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Submission #771952

# Submission time Handle Problem Language Result Execution time Memory
771952 2023-07-03T12:40:29 Z mcdx9524 Circle selection (APIO18_circle_selection) C++17
100 / 100
 1482 ms 112976 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

#define int long long

const int inf = 1e9 + 7;

struct circle {
    int x, y, r, index;
};

vector <vector <circle> > build_matrix(vector <circle> circles, int sz) {
    sort(circles.begin(), circles.end(), [](const circle &a, const circle &b) {
        return a.x < b.x; 
    });
    int n = (int) circles.size();
    vector <circle> cur;
    vector <vector <circle> > res;
    for (int i = 0; i < n; i++) {
        if (cur.empty() || cur.back().x / sz == circles[i].x / sz) {
            cur.push_back(circles[i]);
        } else {
            res.push_back(cur);
            cur = {circles[i]};
        }
    }   
    if (!cur.empty()) {
        res.push_back(cur);
    }
    for (auto &to : res) {
        sort(to.begin(), to.end(), [](const circle &a, const circle &b) {
            return a.y < b.y;
        });
    }
    return res;
}

bool query(const circle &a, const circle &b) {
    long long distance = (a.x - b.x) * 1ll * (a.x - b.x) + (a.y - b.y) * 1ll * (a.y - b.y);
    return distance <= (a.r + b.r) * 1ll * (a.r + b.r);
}

int32_t main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n;
    cin >> n;
    vector <circle> c;
    set <pair <int, int>, greater <pair <int, int> > > rads;
    for (int i = 0; i < n; i++) {
        int x, y, r;
        cin >> x >> y >> r;
        x += inf;
        y += inf;
        c.push_back({x, y, r, i});
        rads.insert({r, -i});
    }
    int sz = rads.begin()->first;
    auto result = build_matrix(c, sz);
    vector <int> rem(n, -1);
    for (int i = 0; i < n; i++) {
        auto it = rads.begin();
        int index = -it->second;
        int cur_rad = it->first;
        rads.erase(it);
        if (rem[index] != -1) {
            continue;
        }
        rem[index] = index;
        if (cur_rad <= sz / 2) {
            sz = cur_rad;
            result = build_matrix(c, sz);
        }
        int xl = n, xr = -1;
        {
            int starting_point = (c[index].x / sz) * sz;
            int prev_point = starting_point - 2 * sz;
            int l = 0, r = (int) result.size() - 1;
            int res = n;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (result[mid][0].x >= prev_point) {
                    r = mid - 1;
                    res = mid;
                } else {
                    l = mid + 1;
                }
            }
            xl = res;
        }
        {
            int starting_point = (c[index].x / sz) * sz;
            int next_point = starting_point + 3 * sz;
            int l = 0, r = (int) result.size() - 1;
            int res = n;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (result[mid][0].x >= next_point) {
                    r = mid - 1;
                    res = mid;
                } else {
                    l = mid + 1;
                }
            }
            xr = res;
            xr--;
        }
        xl = max(0ll, xl);
        xr = min((int) result.size() - 1, xr);
        for (int j = xl; j <= xr; j++) {
            int yl = n, yr = -1;
            {
                int starting_point = (c[index].y / sz) * sz;
                int prev_point = starting_point - 2 * sz;
                int l = 0, r = (int) result[j].size() - 1;
                int res = n;
                while (l <= r) {
                    int mid = (l + r) / 2;
                    if (result[j][mid].y >= prev_point) {
                        r = mid - 1;
                        res = mid;
                    } else {
                        l = mid + 1;
                    }
                }
                yl = res;
            }
            {
                int starting_point = (c[index].y / sz) * sz;
                int next_point = starting_point + 3 * sz;
                int l = 0, r = (int) result[j].size() - 1;
                int res = n;
                while (l <= r) {
                    int mid = (l + r) / 2;
                    if (result[j][mid].y >= next_point) {
                        r = mid - 1;
                        res = mid;
                    } else {
                        l = mid + 1;
                    }
                }
                yr = res;
                yr--;
            }
            yl = max(0ll, yl);
            yr = min((int) result[j].size() - 1, yr);
            for (int k = yl; k <= yr; k++) {
                if (rem[result[j][k].index] == -1 && query(c[index], result[j][k])) {
                    rem[result[j][k].index] = index;
                }
            }
        }
    }
    for (int i = 0; i < n; i++) {
        cout << rem[i] + 1 << ' ';
    }
    cout << '\n';
    return 0;
}

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 284 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 4 ms 1324 KB Output is correct
20 Correct 3 ms 1364 KB Output is correct
21 Correct 5 ms 1364 KB Output is correct
22 Correct 11 ms 1772 KB Output is correct
23 Correct 10 ms 1784 KB Output is correct
24 Correct 11 ms 1692 KB Output is correct
25 Correct 10 ms 1632 KB Output is correct
26 Correct 11 ms 1744 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 323 ms 63212 KB Output is correct
2 Correct 318 ms 61688 KB Output is correct
3 Correct 271 ms 52496 KB Output is correct
4 Correct 314 ms 62044 KB Output is correct
5 Correct 440 ms 69100 KB Output is correct
6 Correct 726 ms 92896 KB Output is correct
7 Correct 621 ms 81212 KB Output is correct
8 Correct 589 ms 82460 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 366 ms 28508 KB Output is correct
3 Correct 1468 ms 100448 KB Output is correct
4 Correct 1482 ms 99684 KB Output is correct
5 Correct 1278 ms 105756 KB Output is correct
6 Correct 315 ms 43136 KB Output is correct
7 Correct 147 ms 22924 KB Output is correct
8 Correct 23 ms 5172 KB Output is correct
9 Correct 1383 ms 108304 KB Output is correct
10 Correct 677 ms 72660 KB Output is correct

Subtask #4
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 348 ms 50328 KB Output is correct
2 Correct 355 ms 70424 KB Output is correct
3 Correct 218 ms 55764 KB Output is correct
4 Correct 360 ms 70936 KB Output is correct
5 Correct 374 ms 71096 KB Output is correct
6 Correct 208 ms 55952 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 284 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 4 ms 1324 KB Output is correct
20 Correct 3 ms 1364 KB Output is correct
21 Correct 5 ms 1364 KB Output is correct
22 Correct 11 ms 1772 KB Output is correct
23 Correct 10 ms 1784 KB Output is correct
24 Correct 11 ms 1692 KB Output is correct
25 Correct 10 ms 1632 KB Output is correct
26 Correct 11 ms 1744 KB Output is correct
27 Correct 12 ms 2448 KB Output is correct
28 Correct 7 ms 2124 KB Output is correct
29 Correct 7 ms 2140 KB Output is correct
30 Correct 23 ms 2992 KB Output is correct
31 Correct 22 ms 3196 KB Output is correct
32 Correct 27 ms 3136 KB Output is correct
33 Correct 81 ms 19252 KB Output is correct
34 Correct 79 ms 18096 KB Output is correct
35 Correct 210 ms 20852 KB Output is correct
36 Correct 349 ms 29352 KB Output is correct
37 Correct 338 ms 29032 KB Output is correct
38 Correct 349 ms 29464 KB Output is correct
39 Correct 290 ms 28260 KB Output is correct
40 Correct 302 ms 28156 KB Output is correct
41 Correct 282 ms 25600 KB Output is correct
42 Correct 69 ms 15896 KB Output is correct
43 Correct 96 ms 19760 KB Output is correct
44 Correct 94 ms 22296 KB Output is correct
45 Correct 93 ms 22328 KB Output is correct
46 Correct 93 ms 22376 KB Output is correct
47 Correct 94 ms 22348 KB Output is correct
48 Correct 94 ms 22308 KB Output is correct
49 Correct 101 ms 22448 KB Output is correct
50 Correct 93 ms 22340 KB Output is correct

Subtask #6
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 284 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 4 ms 1324 KB Output is correct
20 Correct 3 ms 1364 KB Output is correct
21 Correct 5 ms 1364 KB Output is correct
22 Correct 11 ms 1772 KB Output is correct
23 Correct 10 ms 1784 KB Output is correct
24 Correct 11 ms 1692 KB Output is correct
25 Correct 10 ms 1632 KB Output is correct
26 Correct 11 ms 1744 KB Output is correct
27 Correct 323 ms 63212 KB Output is correct
28 Correct 318 ms 61688 KB Output is correct
29 Correct 271 ms 52496 KB Output is correct
30 Correct 314 ms 62044 KB Output is correct
31 Correct 440 ms 69100 KB Output is correct
32 Correct 726 ms 92896 KB Output is correct
33 Correct 621 ms 81212 KB Output is correct
34 Correct 589 ms 82460 KB Output is correct
35 Correct 0 ms 212 KB Output is correct
36 Correct 366 ms 28508 KB Output is correct
37 Correct 1468 ms 100448 KB Output is correct
38 Correct 1482 ms 99684 KB Output is correct
39 Correct 1278 ms 105756 KB Output is correct
40 Correct 315 ms 43136 KB Output is correct
41 Correct 147 ms 22924 KB Output is correct
42 Correct 23 ms 5172 KB Output is correct
43 Correct 1383 ms 108304 KB Output is correct
44 Correct 677 ms 72660 KB Output is correct
45 Correct 348 ms 50328 KB Output is correct
46 Correct 355 ms 70424 KB Output is correct
47 Correct 218 ms 55764 KB Output is correct
48 Correct 360 ms 70936 KB Output is correct
49 Correct 374 ms 71096 KB Output is correct
50 Correct 208 ms 55952 KB Output is correct
51 Correct 12 ms 2448 KB Output is correct
52 Correct 7 ms 2124 KB Output is correct
53 Correct 7 ms 2140 KB Output is correct
54 Correct 23 ms 2992 KB Output is correct
55 Correct 22 ms 3196 KB Output is correct
56 Correct 27 ms 3136 KB Output is correct
57 Correct 81 ms 19252 KB Output is correct
58 Correct 79 ms 18096 KB Output is correct
59 Correct 210 ms 20852 KB Output is correct
60 Correct 349 ms 29352 KB Output is correct
61 Correct 338 ms 29032 KB Output is correct
62 Correct 349 ms 29464 KB Output is correct
63 Correct 290 ms 28260 KB Output is correct
64 Correct 302 ms 28156 KB Output is correct
65 Correct 282 ms 25600 KB Output is correct
66 Correct 69 ms 15896 KB Output is correct
67 Correct 96 ms 19760 KB Output is correct
68 Correct 94 ms 22296 KB Output is correct
69 Correct 93 ms 22328 KB Output is correct
70 Correct 93 ms 22376 KB Output is correct
71 Correct 94 ms 22348 KB Output is correct
72 Correct 94 ms 22308 KB Output is correct
73 Correct 101 ms 22448 KB Output is correct
74 Correct 93 ms 22340 KB Output is correct
75 Correct 835 ms 73708 KB Output is correct
76 Correct 401 ms 70188 KB Output is correct
77 Correct 312 ms 71448 KB Output is correct
78 Correct 302 ms 71508 KB Output is correct
79 Correct 819 ms 70372 KB Output is correct
80 Correct 334 ms 64556 KB Output is correct
81 Correct 1390 ms 99816 KB Output is correct
82 Correct 1390 ms 97804 KB Output is correct
83 Correct 1376 ms 110792 KB Output is correct
84 Correct 1261 ms 99860 KB Output is correct
85 Correct 1390 ms 103300 KB Output is correct
86 Correct 1380 ms 97984 KB Output is correct
87 Correct 1211 ms 89728 KB Output is correct
88 Correct 987 ms 81896 KB Output is correct
89 Correct 956 ms 81828 KB Output is correct
90 Correct 980 ms 81892 KB Output is correct
91 Correct 950 ms 81820 KB Output is correct
92 Correct 981 ms 81752 KB Output is correct
93 Correct 704 ms 112976 KB Output is correct
94 Correct 649 ms 76944 KB Output is correct
95 Correct 696 ms 89340 KB Output is correct
96 Correct 793 ms 95572 KB Output is correct
97 Correct 657 ms 67932 KB Output is correct
98 Correct 753 ms 92784 KB Output is correct
99 Correct 813 ms 106640 KB Output is correct
100 Correct 544 ms 88008 KB Output is correct
101 Correct 763 ms 83128 KB Output is correct
102 Correct 798 ms 105800 KB Output is correct
103 Correct 800 ms 70596 KB Output is correct
104 Correct 801 ms 105856 KB Output is correct
105 Correct 225 ms 52120 KB Output is correct
106 Correct 349 ms 64148 KB Output is correct
107 Correct 337 ms 64164 KB Output is correct
108 Correct 349 ms 64108 KB Output is correct
109 Correct 332 ms 64108 KB Output is correct
110 Correct 357 ms 64032 KB Output is correct
111 Correct 343 ms 64196 KB Output is correct
112 Correct 342 ms 64064 KB Output is correct
113 Correct 336 ms 64132 KB Output is correct
114 Correct 352 ms 64196 KB Output is correct
115 Correct 350 ms 64132 KB Output is correct
116 Correct 360 ms 71264 KB Output is correct