#include <vector>

using namespace std;
struct Vector2D {
  int64_t x, y;
  Vector2D(int64_t x, int64_t y) : x(x), y(y) {}
  Vector2D() : x(0), y(0) {}
};

struct Parallelogram {
  Vector2D a, b;
  int64_t area() const { return abs(a.x * b.y - a.y * b.x); }
};

int64_t gcd(int64_t a, int64_t b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}

// gcd for colinear 2d vectors
Vector2D gcd(const Vector2D a, const Vector2D b) {
  return {gcd(a.x, b.x), gcd(a.y, b.y)};
}

bool colinear(Vector2D a, Vector2D b) {
  return Parallelogram{a, b}.area() == 0;
}

Vector2D operator*(const int64_t scalar, const Vector2D &p) {
  return Vector2D(scalar * p.x, scalar * p.y);
}

Vector2D operator-(const Vector2D &p1, const Vector2D &p2) {
  return Vector2D(p1.x - p2.x, p1.y - p2.y);
}

Parallelogram gcd(Parallelogram p, Vector2D q) {
  if (colinear(p.a, p.b)) {
    p.a = gcd(p.a, p.b);
    p.b = q;
    return p;
  }
  if (colinear(p.a, q)) {
    p.a = gcd(p.a, q);
    return p;
  }
  if (colinear(p.b, q)) {
    p.b = gcd(p.b, q);
    return p;
  }
  // We want to find k and l such that
  // q = k * p.a + l * p.b + remainder
  // The remainder should be inside p
  // q, p.a, p.b are not colinear and 2d vectors as we checked that before
  int64_t denominator = p.a.x * p.b.y - p.a.y * p.b.x;
  int64_t k = (q.x * p.b.y - q.y * p.b.x) / denominator;
  int64_t l = (p.a.x * q.y - p.a.y * q.x) / denominator;
  Vector2D remainder = q - k * p.a - l * p.b;
  Parallelogram new_p = {p.a, remainder};
  if (p.area() <= new_p.area()) {
    throw runtime_error("The parallelogram did not decrease in size. This "
                        "should never happen.");
  }
  return gcd(new_p, p.b);
}

int main() {
  size_t N;
  cin >> N;
  if (N <= 2) {
    cout << -1 << endl;
    return 0;
  }
  vector<Vector2D> portals(N);
  for (size_t i = 0; i < N; i++) {
    cin >> portals[i].x >> portals[i].y;
  }

  for (size_t i = 0; i < portals.size(); i++) {
    portals[i].x -= portals[N - 1].x;
    portals[i].y -= portals[N - 1].y;
  }
  portals.pop_back();

  // Try to form a parallelegram with non-0 area
  Parallelogram p;
  p.a = portals[0];
  for (size_t i = 1; i < portals.size(); i++) {
    swap(portals[1], portals[i]);
    p.b = portals[1];
    if (p.area() != 0) {
      break;
    }
  }
  if (p.area() == 0) {
    // All portals are colinear, so we can use infinitely many colours
    cout << -1 << endl;
    return 0;
  }
  for (size_t i = 2; i < N; i++) {
    // Compute the gcd of all portal
    p = gcd(p, portals[i]);
  }
  // The solution is the area of the gcd parallelogram
  cout << p.area() << endl;
}

Subtask #1
1.0 / 1.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 344 KB Output is correct
18 Correct 0 ms 348 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 344 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 504 KB Output is correct
24 Correct 0 ms 344 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 0 ms 348 KB Output is correct
29 Correct 1 ms 344 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 0 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 1 ms 344 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 0 ms 348 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 40 ms 1884 KB Output is correct
3 Correct 39 ms 1880 KB Output is correct
4 Correct 40 ms 1884 KB Output is correct
5 Correct 42 ms 1884 KB Output is correct
6 Correct 41 ms 1884 KB Output is correct
7 Correct 36 ms 1880 KB Output is correct
8 Correct 38 ms 1888 KB Output is correct
9 Correct 38 ms 1880 KB Output is correct
10 Correct 40 ms 2016 KB Output is correct
11 Correct 38 ms 1884 KB Output is correct
12 Correct 39 ms 1888 KB Output is correct
13 Correct 0 ms 352 KB Output is correct
14 Correct 39 ms 1884 KB Output is correct
15 Correct 41 ms 1880 KB Output is correct
16 Correct 40 ms 1880 KB Output is correct
17 Correct 41 ms 1884 KB Output is correct
18 Correct 41 ms 1884 KB Output is correct
19 Correct 40 ms 1880 KB Output is correct
20 Correct 40 ms 1884 KB Output is correct

Subtask #4
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 344 KB Output is correct
19 Correct 1 ms 344 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 1 ms 600 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 0 ms 344 KB Output is correct
29 Correct 0 ms 348 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 0 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 344 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 344 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 504 KB Output is correct
24 Correct 0 ms 344 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 0 ms 348 KB Output is correct
29 Correct 1 ms 344 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 0 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 1 ms 344 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 0 ms 348 KB Output is correct
42 Correct 0 ms 348 KB Output is correct
43 Correct 0 ms 348 KB Output is correct
44 Correct 1 ms 348 KB Output is correct
45 Correct 0 ms 344 KB Output is correct
46 Correct 0 ms 344 KB Output is correct
47 Correct 0 ms 348 KB Output is correct
48 Correct 0 ms 348 KB Output is correct
49 Correct 0 ms 348 KB Output is correct
50 Correct 0 ms 348 KB Output is correct
51 Correct 0 ms 348 KB Output is correct
52 Correct 0 ms 348 KB Output is correct
53 Correct 0 ms 348 KB Output is correct
54 Correct 0 ms 348 KB Output is correct
55 Correct 0 ms 348 KB Output is correct
56 Correct 0 ms 348 KB Output is correct
57 Correct 0 ms 344 KB Output is correct
58 Correct 1 ms 344 KB Output is correct
59 Correct 0 ms 348 KB Output is correct
60 Correct 0 ms 348 KB Output is correct
61 Correct 0 ms 348 KB Output is correct
62 Correct 0 ms 348 KB Output is correct
63 Correct 0 ms 348 KB Output is correct
64 Correct 1 ms 600 KB Output is correct
65 Correct 0 ms 348 KB Output is correct
66 Correct 0 ms 348 KB Output is correct
67 Correct 0 ms 344 KB Output is correct
68 Correct 0 ms 348 KB Output is correct
69 Correct 0 ms 348 KB Output is correct
70 Correct 0 ms 348 KB Output is correct
71 Correct 0 ms 348 KB Output is correct
72 Correct 0 ms 348 KB Output is correct
73 Correct 0 ms 348 KB Output is correct
74 Correct 0 ms 348 KB Output is correct
75 Correct 0 ms 348 KB Output is correct
76 Correct 0 ms 348 KB Output is correct
77 Correct 0 ms 344 KB Output is correct
78 Correct 0 ms 348 KB Output is correct
79 Correct 0 ms 348 KB Output is correct
80 Correct 1 ms 348 KB Output is correct
81 Correct 1 ms 348 KB Output is correct
82 Correct 1 ms 348 KB Output is correct
83 Correct 1 ms 348 KB Output is correct
84 Correct 0 ms 348 KB Output is correct
85 Correct 1 ms 348 KB Output is correct
86 Correct 1 ms 348 KB Output is correct
87 Correct 1 ms 348 KB Output is correct
88 Correct 0 ms 348 KB Output is correct
89 Correct 1 ms 348 KB Output is correct
90 Correct 1 ms 348 KB Output is correct
91 Correct 1 ms 348 KB Output is correct
92 Correct 1 ms 348 KB Output is correct
93 Correct 1 ms 348 KB Output is correct
94 Correct 1 ms 348 KB Output is correct
95 Correct 1 ms 348 KB Output is correct
96 Correct 1 ms 348 KB Output is correct
97 Correct 1 ms 348 KB Output is correct
98 Correct 2 ms 348 KB Output is correct
99 Correct 2 ms 348 KB Output is correct
100 Correct 1 ms 348 KB Output is correct
101 Correct 1 ms 348 KB Output is correct
102 Correct 1 ms 348 KB Output is correct
103 Correct 1 ms 348 KB Output is correct
104 Correct 1 ms 348 KB Output is correct
105 Correct 1 ms 348 KB Output is correct
106 Correct 1 ms 348 KB Output is correct
107 Correct 1 ms 348 KB Output is correct
108 Correct 1 ms 348 KB Output is correct
109 Correct 1 ms 348 KB Output is correct
110 Correct 1 ms 348 KB Output is correct
111 Correct 0 ms 348 KB Output is correct
112 Correct 0 ms 348 KB Output is correct
113 Correct 0 ms 344 KB Output is correct
114 Correct 1 ms 348 KB Output is correct
115 Correct 1 ms 344 KB Output is correct
116 Correct 1 ms 348 KB Output is correct

Subtask #6
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 344 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 504 KB Output is correct
24 Correct 0 ms 344 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 0 ms 348 KB Output is correct
29 Correct 1 ms 344 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 0 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 1 ms 344 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 40 ms 1884 KB Output is correct
42 Correct 39 ms 1880 KB Output is correct
43 Correct 40 ms 1884 KB Output is correct
44 Correct 42 ms 1884 KB Output is correct
45 Correct 41 ms 1884 KB Output is correct
46 Correct 36 ms 1880 KB Output is correct
47 Correct 38 ms 1888 KB Output is correct
48 Correct 38 ms 1880 KB Output is correct
49 Correct 40 ms 2016 KB Output is correct
50 Correct 38 ms 1884 KB Output is correct
51 Correct 39 ms 1888 KB Output is correct
52 Correct 0 ms 352 KB Output is correct
53 Correct 39 ms 1884 KB Output is correct
54 Correct 41 ms 1880 KB Output is correct
55 Correct 40 ms 1880 KB Output is correct
56 Correct 41 ms 1884 KB Output is correct
57 Correct 41 ms 1884 KB Output is correct
58 Correct 40 ms 1880 KB Output is correct
59 Correct 40 ms 1884 KB Output is correct
60 Correct 0 ms 348 KB Output is correct
61 Correct 0 ms 348 KB Output is correct
62 Correct 0 ms 348 KB Output is correct
63 Correct 0 ms 348 KB Output is correct
64 Correct 1 ms 348 KB Output is correct
65 Correct 0 ms 344 KB Output is correct
66 Correct 0 ms 344 KB Output is correct
67 Correct 0 ms 348 KB Output is correct
68 Correct 0 ms 348 KB Output is correct
69 Correct 0 ms 348 KB Output is correct
70 Correct 0 ms 348 KB Output is correct
71 Correct 0 ms 348 KB Output is correct
72 Correct 0 ms 348 KB Output is correct
73 Correct 0 ms 348 KB Output is correct
74 Correct 0 ms 348 KB Output is correct
75 Correct 0 ms 348 KB Output is correct
76 Correct 0 ms 348 KB Output is correct
77 Correct 0 ms 344 KB Output is correct
78 Correct 1 ms 344 KB Output is correct
79 Correct 0 ms 348 KB Output is correct
80 Correct 0 ms 348 KB Output is correct
81 Correct 0 ms 348 KB Output is correct
82 Correct 0 ms 348 KB Output is correct
83 Correct 0 ms 348 KB Output is correct
84 Correct 1 ms 600 KB Output is correct
85 Correct 0 ms 348 KB Output is correct
86 Correct 0 ms 348 KB Output is correct
87 Correct 0 ms 344 KB Output is correct
88 Correct 0 ms 348 KB Output is correct
89 Correct 0 ms 348 KB Output is correct
90 Correct 0 ms 348 KB Output is correct
91 Correct 0 ms 348 KB Output is correct
92 Correct 0 ms 348 KB Output is correct
93 Correct 0 ms 348 KB Output is correct
94 Correct 0 ms 348 KB Output is correct
95 Correct 0 ms 348 KB Output is correct
96 Correct 0 ms 348 KB Output is correct
97 Correct 0 ms 344 KB Output is correct
98 Correct 0 ms 348 KB Output is correct
99 Correct 0 ms 348 KB Output is correct
100 Correct 1 ms 348 KB Output is correct
101 Correct 1 ms 348 KB Output is correct
102 Correct 1 ms 348 KB Output is correct
103 Correct 1 ms 348 KB Output is correct
104 Correct 0 ms 348 KB Output is correct
105 Correct 1 ms 348 KB Output is correct
106 Correct 1 ms 348 KB Output is correct
107 Correct 1 ms 348 KB Output is correct
108 Correct 0 ms 348 KB Output is correct
109 Correct 1 ms 348 KB Output is correct
110 Correct 1 ms 348 KB Output is correct
111 Correct 1 ms 348 KB Output is correct
112 Correct 1 ms 348 KB Output is correct
113 Correct 1 ms 348 KB Output is correct
114 Correct 1 ms 348 KB Output is correct
115 Correct 1 ms 348 KB Output is correct
116 Correct 1 ms 348 KB Output is correct
117 Correct 1 ms 348 KB Output is correct
118 Correct 2 ms 348 KB Output is correct
119 Correct 2 ms 348 KB Output is correct
120 Correct 1 ms 348 KB Output is correct
121 Correct 1 ms 348 KB Output is correct
122 Correct 1 ms 348 KB Output is correct
123 Correct 1 ms 348 KB Output is correct
124 Correct 1 ms 348 KB Output is correct
125 Correct 1 ms 348 KB Output is correct
126 Correct 1 ms 348 KB Output is correct
127 Correct 1 ms 348 KB Output is correct
128 Correct 1 ms 348 KB Output is correct
129 Correct 1 ms 348 KB Output is correct
130 Correct 1 ms 348 KB Output is correct
131 Correct 0 ms 348 KB Output is correct
132 Correct 0 ms 348 KB Output is correct
133 Correct 0 ms 344 KB Output is correct
134 Correct 1 ms 348 KB Output is correct
135 Correct 1 ms 344 KB Output is correct
136 Correct 1 ms 348 KB Output is correct
137 Correct 40 ms 2000 KB Output is correct
138 Correct 40 ms 1892 KB Output is correct
139 Correct 39 ms 1896 KB Output is correct
140 Correct 39 ms 2008 KB Output is correct
141 Correct 39 ms 1892 KB Output is correct
142 Correct 3 ms 600 KB Output is correct
143 Correct 4 ms 604 KB Output is correct
144 Correct 3 ms 612 KB Output is correct
145 Correct 4 ms 868 KB Output is correct
146 Correct 4 ms 616 KB Output is correct
147 Correct 4 ms 616 KB Output is correct
148 Correct 0 ms 360 KB Output is correct
149 Correct 42 ms 1996 KB Output is correct
150 Correct 51 ms 1896 KB Output is correct
151 Correct 46 ms 2144 KB Output is correct
152 Correct 39 ms 1896 KB Output is correct
153 Correct 40 ms 1888 KB Output is correct
154 Correct 39 ms 2012 KB Output is correct
155 Correct 39 ms 1888 KB Output is correct
156 Correct 36 ms 1640 KB Output is correct
157 Correct 36 ms 1632 KB Output is correct
158 Correct 66 ms 1628 KB Output is correct
159 Correct 36 ms 1628 KB Output is correct
160 Correct 36 ms 1624 KB Output is correct
161 Correct 37 ms 1624 KB Output is correct
162 Correct 46 ms 1628 KB Output is correct
163 Correct 35 ms 1628 KB Output is correct
164 Correct 41 ms 1784 KB Output is correct
165 Correct 49 ms 1624 KB Output is correct
166 Correct 37 ms 1624 KB Output is correct
167 Correct 68 ms 1844 KB Output is correct
168 Correct 37 ms 1624 KB Output is correct
169 Correct 34 ms 1628 KB Output is correct
170 Correct 35 ms 1624 KB Output is correct
171 Correct 0 ms 348 KB Output is correct
172 Correct 0 ms 348 KB Output is correct
173 Correct 0 ms 348 KB Output is correct