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Submission #1023570

# Submission time Handle Problem Language Result Execution time Memory
1023570 2024-07-15T02:45:07 Z vjudge1 Wish (LMIO19_noras) C++17
100 / 100
 424 ms 16840 KB 
#include <bits/stdc++.h>
using namespace std;

const long double maxd = 1e19;

long double sqrt128(__int128 x) {
	long double l = 0, r = maxd;
	for (int i=0; i<128; i++) {
		long double mid = (l + r) / 2;
		if (mid * mid <= x) {
			l = mid;
		} else {
			r = mid;
		}
	}
	return l;
}

void solve() {
	int n; long long r;
	cin >> n >> r;
	vector<long long> a(n), b(n), c(n), d(n);
	for (int i=0; i<n; i++) cin >> a[i] >> b[i] >> c[i] >> d[i];

	vector<pair<long long, bool>> evs;
	for (int i=0; i<n; i++) {
		// p(t) = (a[i] + t * dx, b[i] + t * dy)
		// cari t sehingga (a[i] + t * dx)^2 + (b[i] + t * dy)^2 = r^2
		// => a[i]^2 + t^2*dx^2 + 2*t*a[i]*dx + b[i]^2 + t^2*dy^2 + 2*t*b[i]*dy = r^2
		// => t^2 * (dx^2 + dy^2) + t * (2*a[i]*dx + 2*b[i]*dy) + a[i]^2 + b[i]^2 - r^2 = 0
		// => t^2 * A + t * B + C = 0
		// pakai rumus akar persamaan kuadrat?

		__int128 dx = c[i] - a[i], dy = d[i] - b[i];
		__int128 A = dx * dx + dy * dy, B = 2 * (a[i] * dx + b[i] * dy), C = a[i] * a[i] + b[i] * b[i] - r * r;
		__int128 D = B * B - 4 * A * C;
		if (D >= 0) {
			long double sd = sqrt128(D);
			long double t1 = (-B + sd) / (2 * A);
			long double t2 = (-B - sd) / (2 * A);
			long long llt1 = ceil(min(t1, t2));
			long long llt2 = floor(max(t1, t2));
			// cout << min(t1, t2) << ' ' << max(t1, t2) << '\n';
			// cout << llt1 << ' ' << llt2 << '\n';
			if (llt1 <= llt2) {
				evs.emplace_back(llt1, 0);
				evs.emplace_back(llt2, 1);
			}
		}
	}

	sort(evs.begin(), evs.end());
	int ans = 0, cnt = 0;
	for (int i=0; i<(int)evs.size(); i++) {
		auto &[t, rem] = evs[i];

		if (t >= 0) ans = max(ans, cnt);

		if (rem) {
			cnt--;
		} else {
			cnt++;
		}
	}

	cout << ans << '\n';
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);
	int tcs = 1;
	// cin >> tcs;
	while (tcs--) {
		solve();
	}
	return 0;
}

Subtask #1
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 488 KB Output is correct
4 Correct 2 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 2 ms 348 KB Output is correct
7 Correct 1 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 0 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 1 ms 348 KB Output is correct
14 Correct 3 ms 348 KB Output is correct
15 Correct 2 ms 348 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 2 ms 348 KB Output is correct
18 Correct 2 ms 348 KB Output is correct
19 Correct 2 ms 348 KB Output is correct
20 Correct 3 ms 544 KB Output is correct
21 Correct 2 ms 496 KB Output is correct
22 Correct 3 ms 348 KB Output is correct

Subtask #2
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 488 KB Output is correct
4 Correct 2 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 2 ms 348 KB Output is correct
7 Correct 1 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 0 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 1 ms 348 KB Output is correct
14 Correct 3 ms 348 KB Output is correct
15 Correct 2 ms 348 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 2 ms 348 KB Output is correct
18 Correct 2 ms 348 KB Output is correct
19 Correct 2 ms 348 KB Output is correct
20 Correct 3 ms 544 KB Output is correct
21 Correct 2 ms 496 KB Output is correct
22 Correct 3 ms 348 KB Output is correct
23 Correct 197 ms 8596 KB Output is correct
24 Correct 173 ms 7880 KB Output is correct
25 Correct 194 ms 9016 KB Output is correct
26 Correct 195 ms 8212 KB Output is correct
27 Correct 194 ms 5776 KB Output is correct
28 Correct 199 ms 9452 KB Output is correct
29 Correct 211 ms 7884 KB Output is correct
30 Correct 198 ms 9416 KB Output is correct
31 Correct 197 ms 8648 KB Output is correct
32 Correct 204 ms 9160 KB Output is correct
33 Correct 195 ms 8132 KB Output is correct
34 Correct 191 ms 8732 KB Output is correct
35 Correct 197 ms 9160 KB Output is correct
36 Correct 197 ms 8272 KB Output is correct
37 Correct 196 ms 5580 KB Output is correct
38 Correct 193 ms 5580 KB Output is correct
39 Correct 187 ms 5580 KB Output is correct
40 Correct 194 ms 5584 KB Output is correct
41 Correct 194 ms 5584 KB Output is correct
42 Correct 194 ms 5768 KB Output is correct
43 Correct 424 ms 15296 KB Output is correct
44 Correct 399 ms 15552 KB Output is correct
45 Correct 415 ms 16056 KB Output is correct
46 Correct 416 ms 15808 KB Output is correct
47 Correct 409 ms 16064 KB Output is correct
48 Correct 393 ms 16320 KB Output is correct
49 Correct 390 ms 16840 KB Output is correct
50 Correct 400 ms 15044 KB Output is correct
51 Correct 361 ms 15040 KB Output is correct
52 Correct 394 ms 16056 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 488 KB Output is correct
4 Correct 2 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 2 ms 348 KB Output is correct
7 Correct 1 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 0 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 1 ms 348 KB Output is correct
14 Correct 3 ms 348 KB Output is correct
15 Correct 2 ms 348 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 2 ms 348 KB Output is correct
18 Correct 2 ms 348 KB Output is correct
19 Correct 2 ms 348 KB Output is correct
20 Correct 3 ms 544 KB Output is correct
21 Correct 2 ms 496 KB Output is correct
22 Correct 3 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 2 ms 348 KB Output is correct
25 Correct 2 ms 348 KB Output is correct
26 Correct 2 ms 348 KB Output is correct
27 Correct 2 ms 348 KB Output is correct
28 Correct 2 ms 348 KB Output is correct

Subtask #4
32.0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 488 KB Output is correct
4 Correct 2 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 2 ms 348 KB Output is correct
7 Correct 1 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 0 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 1 ms 348 KB Output is correct
14 Correct 3 ms 348 KB Output is correct
15 Correct 2 ms 348 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 2 ms 348 KB Output is correct
18 Correct 2 ms 348 KB Output is correct
19 Correct 2 ms 348 KB Output is correct
20 Correct 3 ms 544 KB Output is correct
21 Correct 2 ms 496 KB Output is correct
22 Correct 3 ms 348 KB Output is correct
23 Correct 197 ms 8596 KB Output is correct
24 Correct 173 ms 7880 KB Output is correct
25 Correct 194 ms 9016 KB Output is correct
26 Correct 195 ms 8212 KB Output is correct
27 Correct 194 ms 5776 KB Output is correct
28 Correct 199 ms 9452 KB Output is correct
29 Correct 211 ms 7884 KB Output is correct
30 Correct 198 ms 9416 KB Output is correct
31 Correct 197 ms 8648 KB Output is correct
32 Correct 204 ms 9160 KB Output is correct
33 Correct 195 ms 8132 KB Output is correct
34 Correct 191 ms 8732 KB Output is correct
35 Correct 197 ms 9160 KB Output is correct
36 Correct 197 ms 8272 KB Output is correct
37 Correct 196 ms 5580 KB Output is correct
38 Correct 193 ms 5580 KB Output is correct
39 Correct 187 ms 5580 KB Output is correct
40 Correct 194 ms 5584 KB Output is correct
41 Correct 194 ms 5584 KB Output is correct
42 Correct 194 ms 5768 KB Output is correct
43 Correct 424 ms 15296 KB Output is correct
44 Correct 399 ms 15552 KB Output is correct
45 Correct 415 ms 16056 KB Output is correct
46 Correct 416 ms 15808 KB Output is correct
47 Correct 409 ms 16064 KB Output is correct
48 Correct 393 ms 16320 KB Output is correct
49 Correct 390 ms 16840 KB Output is correct
50 Correct 400 ms 15044 KB Output is correct
51 Correct 361 ms 15040 KB Output is correct
52 Correct 394 ms 16056 KB Output is correct
53 Correct 0 ms 348 KB Output is correct
54 Correct 2 ms 348 KB Output is correct
55 Correct 2 ms 348 KB Output is correct
56 Correct 2 ms 348 KB Output is correct
57 Correct 2 ms 348 KB Output is correct
58 Correct 2 ms 348 KB Output is correct
59 Correct 197 ms 8648 KB Output is correct
60 Correct 171 ms 9668 KB Output is correct
61 Correct 168 ms 9068 KB Output is correct
62 Correct 166 ms 5584 KB Output is correct
63 Correct 172 ms 9492 KB Output is correct
64 Correct 169 ms 9420 KB Output is correct
65 Correct 174 ms 9348 KB Output is correct
66 Correct 181 ms 8392 KB Output is correct
67 Correct 171 ms 7944 KB Output is correct
68 Correct 205 ms 8640 KB Output is correct
69 Correct 206 ms 7864 KB Output is correct
70 Correct 208 ms 7888 KB Output is correct
71 Correct 199 ms 9160 KB Output is correct
72 Correct 201 ms 8652 KB Output is correct
73 Correct 197 ms 5584 KB Output is correct
74 Correct 189 ms 8648 KB Output is correct
75 Correct 198 ms 8284 KB Output is correct
76 Correct 208 ms 5580 KB Output is correct
77 Correct 396 ms 16684 KB Output is correct
78 Correct 396 ms 16640 KB Output is correct
79 Correct 391 ms 15808 KB Output is correct
80 Correct 403 ms 15552 KB Output is correct
81 Correct 400 ms 15044 KB Output is correct
82 Correct 402 ms 15040 KB Output is correct
83 Correct 385 ms 16068 KB Output is correct
84 Correct 399 ms 15300 KB Output is correct
85 Correct 378 ms 15252 KB Output is correct
86 Correct 401 ms 15916 KB Output is correct

Subtask #5
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 488 KB Output is correct
4 Correct 2 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 2 ms 348 KB Output is correct
7 Correct 1 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 0 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 1 ms 348 KB Output is correct
14 Correct 3 ms 348 KB Output is correct
15 Correct 2 ms 348 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 2 ms 348 KB Output is correct
18 Correct 2 ms 348 KB Output is correct
19 Correct 2 ms 348 KB Output is correct
20 Correct 3 ms 544 KB Output is correct
21 Correct 2 ms 496 KB Output is correct
22 Correct 3 ms 348 KB Output is correct
23 Correct 197 ms 8596 KB Output is correct
24 Correct 173 ms 7880 KB Output is correct
25 Correct 194 ms 9016 KB Output is correct
26 Correct 195 ms 8212 KB Output is correct
27 Correct 194 ms 5776 KB Output is correct
28 Correct 199 ms 9452 KB Output is correct
29 Correct 211 ms 7884 KB Output is correct
30 Correct 198 ms 9416 KB Output is correct
31 Correct 197 ms 8648 KB Output is correct
32 Correct 204 ms 9160 KB Output is correct
33 Correct 195 ms 8132 KB Output is correct
34 Correct 191 ms 8732 KB Output is correct
35 Correct 197 ms 9160 KB Output is correct
36 Correct 197 ms 8272 KB Output is correct
37 Correct 196 ms 5580 KB Output is correct
38 Correct 193 ms 5580 KB Output is correct
39 Correct 187 ms 5580 KB Output is correct
40 Correct 194 ms 5584 KB Output is correct
41 Correct 194 ms 5584 KB Output is correct
42 Correct 194 ms 5768 KB Output is correct
43 Correct 424 ms 15296 KB Output is correct
44 Correct 399 ms 15552 KB Output is correct
45 Correct 415 ms 16056 KB Output is correct
46 Correct 416 ms 15808 KB Output is correct
47 Correct 409 ms 16064 KB Output is correct
48 Correct 393 ms 16320 KB Output is correct
49 Correct 390 ms 16840 KB Output is correct
50 Correct 400 ms 15044 KB Output is correct
51 Correct 361 ms 15040 KB Output is correct
52 Correct 394 ms 16056 KB Output is correct
53 Correct 197 ms 8648 KB Output is correct
54 Correct 171 ms 9668 KB Output is correct
55 Correct 168 ms 9068 KB Output is correct
56 Correct 166 ms 5584 KB Output is correct
57 Correct 172 ms 9492 KB Output is correct
58 Correct 169 ms 9420 KB Output is correct
59 Correct 174 ms 9348 KB Output is correct
60 Correct 181 ms 8392 KB Output is correct
61 Correct 171 ms 7944 KB Output is correct
62 Correct 205 ms 8640 KB Output is correct
63 Correct 206 ms 7864 KB Output is correct
64 Correct 208 ms 7888 KB Output is correct
65 Correct 199 ms 9160 KB Output is correct
66 Correct 201 ms 8652 KB Output is correct
67 Correct 197 ms 5584 KB Output is correct
68 Correct 189 ms 8648 KB Output is correct
69 Correct 198 ms 8284 KB Output is correct
70 Correct 208 ms 5580 KB Output is correct
71 Correct 396 ms 16684 KB Output is correct
72 Correct 396 ms 16640 KB Output is correct
73 Correct 391 ms 15808 KB Output is correct
74 Correct 403 ms 15552 KB Output is correct
75 Correct 400 ms 15044 KB Output is correct
76 Correct 402 ms 15040 KB Output is correct
77 Correct 385 ms 16068 KB Output is correct
78 Correct 399 ms 15300 KB Output is correct
79 Correct 378 ms 15252 KB Output is correct
80 Correct 401 ms 15916 KB Output is correct
81 Correct 0 ms 348 KB Output is correct
82 Correct 2 ms 348 KB Output is correct
83 Correct 2 ms 348 KB Output is correct
84 Correct 2 ms 348 KB Output is correct
85 Correct 2 ms 348 KB Output is correct
86 Correct 2 ms 348 KB Output is correct
87 Correct 185 ms 8396 KB Output is correct
88 Correct 177 ms 12748 KB Output is correct
89 Correct 178 ms 11976 KB Output is correct
90 Correct 181 ms 13424 KB Output is correct
91 Correct 180 ms 12492 KB Output is correct
92 Correct 178 ms 13372 KB Output is correct
93 Correct 177 ms 12224 KB Output is correct
94 Correct 180 ms 11724 KB Output is correct
95 Correct 175 ms 12704 KB Output is correct
96 Correct 177 ms 11980 KB Output is correct
97 Correct 205 ms 11852 KB Output is correct
98 Correct 188 ms 11212 KB Output is correct
99 Correct 201 ms 11468 KB Output is correct
100 Correct 199 ms 11184 KB Output is correct
101 Correct 197 ms 11716 KB Output is correct
102 Correct 197 ms 10952 KB Output is correct
103 Correct 199 ms 10952 KB Output is correct
104 Correct 202 ms 10736 KB Output is correct
105 Correct 213 ms 10952 KB Output is correct
106 Correct 198 ms 11720 KB Output is correct