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답안 #998078

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
998078 2024-06-13T09:23:12 Z arbuzick Izvanzemaljci (COI21_izvanzemaljci) C++17
26 / 100
 3000 ms 8264 KB 
#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

# 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 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

# 결과 실행 시간 메모리 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

# 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 600 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 348 KB Output is correct
8 Correct 0 ms 600 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 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 348 KB Output is correct
14 Incorrect 0 ms 348 KB Output isn't correct
15 Halted 0 ms 0 KB -

Subtask #4
0 / 30.0

# 결과 실행 시간 메모리 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

# 결과 실행 시간 메모리 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 -