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Submission #680774

# Submission time Handle Problem Language Result Execution time Memory
680774 2023-01-11T18:53:00 Z Kamisama None (KOI16_dist) C++14
100 / 100
 363 ms 3156 KB 
#include <iostream>
#include <cstdlib>
#include <climits>
#include <algorithm>
using namespace std;
const int MAXN = 3e4 + 7;

struct Star {
    long long x, y, dx, dy;
    Star(long long x=0, long long y=0, long long dx=0, long long dy=0)
        : x(x), y(y), dx(dx), dy(dy) {}

    Star operator-(const Star &other) const {
        return Star(x - other.x, y - other.y);
    }

    long long operator%(const Star &other) const {
        return x * other.y - y * other.x;
    }
};

int n, t, hull_size;
Star a[MAXN], p[MAXN];
Star convex_hull[MAXN];

int ccw(const Star &A, const Star &B, const Star &C) {
    long long res = A % B + B % C + C % A;
    return (res > 0) - (res < 0);
}

long long get_distance(const Star &A, const Star &B) {
    long long dx = A.x - B.x;
    long long dy = A.y - B.y;
    return dx * dx + dy * dy;
}

long long solve(int k) {
    for(int i = 1; i <= n; i++) {
        p[i] = Star(a[i].x + k * a[i].dx, a[i].y + k * a[i].dy);
    }

    swap(p[1], *min_element(p + 1, p + n + 1, [](const Star &A, const Star &B) {
        return A.x < B.x || (A.x == B.x && A.y < B.y);
    }));
    sort(p + 2, p + n + 1, [](const Star &A, const Star &B) {
        int not_linear = ccw(p[1], A, B);
        if(not_linear) return not_linear > 0;
        return get_distance(p[1], A) < get_distance(p[1], B);
    });

    hull_size = 0;
    for(int i = 1; i <= n; i++) {
        while(hull_size >= 2 && ccw(convex_hull[hull_size - 1], convex_hull[hull_size], p[i]) <= 0){
            hull_size--;
        }
        convex_hull[++hull_size] = p[i];
    }

    long long res = 0;
    for(int i = 1, j = 1; i <= hull_size; i++) {
        while(j < hull_size && ccw(Star(0, 0), convex_hull[i + 1] - convex_hull[i], convex_hull[j + 1] - convex_hull[j]) >= 0) {
            res = max(res, get_distance(convex_hull[i], convex_hull[j]));
            j++;
        }
        res = max(res, get_distance(convex_hull[i], convex_hull[j]));
    }

    return res;
}

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

    cin >> n >> t;
    for(int i = 1; i <= n; i++) cin >> a[i].x >> a[i].y >> a[i].dx >> a[i].dy;

    int l = 0, r = t;
    while(r - l >= 3) {
        int m1 = (2 * l + r) / 3;
        int m2 = (l + 2 *  r) / 3;
        if(solve(m1) > solve(m2)) l = m1;
        else r = m2;
    }

    int date = 0;
    long long res = LLONG_MAX;
    for(int k = l; k <= r; k++) {
        long long potential = solve(k);
        if(res > potential) {
            res = potential;
            date = k;
        }
    }

    cout << date << '\n' <<  res;

    return 0;
}

Subtask #1
2.0 / 2.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 2 ms 3028 KB Output is correct
3 Correct 1 ms 3028 KB Output is correct
4 Correct 2 ms 3028 KB Output is correct
5 Correct 2 ms 3028 KB Output is correct
6 Correct 2 ms 3156 KB Output is correct
7 Correct 2 ms 3028 KB Output is correct
8 Correct 2 ms 3044 KB Output is correct
9 Correct 1 ms 3028 KB Output is correct
10 Correct 2 ms 3028 KB Output is correct

Subtask #2
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 2 ms 3028 KB Output is correct
3 Correct 1 ms 3028 KB Output is correct
4 Correct 2 ms 3028 KB Output is correct
5 Correct 2 ms 3028 KB Output is correct
6 Correct 2 ms 3156 KB Output is correct
7 Correct 2 ms 3028 KB Output is correct
8 Correct 2 ms 3044 KB Output is correct
9 Correct 1 ms 3028 KB Output is correct
10 Correct 2 ms 3028 KB Output is correct
11 Correct 9 ms 3028 KB Output is correct
12 Correct 11 ms 3140 KB Output is correct
13 Correct 8 ms 3028 KB Output is correct
14 Correct 9 ms 3028 KB Output is correct
15 Correct 11 ms 3140 KB Output is correct
16 Correct 13 ms 3144 KB Output is correct
17 Correct 9 ms 3136 KB Output is correct
18 Correct 6 ms 3028 KB Output is correct
19 Correct 7 ms 3144 KB Output is correct
20 Correct 12 ms 3028 KB Output is correct

Subtask #3
39.0 / 39.0

# Verdict Execution time Memory Grader output
1 Correct 83 ms 3120 KB Output is correct
2 Correct 70 ms 3028 KB Output is correct
3 Correct 70 ms 3116 KB Output is correct
4 Correct 61 ms 3028 KB Output is correct
5 Correct 88 ms 3124 KB Output is correct
6 Correct 88 ms 3028 KB Output is correct
7 Correct 59 ms 3028 KB Output is correct
8 Correct 46 ms 3120 KB Output is correct
9 Correct 63 ms 3028 KB Output is correct
10 Correct 93 ms 3120 KB Output is correct

Subtask #4
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 2 ms 3028 KB Output is correct
3 Correct 1 ms 3028 KB Output is correct
4 Correct 2 ms 3028 KB Output is correct
5 Correct 2 ms 3028 KB Output is correct
6 Correct 2 ms 3156 KB Output is correct
7 Correct 2 ms 3028 KB Output is correct
8 Correct 2 ms 3044 KB Output is correct
9 Correct 1 ms 3028 KB Output is correct
10 Correct 2 ms 3028 KB Output is correct
11 Correct 9 ms 3028 KB Output is correct
12 Correct 11 ms 3140 KB Output is correct
13 Correct 8 ms 3028 KB Output is correct
14 Correct 9 ms 3028 KB Output is correct
15 Correct 11 ms 3140 KB Output is correct
16 Correct 13 ms 3144 KB Output is correct
17 Correct 9 ms 3136 KB Output is correct
18 Correct 6 ms 3028 KB Output is correct
19 Correct 7 ms 3144 KB Output is correct
20 Correct 12 ms 3028 KB Output is correct
21 Correct 83 ms 3120 KB Output is correct
22 Correct 70 ms 3028 KB Output is correct
23 Correct 70 ms 3116 KB Output is correct
24 Correct 61 ms 3028 KB Output is correct
25 Correct 88 ms 3124 KB Output is correct
26 Correct 88 ms 3028 KB Output is correct
27 Correct 59 ms 3028 KB Output is correct
28 Correct 46 ms 3120 KB Output is correct
29 Correct 63 ms 3028 KB Output is correct
30 Correct 93 ms 3120 KB Output is correct
31 Correct 354 ms 3120 KB Output is correct
32 Correct 333 ms 3124 KB Output is correct
33 Correct 335 ms 3124 KB Output is correct
34 Correct 326 ms 3116 KB Output is correct
35 Correct 363 ms 3116 KB Output is correct
36 Correct 294 ms 3116 KB Output is correct
37 Correct 304 ms 3120 KB Output is correct
38 Correct 181 ms 3116 KB Output is correct
39 Correct 264 ms 3128 KB Output is correct
40 Correct 350 ms 3132 KB Output is correct
41 Correct 335 ms 3124 KB Output is correct
42 Correct 359 ms 3120 KB Output is correct