Submission #998078

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
998078	2024-06-13T09:23:12 Z	arbuzick	Izvanzemaljci (COI21_izvanzemaljci)	C++17	26 / 100	3000 ms	8264 KB

izvanzemaljci

#include <bits/stdc++.h>
#define int long long

using namespace std;

constexpr long long inf = (long long)1e18 + 7;

constexpr long long vl = 3000000001;

struct Point {
    int x, y;

    Point(int _x = 0, int _y = 0) {
        x = _x, y = _y;
    }
};

struct Answer {
    vector<pair<Point, int>> squares;
    int mx;

    Answer() {
        mx = 0;
    }

    void add(Point p, int side) {
        squares.emplace_back(p, side);
        mx = max(mx, side);
    }

    bool operator<(Answer b) {
        return mx < b.mx;
    }
};

Answer split2(vector<Point> a, long long mn_x, long long mx_x, long long mn_y, long long mx_y) {
    auto check = [&](Answer ans) -> bool {
        for (int i = 0; i < (int)ans.squares.size(); ++i) {
            if (ans.squares[i].first.x <= mn_x || ans.squares[i].first.x + ans.squares[i].second >= mx_x) {
                return false;
            }
            if (ans.squares[i].first.y < mn_y || ans.squares[i].first.y + ans.squares[i].second >= mx_y) {
                return false;
            }
        }
        return true;
    };
    int n = a.size();
    sort(a.begin(), a.end(), [&](Point a, Point b) -> bool {
        return a.x < b.x;
    });
    vector<int> pr_mn(n + 1, inf), pr_mx(n + 1, -inf), suf_mn(n + 1, inf), suf_mx(n + 1, -inf);
    for (int i = 0; i < n; ++i) {
        pr_mn[i + 1] = min(pr_mn[i], a[i].y);
        pr_mx[i + 1] = max(pr_mx[i], a[i].y);
    }
    for (int i = n - 1; i >= 0; --i) {
        suf_mn[i] = min(suf_mn[i + 1], a[i].y);
        suf_mx[i] = max(suf_mx[i + 1], a[i].y);
    }
    Answer ans;
    ans.add(Point(0, 0), inf);
    for (int i = 0; i + 1 < n; ++i) {
        if (a[i].x == a[i + 1].x) {
            continue;
        }
        Answer ans_nw;
        int side1 = max(1LL, max(a[i].x - a[0].x, pr_mx[i + 1] - pr_mn[i + 1]));
        Point p1(a[i].x - side1, pr_mn[i + 1]);
        if (p1.x <= mn_x) {
            p1.x = a[i + 1].x - 1 - side1;
            if (p1.x <= mn_x) {
                continue;
            }
        }
        if (p1.y + side1 >= mx_y) {
            p1.y = pr_mx[i + 1] - side1;
        }
        ans_nw.add(p1, side1);
        int side2 = max(1LL, max(a[n - 1].x - a[i + 1].x, suf_mx[i + 1] - suf_mn[i + 1]));
        Point p2(a[i + 1].x, suf_mn[i + 1]);
        if (p2.x + side2 >= mx_x) {
            p2.x = max(a[i].x + 1, a[n - 1].x - side2);
            if (p2.x + side2 >= mx_x) {
                continue;
            }
        }
        if (p2.y + side2 >= mx_y) {
            p2.y = suf_mx[i + 1] - side2;
        }
        ans_nw.add(p2, side2);
        if (check(ans_nw) && ans_nw < ans) {
            ans = ans_nw;
        }
    }
    int side = max(1LL, max(a[n - 1].x - a[0].x, pr_mx[n] - pr_mn[n]));
    Point p(a[0].x, pr_mn[n]);
    if (p.x + side >= mx_x) {
        p.x = a[n - 1].x - side;
    }
    if (p.y + side >= mx_y) {
        p.y = pr_mx[n] - side;
    }
    Answer ans_nw;
    ans_nw.add(p, side);
    if (p.x - 2 >= mn_x && p.y - 2 >= mn_y) {
        ans_nw.add(Point(p.x - 2, p.y - 2), 1);
        if (check(ans_nw) && ans_nw < ans) {
            ans = ans_nw;
        }
    } else if (p.x - 2 >= mn_x && p.y + side + 2 <= mx_y) {
        ans_nw.add(Point(p.x - 2, p.y + side + 1), 1);
        if (check(ans_nw) && ans_nw < ans) {
            ans = ans_nw;
        }
    } else if (p.x + side + 2 <= mx_x && p.y - 2 >= mn_y) {
        ans_nw.add(Point(p.x + side + 1, p.y - 2), 1);
        if (check(ans_nw) && ans_nw < ans) {
            ans = ans_nw;
        }
    } else if (p.x + side + 2 <= mx_x && p.y + side + 2 <= mx_y) {
        ans_nw.add(Point(p.x + side + 1, p.y + side + 1), 1);
        if (check(ans_nw) && ans_nw < ans) {
            ans = ans_nw;
        }
    }
    return ans;
}

Answer get_ans(int n, vector<Point> a) {
    auto check = [&](Answer ans) -> bool {
        for (int i = 0; i < 3; ++i) {
            if (ans.squares[i].first.x < -vl || ans.squares[i].first.x > vl) {
                return false;
            }
            if (ans.squares[i].first.y < -vl || ans.squares[i].first.y > vl) {
                return false;
            }
        }
        for (int i = 0; i < 3; ++i) {
            for (int j = i + 1; j < 3; ++j) {
                if (min(ans.squares[i].first.x + ans.squares[i].second, ans.squares[j].first.x + ans.squares[j].second) >= max(ans.squares[i].first.x, ans.squares[j].first.x) &&
                    min(ans.squares[i].first.y + ans.squares[i].second, ans.squares[j].first.y + ans.squares[j].second) >= max(ans.squares[i].first.y, ans.squares[j].first.y)) {
                    return false;
                }
            }
        }
        return true;
    };

    sort(a.begin(), a.end(), [&](Point a, Point b) -> bool {
        return a.x < b.x;
    });
    Answer ans;
    ans.add(Point(0, 0), inf);
    int mn_y = inf, mx_y = -inf;
    for (int i = 0; i < n; ++i) {
        mn_y = min(mn_y, a[i].y);
        mx_y = max(mx_y, a[i].y);
        if (i == n - 1 || a[i].x == a[i + 1].x) {
            continue;
        }
        vector<Point> b;
        for (int j = i + 1; j < n; ++j) {
            b.push_back(a[j]);
        }
        Answer ans1_ans = split2(b, a[i].x, vl, -vl, vl);
        for (int j = 0; j < (int)b.size(); ++j) {
            swap(b[j].x, b[j].y);
        }
        Answer ans2_ans = split2(b, -vl, vl, a[i].x, vl);
        for (int i = 0; i < 2; ++i) {
            swap(ans2_ans.squares[i].first.x, ans2_ans.squares[i].first.y);
        }
        if (ans2_ans < ans1_ans) {
            ans1_ans = ans2_ans;
        }
        int side = max(1LL, max(a[i].x - a[0].x, mx_y - mn_y));
        ans1_ans.add(Point(a[i].x - side, mn_y), side);
        if (ans1_ans < ans) {
            ans = ans1_ans;
        }
    }
    int side = max(1LL, max(a[n - 1].x - a[0].x, mx_y - mn_y));
    Point p(a[0].x, mn_y);
    Answer ans_nw;
    ans_nw.add(p, side);
    if (p.x - 4 >= -vl && p.y - 4 >= -vl) {
        ans_nw.add(Point(p.x - 2, p.y - 2), 1);
        ans_nw.add(Point(p.x - 4, p.y - 4), 1);
        if (ans_nw < ans) {
            ans = ans_nw;
        }
    } else if (p.x - 4 >= -vl && p.y + 4 <= vl) {
        ans_nw.add(Point(p.x - 2, p.y + 1), 1);
        ans_nw.add(Point(p.x - 4, p.y + 3), 1);
        if (ans_nw < ans) {
            ans = ans_nw;
        }
    } else if (p.x + 4 <= vl && p.y - 4 >= vl) {
        ans_nw.add(Point(p.x + 1, p.y - 2), 1);
        ans_nw.add(Point(p.x + 3, p.y - 4), 1);
        if (ans_nw < ans) {
            ans = ans_nw;
        }
    } else if (p.x + 4 <= vl && p.y + 4 <= vl) {
        ans_nw.add(Point(p.x + 1, p.y + 1), 1);
        ans_nw.add(Point(p.x + 3, p.y + 3), 1);
        if (ans_nw < ans) {
            ans = ans_nw;
        }
    }

    mn_y = inf, mx_y = -inf;
    for (int i = n - 1; i > 0; --i) {
        mn_y = min(mn_y, a[i].y);
        mx_y = max(mx_y, a[i].y);
        if (i == 0 || a[i].x == a[i - 1].x) {
            continue;
        }
        vector<Point> b;
        for (int j = 0; j < i; ++j) {
            b.push_back(a[j]);
        }
        Answer ans1_ans = split2(b, -vl, a[i].x, -vl, vl);
        for (int j = 0; j < (int)b.size(); ++j) {
            swap(b[j].x, b[j].y);
        }
        Answer ans2_ans = split2(b, -vl, vl, -vl, a[i].x);
        for (int i = 0; i < 2; ++i) {
            swap(ans2_ans.squares[i].first.x, ans2_ans.squares[i].first.y);
        }
        if (ans2_ans < ans1_ans) {
            ans1_ans = ans2_ans;
        }
        int side = max(1LL, max(a[n - 1].x - a[i].x, mx_y - mn_y));
        ans1_ans.add(Point(a[i].x, mn_y), side);
        if (ans1_ans < ans) {
            ans = ans1_ans;
        }
    }

    assert(check(ans));

    return ans;
}

void solve() {
    int n, k;
    cin >> n >> k;
    vector<Point> a(n);
    for (int i = 0; i < n; ++i) {
        cin >> a[i].x >> a[i].y;
    }
    if (k == 1) {
        int mn_x = inf, mx_x = -inf, mn_y = inf, mx_y = -inf;
        for (int i = 0; i < n; ++i) {
            mn_x = min(mn_x, a[i].x);
            mx_x = max(mx_x, a[i].x);
            mn_y = min(mn_y, a[i].y);
            mx_y = max(mx_y, a[i].y);
        }
        cout << mn_x << ' ' << mn_y << ' ' << max(1LL, max(mx_x - mn_x, mx_y - mn_y)) << '\n';
    } else if (k == 2) {
        auto ans1 = split2(a, -vl, vl, -vl, vl);
        for (int i = 0; i < n; ++i) {
            swap(a[i].x, a[i].y);
        }
        auto ans2 = split2(a, -vl, vl, -vl, vl);
        for (int i = 0; i < k; ++i) {
            swap(ans2.squares[i].first.x, ans2.squares[i].first.y);
        }
        if (ans1 < ans2) {
            for (int i = 0; i < k; ++i) {
                cout << ans1.squares[i].first.x << ' ' << ans1.squares[i].first.y << ' ' << ans1.squares[i].second << '\n';
            }
        } else {
            for (int i = 0; i < k; ++i) {
                cout << ans2.squares[i].first.x << ' ' << ans2.squares[i].first.y << ' ' << ans2.squares[i].second << '\n';
            }
        }
    } else if (k == 3) {
        auto ans1 = get_ans(n, a);
        for (int i = 0; i < n; ++i) {
            swap(a[i].x, a[i].y);
        }
        auto ans2 = get_ans(n, a);
        for (int i = 0; i < k; ++i) {
            swap(ans2.squares[i].first.x, ans2.squares[i].first.y);
        }
        auto check = [&](Answer ans) -> bool {
            for (int i = 0; i < k; ++i) {
                if (ans.squares[i].first.x < -vl || ans.squares[i].first.x > vl) {
                    return false;
                }
                if (ans.squares[i].first.y < -vl || ans.squares[i].first.y > vl) {
                    return false;
                }
            }
            for (int i = 0; i < k; ++i) {
                for (int j = i + 1; j < k; ++j) {
                    if (min(ans.squares[i].first.x + ans.squares[i].second, ans.squares[j].first.x + ans.squares[j].second) >= max(ans.squares[i].first.x, ans.squares[j].first.x) &&
                        min(ans.squares[i].first.y + ans.squares[i].second, ans.squares[j].first.y + ans.squares[j].second) >= max(ans.squares[i].first.y, ans.squares[j].first.y)) {
                        return false;
                    }
                }
            }
            return true;
        };
        assert(check(ans1));
        assert(check(ans2));
        if (ans1 < ans2) {
            for (int i = 0; i < k; ++i) {
                cout << ans1.squares[i].first.x << ' ' << ans1.squares[i].first.y << ' ' << ans1.squares[i].second << '\n';
            }
        } else {
            for (int i = 0; i < k; ++i) {
                cout << ans2.squares[i].first.x << ' ' << ans2.squares[i].first.y << ' ' << ans2.squares[i].second << '\n';
            }
        }
    }
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}

Subtask #1
5.0 / 5.0

#	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	14 ms	1884 KB	Output is correct
8	Correct	16 ms	1880 KB	Output is correct
9	Correct	16 ms	1884 KB	Output is correct
10	Correct	16 ms	1884 KB	Output is correct
11	Correct	15 ms	1880 KB	Output is correct

Subtask #2
21.0 / 21.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	348 KB	Output is correct
2	Correct	1 ms	356 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	344 KB	Output is correct
8	Correct	0 ms	344 KB	Output is correct
9	Correct	0 ms	348 KB	Output is correct
10	Correct	43 ms	6660 KB	Output is correct
11	Correct	45 ms	6644 KB	Output is correct
12	Correct	43 ms	6644 KB	Output is correct
13	Correct	43 ms	6648 KB	Output is correct
14	Correct	45 ms	6644 KB	Output is correct
15	Correct	44 ms	6648 KB	Output is correct
16	Correct	42 ms	6644 KB	Output is correct
17	Correct	38 ms	6040 KB	Output is correct
18	Correct	37 ms	5948 KB	Output is correct
19	Correct	37 ms	5468 KB	Output is correct
20	Correct	36 ms	5756 KB	Output is correct
21	Correct	44 ms	6644 KB	Output is correct
22	Correct	46 ms	6492 KB	Output is correct
23	Correct	43 ms	6648 KB	Output is correct

Subtask #3
0 / 12.0

#	Verdict	Memory	Grader output
1	Correct	348 KB	Output is correct
2	Correct	348 KB	Output is correct
3	Correct	600 KB	Output is correct
4	Correct	348 KB	Output is correct
5	Correct	348 KB	Output is correct
6	Correct	348 KB	Output is correct
7	Correct	348 KB	Output is correct
8	Correct	600 KB	Output is correct
9	Correct	348 KB	Output is correct
10	Correct	348 KB	Output is correct
11	Correct	348 KB	Output is correct
12	Correct	348 KB	Output is correct
13	Correct	348 KB	Output is correct
14	Incorrect	348 KB	Output isn't correct
15	Halted	0 KB	-

Subtask #4
0 / 30.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	269 ms	552 KB	Output is correct
2	Correct	282 ms	540 KB	Output is correct
3	Correct	261 ms	596 KB	Output is correct
4	Correct	287 ms	804 KB	Output is correct
5	Correct	259 ms	536 KB	Output is correct
6	Correct	260 ms	596 KB	Output is correct
7	Correct	261 ms	592 KB	Output is correct
8	Correct	260 ms	852 KB	Output is correct
9	Correct	287 ms	852 KB	Output is correct
10	Correct	260 ms	548 KB	Output is correct
11	Correct	270 ms	536 KB	Output is correct
12	Correct	261 ms	560 KB	Output is correct
13	Correct	209 ms	596 KB	Output is correct
14	Correct	214 ms	544 KB	Output is correct
15	Correct	207 ms	652 KB	Output is correct
16	Correct	250 ms	592 KB	Output is correct
17	Correct	216 ms	592 KB	Output is correct
18	Correct	215 ms	592 KB	Output is correct
19	Correct	200 ms	596 KB	Output is correct
20	Correct	203 ms	596 KB	Output is correct
21	Incorrect	237 ms	660 KB	Output isn't correct
22	Halted	0 ms	0 KB	-

Subtask #5
0 / 32.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	269 ms	532 KB	Output is correct
2	Correct	269 ms	592 KB	Output is correct
3	Correct	286 ms	592 KB	Output is correct
4	Correct	274 ms	852 KB	Output is correct
5	Correct	261 ms	592 KB	Output is correct
6	Correct	262 ms	532 KB	Output is correct
7	Correct	268 ms	532 KB	Output is correct
8	Correct	263 ms	848 KB	Output is correct
9	Correct	265 ms	852 KB	Output is correct
10	Correct	260 ms	548 KB	Output is correct
11	Correct	298 ms	548 KB	Output is correct
12	Correct	281 ms	852 KB	Output is correct
13	Correct	261 ms	592 KB	Output is correct
14	Execution timed out	3027 ms	8264 KB	Time limit exceeded
15	Halted	0 ms	0 KB	-

Submission #998078

Compilation message

Subtask #1 5.0 / 5.0

Subtask #2 21.0 / 21.0

Subtask #3 0 / 12.0

Subtask #4 0 / 30.0

Subtask #5 0 / 32.0

Subtask #1
5.0 / 5.0

Subtask #2
21.0 / 21.0

Subtask #3
0 / 12.0

Subtask #4
0 / 30.0

Subtask #5
0 / 32.0