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Submission #998077

# Submission time Handle Problem Language Result Execution time Memory
998077 2024-06-13T09:22:34 Z arbuzick Izvanzemaljci (COI21_izvanzemaljci) C++17
26 / 100
 3000 ms 8268 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;
}

Compilation message

izvanzemaljci.cpp: In function 'void solve()':
izvanzemaljci.cpp:291:14: warning: variable 'check' set but not used [-Wunused-but-set-variable]
  291 |         auto check = [&](Answer ans) -> bool {
      |              ^~~~~

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 360 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 15 ms 1884 KB Output is correct
8 Correct 15 ms 1884 KB Output is correct
9 Correct 15 ms 1884 KB Output is correct
10 Correct 15 ms 1880 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 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 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 44 ms 6648 KB Output is correct
11 Correct 45 ms 6652 KB Output is correct
12 Correct 43 ms 6668 KB Output is correct
13 Correct 45 ms 6648 KB Output is correct
14 Correct 43 ms 6648 KB Output is correct
15 Correct 49 ms 6644 KB Output is correct
16 Correct 70 ms 6668 KB Output is correct
17 Correct 39 ms 6284 KB Output is correct
18 Correct 37 ms 5968 KB Output is correct
19 Correct 35 ms 5520 KB Output is correct
20 Correct 37 ms 5768 KB Output is correct
21 Correct 45 ms 6632 KB Output is correct
22 Correct 43 ms 6648 KB Output is correct
23 Correct 43 ms 6744 KB Output is correct

Subtask #3
0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 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

# Verdict Execution time Memory Grader output
1 Correct 272 ms 804 KB Output is correct
2 Correct 271 ms 552 KB Output is correct
3 Correct 264 ms 536 KB Output is correct
4 Correct 272 ms 536 KB Output is correct
5 Correct 263 ms 596 KB Output is correct
6 Correct 265 ms 592 KB Output is correct
7 Correct 263 ms 592 KB Output is correct
8 Correct 263 ms 600 KB Output is correct
9 Correct 269 ms 592 KB Output is correct
10 Correct 264 ms 592 KB Output is correct
11 Correct 272 ms 544 KB Output is correct
12 Correct 308 ms 596 KB Output is correct
13 Correct 212 ms 592 KB Output is correct
14 Correct 217 ms 596 KB Output is correct
15 Correct 211 ms 596 KB Output is correct
16 Correct 213 ms 592 KB Output is correct
17 Correct 211 ms 540 KB Output is correct
18 Correct 219 ms 592 KB Output is correct
19 Correct 201 ms 528 KB Output is correct
20 Correct 206 ms 592 KB Output is correct
21 Incorrect 240 ms 548 KB Output isn't correct
22 Halted 0 ms 0 KB -

Subtask #5
0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 273 ms 664 KB Output is correct
2 Correct 282 ms 540 KB Output is correct
3 Correct 266 ms 664 KB Output is correct
4 Correct 266 ms 548 KB Output is correct
5 Correct 269 ms 596 KB Output is correct
6 Correct 270 ms 796 KB Output is correct
7 Correct 272 ms 596 KB Output is correct
8 Correct 264 ms 592 KB Output is correct
9 Correct 267 ms 668 KB Output is correct
10 Correct 268 ms 532 KB Output is correct
11 Correct 273 ms 596 KB Output is correct
12 Correct 266 ms 596 KB Output is correct
13 Correct 276 ms 848 KB Output is correct
14 Execution timed out 3078 ms 8268 KB Time limit exceeded
15 Halted 0 ms 0 KB -