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Submission #386346

# Submission time Handle Problem Language Result Execution time Memory
386346 2021-04-06T12:25:09 Z model_code Geometrija (COCI21_geometrija) C++17
110 / 110
 696 ms 876 KB 
#include <bits/stdc++.h>
using namespace std;

#define TRACE(x) cerr << #x << " = " << x << endl
#define _ << " _ " <<

#define fi first
#define se second

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef vector<int> vi;

int sign(ll x) {
    if (x > 0) return 1;
    if (x < 0) return -1;
    return 0;
}

int ccw(const pii& a, const pii& b, const pii& c) {
    return sign((ll)a.fi * (b.se - c.se) +
                (ll)b.fi * (c.se - a.se) +
                (ll)c.fi * (a.se - b.se));
}


bool intersect(const pii& a, const pii& b, const pii& c, const pii& d) {
    if (a == b || a == c || a == d || b == c || b == d || c == d) return false;
    return ccw(a, b, c) != ccw(a, b, d) && ccw(c, d, a) != ccw(c, d, b);
}


int n;
vector<pii> pts;

int ccw(int i, int j, int k) {
    return ccw(pts[i], pts[j], pts[k]);
}

bool intersect(int i, int j, int k, int l) {
    return intersect(pts[i], pts[j], pts[k], pts[l]);
}


int cmp_center;
bool cmp(int i, int j) {
    return ccw(cmp_center, i, j) == 1;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    cin >> n;
    pts.resize(n);
    for (auto& it : pts) cin >> it.fi >> it.se;

    vector<pii> edges;
    set<vi> triangles;

    sort(pts.begin(), pts.end());
    vector<bool> on_hull(n);
    int last = 0;
    do {
        on_hull[last] = true;

        int nxt = 0;
        if (last == 0) nxt = 1;

        for (int i = 0; i < n; i++)
            if (ccw(last, nxt, i) == 1)
                nxt = i;

        edges.push_back({last, nxt});
        if (last != 0 && nxt != 0)
            triangles.insert({0, nxt, last});

        last = nxt;
    } while (last != 0);

    for (int i = 0; i < n; i++) {
        if (on_hull[i]) continue;

        vi tr;
        for (auto& it : triangles)
            if (ccw(it[0], it[1], i) == 1 &&
                ccw(it[1], it[2], i) == 1 &&
                ccw(it[2], it[0], i) == 1) {
                tr = it;
                break;
            }

        assert(!tr.empty());
        triangles.erase(tr);
        triangles.insert({tr[0], tr[1], i});
        triangles.insert({tr[1], tr[2], i});
        triangles.insert({tr[2], tr[0], i});

        edges.push_back({i, tr[0]});
        edges.push_back({i, tr[1]});
        edges.push_back({i, tr[2]});
    }

    int sol = 0;
    for (auto& edg : edges) {
        int p = edg.fi, q = edg.se;
        vi a, b;
        for (int i = 0; i < n; i++) {
            if (ccw(p, q, i) == -1) a.push_back(i);
            if (ccw(p, q, i) == +1) b.push_back(i);
        }

        cmp_center = p;
        sort(a.begin(), a.end(), cmp);
        sort(b.begin(), b.end(), cmp);

        vi c = b;
        cmp_center = q;
        sort(c.begin(), c.end(), cmp);
        vi pos(n);
        for (int i = 0; i < (int)c.size(); i++) pos[c[i]] = i;

        bool ok = true;
        int j = 0, k = -1;
        for (int i = 0; i < (int)a.size(); i++) {
            while (j < (int)b.size() && ccw(a[i], p, b[j]) == -1) {
                k = max(k, pos[b[j]]);
                j++;
            }

            if (k != -1)
                ok &= !intersect(p, q, a[i], c[k]);
        }

        if (ok) sol++;
    }

    cout << sol << '\n';

    return 0;
}

Subtask #1
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 364 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 1 ms 364 KB Output is correct
4 Correct 1 ms 364 KB Output is correct
5 Correct 1 ms 364 KB Output is correct
6 Correct 1 ms 364 KB Output is correct
7 Correct 1 ms 364 KB Output is correct
8 Correct 1 ms 364 KB Output is correct
9 Correct 1 ms 364 KB Output is correct
10 Correct 1 ms 364 KB Output is correct
11 Correct 1 ms 364 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 364 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 1 ms 364 KB Output is correct
4 Correct 1 ms 364 KB Output is correct
5 Correct 1 ms 364 KB Output is correct
6 Correct 1 ms 364 KB Output is correct
7 Correct 1 ms 364 KB Output is correct
8 Correct 1 ms 364 KB Output is correct
9 Correct 1 ms 364 KB Output is correct
10 Correct 1 ms 364 KB Output is correct
11 Correct 1 ms 364 KB Output is correct
12 Correct 19 ms 364 KB Output is correct
13 Correct 20 ms 364 KB Output is correct
14 Correct 16 ms 364 KB Output is correct
15 Correct 14 ms 364 KB Output is correct
16 Correct 6 ms 364 KB Output is correct
17 Correct 16 ms 364 KB Output is correct
18 Correct 17 ms 364 KB Output is correct
19 Correct 18 ms 364 KB Output is correct
20 Correct 20 ms 364 KB Output is correct
21 Correct 23 ms 364 KB Output is correct
22 Correct 17 ms 364 KB Output is correct
23 Correct 18 ms 364 KB Output is correct

Subtask #3
60.0 / 60.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 364 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 1 ms 364 KB Output is correct
4 Correct 1 ms 364 KB Output is correct
5 Correct 1 ms 364 KB Output is correct
6 Correct 1 ms 364 KB Output is correct
7 Correct 1 ms 364 KB Output is correct
8 Correct 1 ms 364 KB Output is correct
9 Correct 1 ms 364 KB Output is correct
10 Correct 1 ms 364 KB Output is correct
11 Correct 1 ms 364 KB Output is correct
12 Correct 19 ms 364 KB Output is correct
13 Correct 20 ms 364 KB Output is correct
14 Correct 16 ms 364 KB Output is correct
15 Correct 14 ms 364 KB Output is correct
16 Correct 6 ms 364 KB Output is correct
17 Correct 16 ms 364 KB Output is correct
18 Correct 17 ms 364 KB Output is correct
19 Correct 18 ms 364 KB Output is correct
20 Correct 20 ms 364 KB Output is correct
21 Correct 23 ms 364 KB Output is correct
22 Correct 17 ms 364 KB Output is correct
23 Correct 18 ms 364 KB Output is correct
24 Correct 616 ms 772 KB Output is correct
25 Correct 612 ms 748 KB Output is correct
26 Correct 610 ms 620 KB Output is correct
27 Correct 618 ms 876 KB Output is correct
28 Correct 615 ms 664 KB Output is correct
29 Correct 437 ms 620 KB Output is correct
30 Correct 433 ms 620 KB Output is correct
31 Correct 139 ms 516 KB Output is correct
32 Correct 146 ms 492 KB Output is correct
33 Correct 386 ms 620 KB Output is correct
34 Correct 369 ms 492 KB Output is correct
35 Correct 552 ms 748 KB Output is correct
36 Correct 602 ms 640 KB Output is correct
37 Correct 636 ms 620 KB Output is correct
38 Correct 696 ms 664 KB Output is correct
39 Correct 575 ms 652 KB Output is correct
40 Correct 549 ms 784 KB Output is correct
41 Correct 642 ms 748 KB Output is correct
42 Correct 667 ms 660 KB Output is correct