oj.uz

Submission #510751

# Submission time Handle Problem Language Result Execution time Memory
510751 2022-01-15T02:50:45 Z KoD Kućice (COCI21_kucice) C++17
110 / 110
 432 ms 460 KB 
#include <bits/stdc++.h>

using std::vector;
using std::array;
using std::pair;
using std::tuple;

using i64 = std::int64_t;

struct Point {
    int x, y;
    Point() : x(0), y(0) {}
    Point(int x, int y) : x(x), y(y) {}
    friend Point operator-(const Point& p, const Point& q) {
        return Point(p.x - q.x, p.y - q.y);
    }
    friend i64 cross(const Point& p, const Point& q) {
        return (i64)p.x * q.y - (i64)p.y * q.x;
    }
};

constexpr int MOD = 1000000007;

struct Fp {
    int x;
    Fp(int x = 0) : x(x) {}
    Fp& operator+=(const Fp& t) {
        if ((x += t.x) >= MOD) x -= MOD;
        return *this;
    }
    Fp& operator-=(const Fp& t) {
        if ((x -= t.x) < 0) x += MOD;
        return *this;
    }
    Fp& operator*=(const Fp& t) {
        x = (i64)x * t.x % MOD;
        return *this;
    }
    Fp operator+(const Fp& t) const {
        return Fp(*this) += t;
    }
    Fp operator-(const Fp& t) const {
        return Fp(*this) -= t;
    }
    Fp operator*(const Fp& t) const {
        return Fp(*this) *= t;
    }
    Fp pow(int e) const {
        Fp ret(1), mul(*this);
        while (e > 0) {
            if (e & 1) ret *= mul;
            mul *= mul;
            e >>= 1;
        }
        return ret;
    }
    Fp inv() const {
        return pow(MOD - 2);
    }
};

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int N;
    std::cin >> N;
    vector<Point> P(N);
    for (auto& [x, y] : P) {
        std::cin >> x >> y;
    }
    Fp ans = 0;
    for (int pivot = 0; pivot < N; ++pivot) {
        ans += Fp(2).pow(N - 1);
        vector<Point> above, below;
        for (int i = 0; i < N; ++i) {
            if (i != pivot) {
                const Point p = P[i] - P[pivot];
                if (p.y > 0 or (p.x >= 0 and p.y == 0)) {
                    above.push_back(p);
                } else {
                    below.push_back(p);
                }
            }
        }
        std::sort(above.begin(), above.end(), [&](const Point& p, const Point& q) {
            return cross(p, q) > 0;
        });
        std::sort(below.begin(), below.end(), [&](const Point& p, const Point& q) {
            return cross(p, q) > 0;
        });
        const int n = above.size(), m = below.size();
        vector<int> to(n), from(m);
        for (int i = 0, j = 0; i < n; ++i) {
            while (j < m and cross(above[i], below[j]) > 0) {
                j += 1;
            }
            to[i] = j;
        }
        for (int j = 0, i = 0; j < m; ++j) {
            while (i < n and cross(below[j], above[i]) > 0) {
                i += 1;
            }
            from[j] = i;
        }
        // for (int l = 0; l < n; ++l) {
        //     for (int r = to[l]; r < m; ++r) {
        //         const int all = (n - l - 1) + (m - r - 1) + to[l];
        //         const int between = to[l] + (n - from[r]);
        //         ans += Fp(2).pow(all);
        //         ans -= Fp(2).pow(all - between);
        //     }
        // }
        {
            int l = 0;
            Fp coeff = 0;
            for (int r = 0; r < m; ++r) {
                while (l < from[r]) {
                    coeff += Fp(2).pow(l).inv();
                    l += 1;
                }
                ans -= coeff * Fp(2).pow(from[r] - 1 + m - r - 1);
            }
        }
        {
            int r = m;
            Fp coeff = 0;
            for (int l = n - 1; l >= 0; --l) {
                while (to[l] < r) {
                    r -= 1;
                    coeff += Fp(2).pow(r).inv();
                }
                ans += coeff * Fp(2).pow(n - l - 1 + m - 1 + to[l]);
            }
        }
    }
    std::cout << ans.x << '\n';
    return 0;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 277 ms 360 KB Output is correct
7 Correct 309 ms 360 KB Output is correct
8 Correct 285 ms 360 KB Output is correct
9 Correct 327 ms 356 KB Output is correct
10 Correct 261 ms 360 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 256 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 247 ms 364 KB Output is correct
7 Correct 292 ms 364 KB Output is correct
8 Correct 274 ms 372 KB Output is correct
9 Correct 320 ms 388 KB Output is correct
10 Correct 287 ms 372 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct

Subtask #4
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 0 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 3 ms 204 KB Output is correct
23 Correct 3 ms 204 KB Output is correct
24 Correct 4 ms 256 KB Output is correct
25 Correct 4 ms 204 KB Output is correct
26 Correct 4 ms 204 KB Output is correct
27 Correct 4 ms 204 KB Output is correct
28 Correct 3 ms 204 KB Output is correct
29 Correct 3 ms 204 KB Output is correct
30 Correct 3 ms 204 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 277 ms 360 KB Output is correct
7 Correct 309 ms 360 KB Output is correct
8 Correct 285 ms 360 KB Output is correct
9 Correct 327 ms 356 KB Output is correct
10 Correct 261 ms 360 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 256 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 247 ms 364 KB Output is correct
17 Correct 292 ms 364 KB Output is correct
18 Correct 274 ms 372 KB Output is correct
19 Correct 320 ms 388 KB Output is correct
20 Correct 287 ms 372 KB Output is correct
21 Correct 0 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 0 ms 204 KB Output is correct
25 Correct 1 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 1 ms 204 KB Output is correct
28 Correct 1 ms 204 KB Output is correct
29 Correct 1 ms 204 KB Output is correct
30 Correct 0 ms 204 KB Output is correct
31 Correct 1 ms 204 KB Output is correct
32 Correct 1 ms 204 KB Output is correct
33 Correct 1 ms 204 KB Output is correct
34 Correct 1 ms 204 KB Output is correct
35 Correct 1 ms 204 KB Output is correct
36 Correct 1 ms 204 KB Output is correct
37 Correct 0 ms 204 KB Output is correct
38 Correct 1 ms 204 KB Output is correct
39 Correct 1 ms 204 KB Output is correct
40 Correct 1 ms 204 KB Output is correct
41 Correct 1 ms 204 KB Output is correct
42 Correct 3 ms 204 KB Output is correct
43 Correct 3 ms 204 KB Output is correct
44 Correct 4 ms 256 KB Output is correct
45 Correct 4 ms 204 KB Output is correct
46 Correct 4 ms 204 KB Output is correct
47 Correct 4 ms 204 KB Output is correct
48 Correct 3 ms 204 KB Output is correct
49 Correct 3 ms 204 KB Output is correct
50 Correct 3 ms 204 KB Output is correct
51 Correct 1 ms 288 KB Output is correct
52 Correct 0 ms 204 KB Output is correct
53 Correct 1 ms 212 KB Output is correct
54 Correct 1 ms 204 KB Output is correct
55 Correct 1 ms 204 KB Output is correct
56 Correct 1 ms 204 KB Output is correct
57 Correct 311 ms 368 KB Output is correct
58 Correct 261 ms 388 KB Output is correct
59 Correct 432 ms 372 KB Output is correct
60 Correct 319 ms 376 KB Output is correct
61 Correct 417 ms 376 KB Output is correct
62 Correct 366 ms 368 KB Output is correct
63 Correct 301 ms 376 KB Output is correct
64 Correct 374 ms 380 KB Output is correct
65 Correct 340 ms 460 KB Output is correct