oj.uz

Submission #1097570

# Submission time Handle Problem Language Result Execution time Memory
1097570 2024-10-07T15:08:41 Z Requiem Circle selection (APIO18_circle_selection) C++17
19 / 100
 1611 ms 114752 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]);
        }

        while (sortR.size() > 0){
            Circle ToErase = *sortR.rbegin();
            int L = ToErase.x;
            int R = ToErase.y;
            set<Circle, cmp1> eraseList;
//            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 = next(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 = next(s2);
            }
            for(auto p: eraseList){
                answer[p.id] = ToErase.id;
//                cout << p.id << ' ';
                if (sortX.find(p) != sortX.end()) sortX.erase(sortX.find(p));
                if (sortY.find(p) != sortY.end()) sortY.erase(sortY.find(p));
                if (sortR.find(p) != sortR.end()) sortR.erase(sortR.find(p));
            }
//            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:207:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
  207 | main()
      | ^~~~
circle_selection.cpp: In function 'int main()':
circle_selection.cpp:211:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  211 |         freopen(TASKNAME".inp","r",stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~
circle_selection.cpp:212:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  212 |         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 10076 KB Output is correct
4 Correct 3 ms 10076 KB Output is correct
5 Correct 4 ms 10072 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 10072 KB Output is correct
9 Correct 5 ms 10112 KB Output is correct
10 Correct 4 ms 10076 KB Output is correct
11 Correct 5 ms 10076 KB Output is correct
12 Correct 4 ms 10080 KB Output is correct
13 Correct 3 ms 10076 KB Output is correct
14 Correct 4 ms 10076 KB Output is correct
15 Correct 4 ms 10072 KB Output is correct
16 Correct 6 ms 10076 KB Output is correct
17 Correct 5 ms 9988 KB Output is correct
18 Correct 5 ms 10076 KB Output is correct
19 Correct 39 ms 10328 KB Output is correct
20 Correct 38 ms 10332 KB Output is correct
21 Correct 39 ms 10232 KB Output is correct
22 Correct 60 ms 10320 KB Output is correct
23 Correct 66 ms 10320 KB Output is correct
24 Correct 60 ms 10320 KB Output is correct
25 Correct 61 ms 10072 KB Output is correct
26 Correct 63 ms 10220 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1527 ms 114616 KB Output is correct
2 Correct 1516 ms 103128 KB Output is correct
3 Correct 1611 ms 110956 KB Output is correct
4 Correct 1583 ms 114752 KB Output is correct
5 Correct 1074 ms 89132 KB Output is correct
6 Correct 963 ms 89172 KB Output is correct
7 Correct 1025 ms 89212 KB Output is correct
8 Correct 1150 ms 89108 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 30 ms 12396 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #4
0 / 23.0

# Verdict Execution time Memory Grader output
1 Incorrect 75 ms 17620 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 10076 KB Output is correct
4 Correct 3 ms 10076 KB Output is correct
5 Correct 4 ms 10072 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 10072 KB Output is correct
9 Correct 5 ms 10112 KB Output is correct
10 Correct 4 ms 10076 KB Output is correct
11 Correct 5 ms 10076 KB Output is correct
12 Correct 4 ms 10080 KB Output is correct
13 Correct 3 ms 10076 KB Output is correct
14 Correct 4 ms 10076 KB Output is correct
15 Correct 4 ms 10072 KB Output is correct
16 Correct 6 ms 10076 KB Output is correct
17 Correct 5 ms 9988 KB Output is correct
18 Correct 5 ms 10076 KB Output is correct
19 Correct 39 ms 10328 KB Output is correct
20 Correct 38 ms 10332 KB Output is correct
21 Correct 39 ms 10232 KB Output is correct
22 Correct 60 ms 10320 KB Output is correct
23 Correct 66 ms 10320 KB Output is correct
24 Correct 60 ms 10320 KB Output is correct
25 Correct 61 ms 10072 KB Output is correct
26 Correct 63 ms 10220 KB Output is correct
27 Incorrect 6 ms 10076 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 10076 KB Output is correct
4 Correct 3 ms 10076 KB Output is correct
5 Correct 4 ms 10072 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 10072 KB Output is correct
9 Correct 5 ms 10112 KB Output is correct
10 Correct 4 ms 10076 KB Output is correct
11 Correct 5 ms 10076 KB Output is correct
12 Correct 4 ms 10080 KB Output is correct
13 Correct 3 ms 10076 KB Output is correct
14 Correct 4 ms 10076 KB Output is correct
15 Correct 4 ms 10072 KB Output is correct
16 Correct 6 ms 10076 KB Output is correct
17 Correct 5 ms 9988 KB Output is correct
18 Correct 5 ms 10076 KB Output is correct
19 Correct 39 ms 10328 KB Output is correct
20 Correct 38 ms 10332 KB Output is correct
21 Correct 39 ms 10232 KB Output is correct
22 Correct 60 ms 10320 KB Output is correct
23 Correct 66 ms 10320 KB Output is correct
24 Correct 60 ms 10320 KB Output is correct
25 Correct 61 ms 10072 KB Output is correct
26 Correct 63 ms 10220 KB Output is correct
27 Correct 1527 ms 114616 KB Output is correct
28 Correct 1516 ms 103128 KB Output is correct
29 Correct 1611 ms 110956 KB Output is correct
30 Correct 1583 ms 114752 KB Output is correct
31 Correct 1074 ms 89132 KB Output is correct
32 Correct 963 ms 89172 KB Output is correct
33 Correct 1025 ms 89212 KB Output is correct
34 Correct 1150 ms 89108 KB Output is correct
35 Correct 4 ms 10076 KB Output is correct
36 Incorrect 30 ms 12396 KB Output isn't correct
37 Halted 0 ms 0 KB -