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답안 #985637

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
985637 2024-05-18T11:35:53 Z alextodoran Fences (JOI18_fences) C++17
100 / 100
 330 ms 8992 KB 
/**
 _  _   __  _ _ _  _  _ _
 |a  ||t  ||o    d | |o  |
| __    _| | _ | __|  _ |
| __ |/_  | __  /__\ / _\|

**/

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;

const int N_MAX = 100;
const int V_MAX = N_MAX * 4 + 4;
const ld INF = LLONG_MAX;
const int R = 40;

int N, S;
struct Point {
    ld x, y;
};
ld dist (Point A, Point B) {
    return sqrt((A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y));
}
struct Segment {
    Point A, B;
    ld len () {
        return dist(A, B);
    }
};
Segment fence[N_MAX + 2];

Point project (Point P, Segment s) {
    if (s.A.x == s.B.x) {
        return Point{s.A.x, P.y};
    } else if (s.A.y == s.B.y) {
        return Point{P.x, s.A.y};
    } else {
        ld mAB = (ld) (s.A.y - s.B.y) / (s.A.x - s.B.x);
        ld mPQ = -1 / mAB;
        Point Q;
        Q.x = (P.y - s.A.y - P.x * mPQ + s.A.x * mAB) / (mAB - mPQ);
        Q.y = P.y + (Q.x - P.x) * mPQ;
        return Q;
    }
}
bool is_inside (Point P, Segment s) {
    return (min(s.A.x, s.B.x) <= P.x && P.x <= max(s.A.x, s.B.x)
         && min(s.A.y, s.B.y) <= P.y && P.y <= max(s.A.y, s.B.y));
}
bool check (Segment s) {
    Point mid = Point{(s.A.x + s.B.x) / 2, (s.A.y + s.B.y) / 2};
    if (-S < mid.x && mid.x < S && -S < mid.y && mid.y < S) {
        return false;
    }
    for (int side = 0; side < 4; side++) {
        if (s.A.y > s.B.y) {
            swap(s.A, s.B);
        }
        if (s.A.y < S && S < s.B.y) {
            ld x;
            if (s.A.x != s.B.x) {
                x = s.A.x + (ld) (s.B.x - s.A.x) * (S - s.A.y) / (s.B.y - s.A.y);
            } else {
                x = s.A.x;
            }
            if (-S < x && x < S) {
                return false;
            }
        }
        swap(s.A.x, s.A.y); s.A.x *= -1;
        swap(s.B.x, s.B.y); s.B.x *= -1;
    }
    return true;
}

Point corner[4];

int V;
Point get_point (int u) {
    if (u <= N * 2) {
        if (u % 2 == 1) {
            return fence[u / 2 + 1].A;
        } else {
            return fence[u / 2].B;
        }
    } else {
        return corner[u - N * 2 - 1];
    }
}
struct Edge {
    int to;
    ld len;
    bool trigo;
};
bool is_trigo (Segment s) {
    return (s.A.x * s.B.y - s.A.y * s.B.x > 0);
}
vector <Edge> out[V_MAX + 2];
void add_edge (int u, int v, Segment s, bool is_fence = false) {
    Point A = s.A, P = s.B, B = get_point(v);
    ld len = (is_fence == false ? s.len() : 0);
    bool trigo = is_trigo(Segment{A, B});
    if (P.x != B.x || P.y != B.y) {
        if (is_trigo(Segment{A, P}) != trigo && is_trigo(Segment{P, B}) != trigo) {
            trigo = !trigo;
        }
    }
    out[u].push_back(Edge{v, len, trigo});
    swap(s.A, s.B); trigo = !trigo;
    out[v].push_back(Edge{u, len, trigo});
}

int get_quad (Point P) {
    if (P.x >= 0 && P.y > 0) {
        return 0;
    } else if (P.x < 0 && P.y >= 0) {
        return 1;
    } else if (P.x <= 0 && P.y < 0) {
        return 2;
    } else {
        return 3;
    }
}

ld min_dist[V_MAX + 2][R * 2 + 2];
bool seen[V_MAX + 2][R * 2 + 2];

struct Path {
    int u;
    int var;
    ld len;
};
bool operator < (const Path &p1, const Path &p2) {
    return p1.len > p2.len;
}

ld answer = LLONG_MAX;

void Dijkstra (int start) {
    priority_queue <Path> q;
    for (int u = 1; u <= V; u++) {
        for (int var = -R; var <= R; var++) {
            min_dist[u][var + R] = INF;
            seen[u][var + R] = false;
        }
    }
    min_dist[start][0 + R] = 0;
    q.push(Path{start, 0, 0});
    while (q.empty() == false) {
        Path p = q.top(); q.pop();
        if (seen[p.u][p.var] == true) {
            continue;
        }
        seen[p.u][p.var] = true;
        if (p.len > answer) {
            continue;
        }
        if (p.u == start && p.var == 4) {
            answer = p.len;
        }
        Point A = get_point(p.u);
        for (Edge e : out[p.u]) {
            Point B = get_point(e.to);
            Path pe; pe.u = e.to; pe.len = p.len + e.len;
            int delta = get_quad(B) - get_quad(A);
            if (e.trigo == true) {
                if (delta < 0) {
                    delta += 4;
                }
            } else {
                if (delta > 0) {
                    delta -= 4;
                }
            }
            pe.var = p.var + delta;
            if (-R <= pe.var && pe.var <= R) {
                if (pe.len < min_dist[pe.u][pe.var + R]) {
                    min_dist[pe.u][pe.var + R] = pe.len;
                    q.push(pe);
                }
            }
        }
    }
}

int main () {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(10);

    cin >> N >> S;
    for (int i = 1; i <= N; i++) {
        cin >> fence[i].A.x >> fence[i].A.y;
        cin >> fence[i].B.x >> fence[i].B.y;
    }
    corner[0] = Point{S, S};
    corner[1] = Point{-S, S};
    corner[2] = Point{-S, -S};
    corner[3] = Point{S, -S};
    for (int c = 0; c < 4; c++) {
        add_edge(N * 2 + 1 + c, N * 2 + 1 + (c + 1) % 4, Segment{corner[c], corner[(c + 1) % 4]});
    }
    V = N * 2 + 4;
    for (int i = 1; i <= N; i++) {
        add_edge(i * 2 - 1, i * 2, fence[i], true);
        for (int j = i + 1; j <= N; j++) {
            Segment A1A2 = Segment{fence[i].A, fence[j].A};
            if (check(A1A2) == true) {
                add_edge(i * 2 - 1, j * 2 - 1, A1A2);
            }
            Segment A1B2 = Segment{fence[i].A, fence[j].B};
            if (check(A1B2) == true) {
                add_edge(i * 2 - 1, j * 2, A1B2);
            }
            Segment B1A2 = Segment{fence[i].B, fence[j].A};
            if (check(B1A2) == true) {
                add_edge(i * 2, j * 2 - 1, B1A2);
            }
            Segment B1B2 = Segment{fence[i].B, fence[j].B};
            if (check(B1B2) == true) {
                add_edge(i * 2, j * 2, B1B2);
            }
        }
    }
    for (int i = 1; i <= N; i++) {
        for (int j = 1; j <= N; j++) {
            if (i != j) {
                Point P = project(fence[i].A, fence[j]);
                Segment AP = Segment{fence[i].A, P};
                if (is_inside(P, fence[j]) == true && check(AP) == true) {
                    add_edge(i * 2 - 1, j * 2 - 1, AP);
                    add_edge(i * 2 - 1, j * 2, AP);
                }
                Point Q = project(fence[i].B, fence[j]);
                Segment BQ = Segment{fence[i].B, Q};
                if (is_inside(Q, fence[j]) == true && check(BQ) == true) {
                    add_edge(i * 2, j * 2 - 1, BQ);
                    add_edge(i * 2, j * 2, BQ);
                }
            }
        }
        for (int c = 0; c < 4; c++) {
            Segment AC = Segment{fence[i].A, corner[c]};
            Segment BC = Segment{fence[i].B, corner[c]};
            if (check(AC) == true) {
                add_edge(i * 2 - 1, N * 2 + 1 + c, AC);
            }
            if (check(BC) == true) {
                add_edge(i * 2, N * 2 + 1 + c, BC);
            }
        }
        for (int c = 0; c < 4; c++) {
            Point P = project(corner[c], fence[i]);
            Segment CP = Segment{corner[c], P};
            if (is_inside(P, fence[i]) == true && check(CP) == true) {
                add_edge(N * 2 + 1 + c, i * 2 - 1, CP);
                add_edge(N * 2 + 1 + c, i * 2, CP);
            }
        }
    }
    for (int u = 1; u <= V; u++) {
        Point A = get_point(u);
        Dijkstra(u);
    }
    cout << answer << "\n";

    return 0;
}

Compilation message

fences.cpp: In function 'int main()':
fences.cpp:200:23: warning: narrowing conversion of 'S' from 'int' to 'ld' {aka 'long double'} [-Wnarrowing]
  200 |     corner[0] = Point{S, S};
      |                       ^
fences.cpp:200:26: warning: narrowing conversion of 'S' from 'int' to 'ld' {aka 'long double'} [-Wnarrowing]
  200 |     corner[0] = Point{S, S};
      |                          ^
fences.cpp:201:23: warning: narrowing conversion of '- S' from 'int' to 'ld' {aka 'long double'} [-Wnarrowing]
  201 |     corner[1] = Point{-S, S};
      |                       ^~
fences.cpp:201:27: warning: narrowing conversion of 'S' from 'int' to 'ld' {aka 'long double'} [-Wnarrowing]
  201 |     corner[1] = Point{-S, S};
      |                           ^
fences.cpp:202:23: warning: narrowing conversion of '- S' from 'int' to 'ld' {aka 'long double'} [-Wnarrowing]
  202 |     corner[2] = Point{-S, -S};
      |                       ^~
fences.cpp:202:27: warning: narrowing conversion of '- S' from 'int' to 'ld' {aka 'long double'} [-Wnarrowing]
  202 |     corner[2] = Point{-S, -S};
      |                           ^~
fences.cpp:203:23: warning: narrowing conversion of 'S' from 'int' to 'ld' {aka 'long double'} [-Wnarrowing]
  203 |     corner[3] = Point{S, -S};
      |                       ^
fences.cpp:203:26: warning: narrowing conversion of '- S' from 'int' to 'ld' {aka 'long double'} [-Wnarrowing]
  203 |     corner[3] = Point{S, -S};
      |                          ^~
fences.cpp:266:15: warning: variable 'A' set but not used [-Wunused-but-set-variable]
  266 |         Point A = get_point(u);
      |               ^

Subtask #1
18.0 / 18.0

# 결과 실행 시간 메모리 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 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 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 1 ms 348 KB Output is correct
10 Correct 1 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 344 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 344 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct

Subtask #2
33.0 / 33.0

# 결과 실행 시간 메모리 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 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 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 1 ms 348 KB Output is correct
10 Correct 1 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 344 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 344 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 1 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 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 1 ms 532 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 1 ms 348 KB Output is correct
28 Correct 1 ms 348 KB Output is correct
29 Correct 1 ms 344 KB Output is correct
30 Correct 1 ms 348 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Correct 1 ms 348 KB Output is correct
33 Correct 1 ms 348 KB Output is correct
34 Correct 1 ms 348 KB Output is correct
35 Correct 1 ms 348 KB Output is correct
36 Correct 1 ms 348 KB Output is correct
37 Correct 1 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 1 ms 348 KB Output is correct
40 Correct 1 ms 348 KB Output is correct
41 Correct 1 ms 348 KB Output is correct
42 Correct 1 ms 348 KB Output is correct
43 Correct 2 ms 348 KB Output is correct

Subtask #3
49.0 / 49.0

# 결과 실행 시간 메모리 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 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 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 1 ms 348 KB Output is correct
10 Correct 1 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 344 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 344 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 1 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 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 1 ms 532 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 1 ms 348 KB Output is correct
28 Correct 1 ms 348 KB Output is correct
29 Correct 1 ms 344 KB Output is correct
30 Correct 1 ms 348 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Correct 1 ms 348 KB Output is correct
33 Correct 1 ms 348 KB Output is correct
34 Correct 1 ms 348 KB Output is correct
35 Correct 1 ms 348 KB Output is correct
36 Correct 1 ms 348 KB Output is correct
37 Correct 1 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 1 ms 348 KB Output is correct
40 Correct 1 ms 348 KB Output is correct
41 Correct 1 ms 348 KB Output is correct
42 Correct 1 ms 348 KB Output is correct
43 Correct 2 ms 348 KB Output is correct
44 Correct 132 ms 4956 KB Output is correct
45 Correct 197 ms 3748 KB Output is correct
46 Correct 189 ms 3164 KB Output is correct
47 Correct 160 ms 2688 KB Output is correct
48 Correct 158 ms 4956 KB Output is correct
49 Correct 210 ms 3956 KB Output is correct
50 Correct 207 ms 3268 KB Output is correct
51 Correct 169 ms 2596 KB Output is correct
52 Correct 191 ms 3332 KB Output is correct
53 Correct 150 ms 3316 KB Output is correct
54 Correct 152 ms 3592 KB Output is correct
55 Correct 238 ms 3800 KB Output is correct
56 Correct 216 ms 3680 KB Output is correct
57 Correct 195 ms 3260 KB Output is correct
58 Correct 200 ms 3432 KB Output is correct
59 Correct 213 ms 3764 KB Output is correct
60 Correct 236 ms 4052 KB Output is correct
61 Correct 238 ms 3756 KB Output is correct
62 Correct 1 ms 344 KB Output is correct
63 Correct 1 ms 348 KB Output is correct
64 Correct 323 ms 4252 KB Output is correct
65 Correct 261 ms 2536 KB Output is correct
66 Correct 165 ms 2396 KB Output is correct
67 Correct 330 ms 8992 KB Output is correct
68 Correct 261 ms 6468 KB Output is correct
69 Correct 284 ms 3952 KB Output is correct
70 Correct 231 ms 3456 KB Output is correct
71 Correct 323 ms 3692 KB Output is correct
72 Correct 159 ms 2692 KB Output is correct