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Submission #243455

# Submission time Handle Problem Language Result Execution time Memory
243455 2020-07-01T08:17:10 Z atoiz Circle selection (APIO18_circle_selection) C++14
87 / 100
 3000 ms 19560 KB 
// https://oj.uz/submission/77965

#include <iostream>
#include <vector>
#include <algorithm>
#include <cstdio>

using namespace std;

const int INF = 1000 * 1000 * 1000 + 8;

int64_t sqr(int x) { return (int64_t) x * x; }
void minimize(int &x, int y) { x = (x < y ? x : y); }
void maximize(int &x, int y) { x = (x > y ? x : y); }

struct Box
{
	int x0, x1, y0, y1;
	Box(int _x0 = INF, int _x1 = -INF, int _y0 = INF, int _y1 = -INF): x0(_x0), x1(_x1), y0(_y0), y1(_y1) {}
	bool intersect(const Box &b) const { return (x0 <= b.x1 && b.x0 <= x1 && y0 <= b.y1 && b.y0 <= y1); }
	void expand(const Box &b) { minimize(x0, b.x0), minimize(y0, b.y0), maximize(x1, b.x1), maximize(y1, b.y1); }
};

struct Circle
{
	int x, y, r, i;
	bool intersect(const Circle &c) const { return sqr(c.x - x) + sqr(c.y - y) <= sqr(r + c.r); }
	Box toBox() { return Box(x - r, x + r, y - r, y + r); }
};

bool compX(const Circle &a, const Circle &b) { return (a.x == b.x ? (a.y < b.y) : (a.x < b.x)); }
bool compY(const Circle &a, const Circle &b) { return (a.y == b.y ? (a.x < b.x) : (a.y < b.y)); }
bool compR(const Circle &a, const Circle &b) { return (a.r == b.r ? (a.i < b.i) : (a.r > b.r)); }

int n;
vector<int> ans;
vector<Circle> circles, cirTree;
vector<Box> boxTree;

void build(int lo = 0, int hi = n - 1, bool byX = 0)
{
	int mid = (lo + hi) >> 1;
	nth_element(cirTree.begin() + lo, cirTree.begin() + mid, cirTree.begin() + hi + 1, (byX ? compX : compY));
	boxTree[mid] = cirTree[mid].toBox();

	if (lo < mid) {
		build(lo, mid - 1, !byX);
		boxTree[mid].expand(boxTree[(lo + mid - 1) >> 1]);
	}

	if (mid < hi) {
		build(mid + 1, hi, !byX);
		boxTree[mid].expand(boxTree[(mid + 1 + hi) >> 1]);
	}

	// cout << mid << ' ' << lo << ' ' << hi << ' ' << cirTree[mid].i << ": ";
	// cout << boxTree[mid].x0 << ' ' << boxTree[mid].x1 << ' ' << boxTree[mid].y0 << ' ' << boxTree[mid].y1 << endl;
}

void get(Circle &c, Box &b, int lo = 0, int hi = n - 1, bool byX = 0)
{
	int mid = (lo + hi) >> 1;
	if (ans[cirTree[mid].i] == -1 && cirTree[mid].intersect(c)) ans[cirTree[mid].i] = c.i;
	// cout << c.i << ": " << lo << ' ' << hi << ' ' << cirTree[mid].i << " - ";
	// cout << boxTree[mid].x0 << ' ' << boxTree[mid].x1 << ' ' << boxTree[mid].y0 << ' ' << boxTree[mid].y1 << endl;

	boxTree[mid] = Box(INF, -INF, INF, -INF);
	if (ans[cirTree[mid].i] == -1) boxTree[mid] = cirTree[mid].toBox();
	int lc = (lo + mid - 1) >> 1, rc = (mid + 1 + hi) >> 1;
	if (lo < mid) {
		if (boxTree[lc].intersect(b)) get(c, b, lo, mid - 1, !byX);
		boxTree[mid].expand(boxTree[lc]);
	}
	if (mid < hi) {
		if (boxTree[rc].intersect(b)) get(c, b, mid + 1, hi, !byX);
		boxTree[mid].expand(boxTree[rc]);
	}
}

int main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	cin >> n;
	circles.resize(n);
	for (int i = 0; i < n; ++i) {
		cin >> circles[i].x >> circles[i].y >> circles[i].r;
		circles[i].i = i;
	}
	sort(circles.begin(), circles.end(), compR);

	cirTree = circles;
	boxTree.resize(n);
	ans.assign(n, -1);
	build();

	for (auto &c : circles) if (ans[c.i] == -1) {
		ans[c.i] = c.i;
		Box b = c.toBox();
		get(c, b);
	}
	for (int i = 0; i < n; ++i) cout << ans[i] + 1 << ' ';
}

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 5 ms 384 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 384 KB Output is correct
19 Correct 10 ms 768 KB Output is correct
20 Correct 9 ms 768 KB Output is correct
21 Correct 9 ms 768 KB Output is correct
22 Correct 11 ms 768 KB Output is correct
23 Correct 10 ms 768 KB Output is correct
24 Correct 11 ms 768 KB Output is correct
25 Correct 10 ms 768 KB Output is correct
26 Correct 10 ms 768 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 261 ms 19320 KB Output is correct
2 Correct 260 ms 19320 KB Output is correct
3 Correct 267 ms 18936 KB Output is correct
4 Correct 260 ms 19320 KB Output is correct
5 Correct 260 ms 19064 KB Output is correct
6 Correct 321 ms 19192 KB Output is correct
7 Correct 263 ms 19192 KB Output is correct
8 Correct 271 ms 19192 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 153 ms 7412 KB Output is correct
3 Correct 567 ms 19264 KB Output is correct
4 Correct 568 ms 19448 KB Output is correct
5 Correct 489 ms 19064 KB Output is correct
6 Correct 217 ms 11132 KB Output is correct
7 Correct 107 ms 6776 KB Output is correct
8 Correct 24 ms 1792 KB Output is correct
9 Correct 542 ms 19448 KB Output is correct
10 Correct 454 ms 19448 KB Output is correct

Subtask #4
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 546 ms 19064 KB Output is correct
2 Correct 548 ms 19448 KB Output is correct
3 Correct 311 ms 18680 KB Output is correct
4 Correct 551 ms 19064 KB Output is correct
5 Correct 527 ms 19192 KB Output is correct
6 Correct 305 ms 18424 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 5 ms 384 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 384 KB Output is correct
19 Correct 10 ms 768 KB Output is correct
20 Correct 9 ms 768 KB Output is correct
21 Correct 9 ms 768 KB Output is correct
22 Correct 11 ms 768 KB Output is correct
23 Correct 10 ms 768 KB Output is correct
24 Correct 11 ms 768 KB Output is correct
25 Correct 10 ms 768 KB Output is correct
26 Correct 10 ms 768 KB Output is correct
27 Correct 14 ms 1280 KB Output is correct
28 Correct 13 ms 1256 KB Output is correct
29 Correct 13 ms 1152 KB Output is correct
30 Correct 16 ms 1152 KB Output is correct
31 Correct 16 ms 1152 KB Output is correct
32 Correct 17 ms 1152 KB Output is correct
33 Correct 98 ms 7544 KB Output is correct
34 Correct 101 ms 7544 KB Output is correct
35 Correct 100 ms 7544 KB Output is correct
36 Correct 148 ms 7544 KB Output is correct
37 Correct 149 ms 7800 KB Output is correct
38 Correct 147 ms 7672 KB Output is correct
39 Correct 116 ms 6904 KB Output is correct
40 Correct 118 ms 6904 KB Output is correct
41 Correct 120 ms 6904 KB Output is correct
42 Correct 104 ms 7416 KB Output is correct
43 Correct 132 ms 7672 KB Output is correct
44 Correct 131 ms 7672 KB Output is correct
45 Correct 130 ms 7672 KB Output is correct
46 Correct 134 ms 7672 KB Output is correct
47 Correct 131 ms 7672 KB Output is correct
48 Correct 132 ms 7672 KB Output is correct
49 Correct 132 ms 7672 KB Output is correct
50 Correct 128 ms 7800 KB Output is correct

Subtask #6
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 5 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 5 ms 384 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 384 KB Output is correct
19 Correct 10 ms 768 KB Output is correct
20 Correct 9 ms 768 KB Output is correct
21 Correct 9 ms 768 KB Output is correct
22 Correct 11 ms 768 KB Output is correct
23 Correct 10 ms 768 KB Output is correct
24 Correct 11 ms 768 KB Output is correct
25 Correct 10 ms 768 KB Output is correct
26 Correct 10 ms 768 KB Output is correct
27 Correct 261 ms 19320 KB Output is correct
28 Correct 260 ms 19320 KB Output is correct
29 Correct 267 ms 18936 KB Output is correct
30 Correct 260 ms 19320 KB Output is correct
31 Correct 260 ms 19064 KB Output is correct
32 Correct 321 ms 19192 KB Output is correct
33 Correct 263 ms 19192 KB Output is correct
34 Correct 271 ms 19192 KB Output is correct
35 Correct 5 ms 384 KB Output is correct
36 Correct 153 ms 7412 KB Output is correct
37 Correct 567 ms 19264 KB Output is correct
38 Correct 568 ms 19448 KB Output is correct
39 Correct 489 ms 19064 KB Output is correct
40 Correct 217 ms 11132 KB Output is correct
41 Correct 107 ms 6776 KB Output is correct
42 Correct 24 ms 1792 KB Output is correct
43 Correct 542 ms 19448 KB Output is correct
44 Correct 454 ms 19448 KB Output is correct
45 Correct 546 ms 19064 KB Output is correct
46 Correct 548 ms 19448 KB Output is correct
47 Correct 311 ms 18680 KB Output is correct
48 Correct 551 ms 19064 KB Output is correct
49 Correct 527 ms 19192 KB Output is correct
50 Correct 305 ms 18424 KB Output is correct
51 Correct 14 ms 1280 KB Output is correct
52 Correct 13 ms 1256 KB Output is correct
53 Correct 13 ms 1152 KB Output is correct
54 Correct 16 ms 1152 KB Output is correct
55 Correct 16 ms 1152 KB Output is correct
56 Correct 17 ms 1152 KB Output is correct
57 Correct 98 ms 7544 KB Output is correct
58 Correct 101 ms 7544 KB Output is correct
59 Correct 100 ms 7544 KB Output is correct
60 Correct 148 ms 7544 KB Output is correct
61 Correct 149 ms 7800 KB Output is correct
62 Correct 147 ms 7672 KB Output is correct
63 Correct 116 ms 6904 KB Output is correct
64 Correct 118 ms 6904 KB Output is correct
65 Correct 120 ms 6904 KB Output is correct
66 Correct 104 ms 7416 KB Output is correct
67 Correct 132 ms 7672 KB Output is correct
68 Correct 131 ms 7672 KB Output is correct
69 Correct 130 ms 7672 KB Output is correct
70 Correct 134 ms 7672 KB Output is correct
71 Correct 131 ms 7672 KB Output is correct
72 Correct 132 ms 7672 KB Output is correct
73 Correct 132 ms 7672 KB Output is correct
74 Correct 128 ms 7800 KB Output is correct
75 Correct 303 ms 18928 KB Output is correct
76 Correct 312 ms 19192 KB Output is correct
77 Correct 295 ms 19320 KB Output is correct
78 Correct 298 ms 18936 KB Output is correct
79 Correct 317 ms 19272 KB Output is correct
80 Correct 293 ms 18936 KB Output is correct
81 Correct 631 ms 19192 KB Output is correct
82 Correct 560 ms 19064 KB Output is correct
83 Correct 572 ms 19064 KB Output is correct
84 Correct 646 ms 19168 KB Output is correct
85 Correct 608 ms 19192 KB Output is correct
86 Correct 579 ms 19064 KB Output is correct
87 Correct 569 ms 19192 KB Output is correct
88 Correct 447 ms 19064 KB Output is correct
89 Correct 414 ms 19064 KB Output is correct
90 Correct 430 ms 19320 KB Output is correct
91 Correct 516 ms 19448 KB Output is correct
92 Correct 452 ms 19516 KB Output is correct
93 Correct 1536 ms 19560 KB Output is correct
94 Execution timed out 3078 ms 17504 KB Time limit exceeded
95 Halted 0 ms 0 KB -