Submission #998080

#	Time	Username	Problem	Language	Result	Execution time	Memory
998080		arbuzick	Izvanzemaljci (COI21_izvanzemaljci)	C++17	26 / 100	3045 ms	8264 KiB

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;
        }
    } else {
        exit(1);
    }
    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 / 5
• Subtask 2: 21 / 21
• Subtask 3: 0 / 12
• Subtask 4: 0 / 30
• Subtask 5: 0 / 32