oj.uz

Submission #1097765

# Submission time Handle Problem Language Result Execution time Memory
1097765 2024-10-08T08:46:24 Z Requiem Circle selection (APIO18_circle_selection) C++17
19 / 100
 1236 ms 113232 KB 
#include<bits/stdc++.h>
#define int long long
#define pb push_back
#define fast ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
#define MOD 1000000007
#define inf 1e18
#define fi first
#define se second
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define FORD(i,a,b) for(int i=a;i>=b;i--)
#define sz(a) ((int)(a).size())
#define endl '\n'
#define pi 3.14159265359
#define TASKNAME "circlesec"
using namespace std;
template<typename T> bool maximize(T &res, const T &val) { if (res < val){ res = val; return true; }; return false; }
template<typename T> bool minimize(T &res, const T &val) { if (res > val){ res = val; return true; }; return false; }
typedef pair<int,int> ii;
typedef pair<int,ii> iii;
typedef vector<int> vi;
/**
Cho n đường tròn, đường tròn thứ i: có tâm (xi, yi) và bán kính ri.

Ta có 1 thuật toán:
- Tìm đường tròn có bán kính lớn nhất.
- Xóa đường tròn đó và những đường tròn giao với nó.
- Lặp lại bước 1 và 2 cho đến khi không còn đường tròn nào.

Ta gọi đường tròn i bị loại bởi đường tròn j nếu như khi đường tròn j bị loại ở bước 1 thì đường tròn i sẽ bị loại ở bước 2.

subtask 1: n <= 5000. O(N^2)
subtask 2: n <= 3e5. yi = 0, bài toán đưa về khoảng. Giả sử cho n đoạn [li, ri], ta sẽ xóa đoạn lớn nhất xong tìm những thằng
giao với đoạn đó và loại nó ra.

Subtask này đơn giản ta sweep qua các đoạn, với mỗi đoạn.
Ta lưu 3 cái set. Mỗi set sẽ sort theo 1 thông số li, ri, và radius.

Ta có nhận xét là những đoạn có l nằm trong [l, r] sẽ bị xóa xổ ở cả 3. Khi này, độ phức tạp chỉ là O(N log N) khi mỗi phần
tử chỉ được xóa 1 lần.

subtask 3: n <= 3e5, mỗi đường tròn chỉ giao với 1 đường tròn khác.
2 đường tròn giao nhau khi d(O1, O2) <= R1 + R2.

subtask 4: n <= 3e5, mỗi đường tròn có cùng bán kính.

**/

const int MAXN = 3e5 + 9;
struct Circle{
    int x, y, r, id;
    Circle(int _x = 0, int _y = 0, int _r = 0, int _id = 0): x(_x), y(_y), r(_r), id(_id) {}

    bool operator * (const Circle &other){
        return (x - other.x) * (x - other.x) + (y - other.y) * (y - other.y) <= (r + other.r) * (r + other.r);
    }


} circle[MAXN];

int n;

bool deleted[MAXN];
int answer[MAXN];
namespace subtask1{
    bool check(){
        return n <= 5000;
    }

    void solve(){
        memset(deleted, 0, sizeof(deleted));

        FOR(i, 1, n){
            int delId = 0, maxR = 0;

            FOR(j, 1, n){
                if (deleted[j]) continue;
                if (maximize(maxR, circle[j].r)) delId = j;
            }

//            cout << delId << endl;
            FOR(j, 1, n){
                if (!deleted[j] and circle[delId] * circle[j]) {
                    deleted[j] = true;
                    answer[j] = delId;
//                    cout << j << ' ';
                }
            }
//            cout << endl;
        }

        FOR(i, 1, n){
            cout << answer[i] << ' ';
        }
        cout << endl;

    }
}
namespace subtask2{
    bool check(){
        FOR(i,1 , n){
            if (circle[i].y != 0) return false;
        }
        return n <= 300000;
    }

    struct cmp1{
        bool operator () (const Circle &a, const Circle &b) const{
            if (a.x == b.x) {
                if (a.y == b.y) {
                    if (a.r == b.r) return a.id < b.id;
                    return a.r < b.r;
                }
                return a.y < b.y;
            }
            return a.x < b.x;
        }
    };

    struct cmp2{
        bool operator () (const Circle &a, const Circle &b) const{
            if (a.y == b.y) {
                if (a.x == b.x) {
                    if (a.r == b.r) return a.id < b.id;
                    return a.r < b.r;
                }
                return a.x < b.x;
            }
            return a.y < b.y;
        }
    };

    struct cmp3{
        bool operator () (const Circle &a, const Circle &b) const{
            if (a.r == b.r) {
                if (a.id == b.id) {
                    if (a.y == b.y) return a.x < b.x;
                    return a.y < b.y;
                }
                return a.id > b.id;
            }
            return a.r < b.r;
        }
    };

    set<Circle, cmp1> sortX;
    set<Circle, cmp2> sortY;
    set<Circle, cmp3> sortR;

    void solve(){
        FOR(i, 1, n){
            int x = circle[i].x;
            circle[i].x = x - circle[i].r;
            circle[i].y = x + circle[i].r;
//            cout << circle[i].x << ' ' << circle[i].y << ' ' << circle[i].r << endl;
            sortX.insert(circle[i]);
            sortY.insert(circle[i]);
            sortR.insert(circle[i]);
        }
        set<Circle, cmp1> eraseList;

        while (sortR.size() > 0){
            eraseList.clear();
            Circle ToErase = *sortR.rbegin();
            int L = ToErase.x;
            int R = ToErase.y;
//            cerr << ToErase.id << ' ' << endl;

            auto s1 = sortX.lower_bound(Circle(L, -inf, -inf, -inf));
            while(s1 != sortX.end() and (*s1).x <= R){
                eraseList.insert(*s1);
//                cerr << "X: " << (*s1).x << ' ' << (*s1).id << endl;
                s1++;
            }

            auto s2 = sortY.lower_bound(Circle(-inf, L, -inf, -inf));
            while(s2 != sortY.end() and (*s2).y <= R){
//                cerr << "Y: " << (*s2).y << ' ' << (*s2).id << endl;

                eraseList.insert(*s2);
                s2++;
            }
            for(auto p: eraseList){
                answer[p.id] = ToErase.id;
                auto it1 = sortX.find(p);
                auto it2 = sortY.find(p);
                auto it3 = sortR.find(p);
//                cout << p.id << ' ';
                if (it1 != sortX.end()) sortX.erase(it1);
                if (it2 != sortY.end()) sortY.erase(it2);
                if (it3 != sortR.end()) sortR.erase(it3);
            }
//            cout << endl;
        }

        FOR(i, 1, n){
            cout << answer[i] << ' ';
        }
        cout << endl;
    }
}
void input(){
    cin >> n;
    FOR(i, 1, n){
        cin >> circle[i].x >> circle[i].y >> circle[i].r;
        circle[i].id = i;
    }

    if (subtask1::check()) return subtask1::solve();
    if (subtask2::check()) return subtask2::solve();
}
main()
{
    fast;
    if (fopen(TASKNAME".inp","r")){
        freopen(TASKNAME".inp","r",stdin);
        freopen(TASKNAME".out","w",stdout);
    }

    input();

}
/**
Warning:
Cận lmao
Code imple thiếu case nào không.
Limit.
**/

Compilation message

circle_selection.cpp:211:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
  211 | main()
      | ^~~~
circle_selection.cpp: In function 'int main()':
circle_selection.cpp:215:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  215 |         freopen(TASKNAME".inp","r",stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~
circle_selection.cpp:216:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  216 |         freopen(TASKNAME".out","w",stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10076 KB Output is correct
2 Correct 4 ms 10076 KB Output is correct
3 Correct 4 ms 10036 KB Output is correct
4 Correct 4 ms 10076 KB Output is correct
5 Correct 5 ms 9988 KB Output is correct
6 Correct 4 ms 10076 KB Output is correct
7 Correct 4 ms 10076 KB Output is correct
8 Correct 4 ms 10076 KB Output is correct
9 Correct 3 ms 10076 KB Output is correct
10 Correct 4 ms 10076 KB Output is correct
11 Correct 4 ms 10076 KB Output is correct
12 Correct 4 ms 10076 KB Output is correct
13 Correct 4 ms 10076 KB Output is correct
14 Correct 4 ms 10076 KB Output is correct
15 Correct 3 ms 10076 KB Output is correct
16 Correct 6 ms 10332 KB Output is correct
17 Correct 6 ms 10076 KB Output is correct
18 Correct 5 ms 10076 KB Output is correct
19 Correct 37 ms 10332 KB Output is correct
20 Correct 38 ms 10328 KB Output is correct
21 Correct 39 ms 10332 KB Output is correct
22 Correct 61 ms 10076 KB Output is correct
23 Correct 60 ms 10308 KB Output is correct
24 Correct 64 ms 10320 KB Output is correct
25 Correct 59 ms 10076 KB Output is correct
26 Correct 61 ms 10076 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1177 ms 113052 KB Output is correct
2 Correct 1215 ms 101748 KB Output is correct
3 Correct 1223 ms 109648 KB Output is correct
4 Correct 1236 ms 113232 KB Output is correct
5 Correct 889 ms 88400 KB Output is correct
6 Correct 779 ms 88400 KB Output is correct
7 Correct 820 ms 88400 KB Output is correct
8 Correct 841 ms 88404 KB Output is correct

Subtask #3
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10076 KB Output is correct
2 Incorrect 25 ms 12116 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #4
0 / 23.0

# Verdict Execution time Memory Grader output
1 Incorrect 67 ms 16036 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #5
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10076 KB Output is correct
2 Correct 4 ms 10076 KB Output is correct
3 Correct 4 ms 10036 KB Output is correct
4 Correct 4 ms 10076 KB Output is correct
5 Correct 5 ms 9988 KB Output is correct
6 Correct 4 ms 10076 KB Output is correct
7 Correct 4 ms 10076 KB Output is correct
8 Correct 4 ms 10076 KB Output is correct
9 Correct 3 ms 10076 KB Output is correct
10 Correct 4 ms 10076 KB Output is correct
11 Correct 4 ms 10076 KB Output is correct
12 Correct 4 ms 10076 KB Output is correct
13 Correct 4 ms 10076 KB Output is correct
14 Correct 4 ms 10076 KB Output is correct
15 Correct 3 ms 10076 KB Output is correct
16 Correct 6 ms 10332 KB Output is correct
17 Correct 6 ms 10076 KB Output is correct
18 Correct 5 ms 10076 KB Output is correct
19 Correct 37 ms 10332 KB Output is correct
20 Correct 38 ms 10328 KB Output is correct
21 Correct 39 ms 10332 KB Output is correct
22 Correct 61 ms 10076 KB Output is correct
23 Correct 60 ms 10308 KB Output is correct
24 Correct 64 ms 10320 KB Output is correct
25 Correct 59 ms 10076 KB Output is correct
26 Correct 61 ms 10076 KB Output is correct
27 Incorrect 6 ms 10072 KB Output isn't correct
28 Halted 0 ms 0 KB -

Subtask #6
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10076 KB Output is correct
2 Correct 4 ms 10076 KB Output is correct
3 Correct 4 ms 10036 KB Output is correct
4 Correct 4 ms 10076 KB Output is correct
5 Correct 5 ms 9988 KB Output is correct
6 Correct 4 ms 10076 KB Output is correct
7 Correct 4 ms 10076 KB Output is correct
8 Correct 4 ms 10076 KB Output is correct
9 Correct 3 ms 10076 KB Output is correct
10 Correct 4 ms 10076 KB Output is correct
11 Correct 4 ms 10076 KB Output is correct
12 Correct 4 ms 10076 KB Output is correct
13 Correct 4 ms 10076 KB Output is correct
14 Correct 4 ms 10076 KB Output is correct
15 Correct 3 ms 10076 KB Output is correct
16 Correct 6 ms 10332 KB Output is correct
17 Correct 6 ms 10076 KB Output is correct
18 Correct 5 ms 10076 KB Output is correct
19 Correct 37 ms 10332 KB Output is correct
20 Correct 38 ms 10328 KB Output is correct
21 Correct 39 ms 10332 KB Output is correct
22 Correct 61 ms 10076 KB Output is correct
23 Correct 60 ms 10308 KB Output is correct
24 Correct 64 ms 10320 KB Output is correct
25 Correct 59 ms 10076 KB Output is correct
26 Correct 61 ms 10076 KB Output is correct
27 Correct 1177 ms 113052 KB Output is correct
28 Correct 1215 ms 101748 KB Output is correct
29 Correct 1223 ms 109648 KB Output is correct
30 Correct 1236 ms 113232 KB Output is correct
31 Correct 889 ms 88400 KB Output is correct
32 Correct 779 ms 88400 KB Output is correct
33 Correct 820 ms 88400 KB Output is correct
34 Correct 841 ms 88404 KB Output is correct
35 Correct 4 ms 10076 KB Output is correct
36 Incorrect 25 ms 12116 KB Output isn't correct
37 Halted 0 ms 0 KB -