#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
vector<pair<double, double>> torri;
ll n, L;
bool canCover(double r) {
double curr = 0.0; // Current coverage along the highway
for (int i = 0; i < n; i++) {
double x = torri[i].first;
double y = torri[i].second;
// Calculate the horizontal coverage from the station
if (abs(y) > r) continue; // Ignore stations that cannot reach the highway
double dx = sqrt((r * r) - (y * y)); // Width of coverage
double left = x - dx; // Left end of coverage
double right = x + dx; // Right end of coverage
// If the current position is within the coverage
if (left <= curr + 1e-6) {
curr = max(curr, right); // Extend current coverage
}
// Early exit if the entire highway is covered
if (curr >= L) return true;
}
return curr >= L; // Final check if we covered the highway
}
void solve() {
cin >> n >> L;
torri.resize(n);
for (int i = 0; i < n; i++) {
cin >> torri[i].first >> torri[i].second;
}
double l = 1.0, r = 2e9; // Reasonable bounds for binary search
double ans = r;
// Perform binary search
while (r - l > 1e-4) {
double mid = (l + r) / 2;
if (canCover(mid)) {
ans = mid; // Update best answer
r = mid; // Try for a smaller radius
} else {
l = mid; // Increase radius
}
}
cout << setprecision(18) << ans << endl; // Output the result
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
0 ms |
344 KB |
Output is correct |
2 |
Correct |
0 ms |
344 KB |
Output is correct |
3 |
Correct |
1 ms |
348 KB |
Output is correct |
4 |
Correct |
1 ms |
348 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
348 KB |
Output is correct |
2 |
Correct |
1 ms |
348 KB |
Output is correct |
3 |
Correct |
0 ms |
348 KB |
Output is correct |
4 |
Correct |
0 ms |
348 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
348 KB |
Output is correct |
2 |
Correct |
1 ms |
468 KB |
Output is correct |
3 |
Correct |
1 ms |
348 KB |
Output is correct |
4 |
Correct |
1 ms |
348 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
2 ms |
348 KB |
Output is correct |
2 |
Correct |
2 ms |
348 KB |
Output is correct |
3 |
Correct |
2 ms |
348 KB |
Output is correct |
4 |
Correct |
2 ms |
604 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
2 ms |
344 KB |
Output is correct |
2 |
Correct |
2 ms |
348 KB |
Output is correct |
3 |
Correct |
2 ms |
348 KB |
Output is correct |
4 |
Correct |
2 ms |
608 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
2 ms |
344 KB |
Output is correct |
2 |
Correct |
3 ms |
348 KB |
Output is correct |
3 |
Correct |
2 ms |
348 KB |
Output is correct |
4 |
Correct |
4 ms |
600 KB |
Output is correct |
5 |
Correct |
2 ms |
348 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
31 ms |
1628 KB |
Output is correct |
2 |
Correct |
25 ms |
2552 KB |
Output is correct |
3 |
Correct |
15 ms |
1924 KB |
Output is correct |
4 |
Correct |
34 ms |
2660 KB |
Output is correct |
5 |
Correct |
21 ms |
1492 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
23 ms |
1696 KB |
Output is correct |
2 |
Correct |
21 ms |
2332 KB |
Output is correct |
3 |
Correct |
26 ms |
2628 KB |
Output is correct |
4 |
Correct |
27 ms |
2908 KB |
Output is correct |
5 |
Correct |
38 ms |
3156 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
33 ms |
1628 KB |
Output is correct |
2 |
Correct |
27 ms |
1624 KB |
Output is correct |
3 |
Correct |
25 ms |
2648 KB |
Output is correct |
4 |
Correct |
37 ms |
3928 KB |
Output is correct |
5 |
Correct |
27 ms |
2648 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
33 ms |
1884 KB |
Output is correct |
2 |
Correct |
32 ms |
3424 KB |
Output is correct |
3 |
Correct |
32 ms |
3036 KB |
Output is correct |
4 |
Correct |
43 ms |
3924 KB |
Output is correct |
5 |
Correct |
29 ms |
3164 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
42 ms |
1880 KB |
Output is correct |
2 |
Correct |
33 ms |
1880 KB |
Output is correct |
3 |
Correct |
28 ms |
3044 KB |
Output is correct |
4 |
Correct |
35 ms |
3932 KB |
Output is correct |
5 |
Correct |
32 ms |
3300 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
162 ms |
8280 KB |
Output is correct |
2 |
Correct |
171 ms |
8284 KB |
Output is correct |
3 |
Correct |
147 ms |
8280 KB |
Output is correct |
4 |
Correct |
172 ms |
8284 KB |
Output is correct |
5 |
Correct |
150 ms |
14932 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
175 ms |
8536 KB |
Output is correct |
2 |
Correct |
221 ms |
8528 KB |
Output is correct |
3 |
Correct |
136 ms |
13892 KB |
Output is correct |
4 |
Correct |
183 ms |
17492 KB |
Output is correct |
5 |
Correct |
152 ms |
15568 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
213 ms |
9820 KB |
Output is correct |
2 |
Correct |
191 ms |
9820 KB |
Output is correct |
3 |
Correct |
186 ms |
18284 KB |
Output is correct |
4 |
Correct |
230 ms |
21584 KB |
Output is correct |
5 |
Correct |
196 ms |
17596 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
219 ms |
10064 KB |
Output is correct |
2 |
Correct |
260 ms |
9844 KB |
Output is correct |
3 |
Correct |
172 ms |
16612 KB |
Output is correct |
4 |
Correct |
233 ms |
21464 KB |
Output is correct |
5 |
Correct |
189 ms |
18512 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
303 ms |
11428 KB |
Output is correct |
2 |
Correct |
236 ms |
11404 KB |
Output is correct |
3 |
Correct |
234 ms |
21332 KB |
Output is correct |
4 |
Correct |
256 ms |
24828 KB |
Output is correct |
5 |
Correct |
202 ms |
20304 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
234 ms |
11352 KB |
Output is correct |
2 |
Correct |
326 ms |
11404 KB |
Output is correct |
3 |
Correct |
196 ms |
19540 KB |
Output is correct |
4 |
Correct |
242 ms |
24576 KB |
Output is correct |
5 |
Correct |
210 ms |
21500 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
261 ms |
12892 KB |
Output is correct |
2 |
Correct |
256 ms |
12888 KB |
Output is correct |
3 |
Correct |
263 ms |
24400 KB |
Output is correct |
4 |
Correct |
294 ms |
28500 KB |
Output is correct |
5 |
Correct |
268 ms |
23888 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
355 ms |
12892 KB |
Output is correct |
2 |
Correct |
330 ms |
12888 KB |
Output is correct |
3 |
Correct |
243 ms |
22300 KB |
Output is correct |
4 |
Correct |
291 ms |
28240 KB |
Output is correct |
5 |
Correct |
253 ms |
24488 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
358 ms |
15964 KB |
Output is correct |
2 |
Correct |
291 ms |
15960 KB |
Output is correct |
3 |
Correct |
326 ms |
30400 KB |
Output is correct |
4 |
Correct |
338 ms |
35156 KB |
Output is correct |
5 |
Correct |
328 ms |
29520 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
351 ms |
15960 KB |
Output is correct |
2 |
Correct |
412 ms |
16096 KB |
Output is correct |
3 |
Correct |
312 ms |
28264 KB |
Output is correct |
4 |
Correct |
390 ms |
35408 KB |
Output is correct |
5 |
Correct |
396 ms |
30684 KB |
Output is correct |