Submission #1056877

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
1056877	2024-08-13T12:02:39 Z	TimAni	Mobile (BOI12_mobile)	C++17	100 / 100	960 ms	27628 KB

mobile

#include <bits/stdc++.h>
#define long long long
 
using namespace std;
 
const int N = (int) 1E6;
 
int n, k;
int x[N], y[N];
 
/*
为什么这么做的对的，考虑排序线段。
我们排序线段的目的就是为了 连的上！
所以如果线段 i 在 j 之后出现
且 l(i) < l(j)
一定有 r(i) > r(j)，这就保证了我们不需要使用排序 
*/
 
bool valid(double a) {
	double t = 0;
	// t 表示已经可以覆盖 [0, t] 了，初始为空区间 
	// 因为输入的点的坐标是有序的，所以如果当前的 r 只能覆盖线段
	// 的中段的话，t 还会保持是 0 
	for (int i = 0; i < n; i++) {
		if (a < y[i]) {
			continue;
		} 
		double l = x[i] - sqrt(1.0 * a * a - 1.0 * y[i] * y[i]);
		// 直接 y[i] * y[i] 可能会爆
		// 同时，由于 r 大于最大的 abs(y[i])，所以不会出现 sqrt 负数的情况 
		double r = x[i] + sqrt(1.0 * a * a - 1.0 * y[i] * y[i]);
		if (l <= t && r >= t) {
			t = r;
		}
	}
	return t >= k;
}
 
void solve() {
	cin >> n >> k;
	for (int i = 0; i < n; i++) {
		cin >> x[i] >> y[i];
	}
	
	double l = 0, r = 2E9;
	for (int i = 0; i < 100; i++) {
		double m = (l + r) / 2;
		if (valid(m)) {
			r = m;
		} else {
			l = m;
		}
	}
	cout << fixed << setprecision(6);
	cout << r << "\n";
}
 
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int t;
	t = 1;
	for (int i = 0; i < t; i++) {
		solve();
	}
	return 0;
}

Subtask #1
4.0 / 4.0

#	Verdict	Memory	Grader output
1	Correct	2392 KB	Output is correct
2	Correct	2392 KB	Output is correct
3	Correct	2396 KB	Output is correct
4	Correct	2396 KB	Output is correct

Subtask #2
4.0 / 4.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	2392 KB	Output is correct
2	Correct	0 ms	2396 KB	Output is correct
3	Correct	1 ms	2396 KB	Output is correct
4	Correct	0 ms	2396 KB	Output is correct

Subtask #3
4.0 / 4.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	2392 KB	Output is correct
2	Correct	1 ms	2396 KB	Output is correct
3	Correct	1 ms	2396 KB	Output is correct
4	Correct	1 ms	2396 KB	Output is correct

Subtask #4
4.0 / 4.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	3 ms	2396 KB	Output is correct
2	Correct	2 ms	2568 KB	Output is correct
3	Correct	2 ms	2396 KB	Output is correct
4	Correct	3 ms	2600 KB	Output is correct

Subtask #5
4.0 / 4.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	3 ms	2396 KB	Output is correct
2	Correct	3 ms	2396 KB	Output is correct
3	Correct	2 ms	2396 KB	Output is correct
4	Correct	3 ms	2392 KB	Output is correct

Subtask #6
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	2396 KB	Output is correct
2	Correct	2 ms	2524 KB	Output is correct
3	Correct	2 ms	2392 KB	Output is correct
4	Correct	3 ms	2616 KB	Output is correct
5	Correct	2 ms	2572 KB	Output is correct

Subtask #7
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	37 ms	4700 KB	Output is correct
2	Correct	26 ms	5720 KB	Output is correct
3	Correct	21 ms	5368 KB	Output is correct
4	Correct	68 ms	5724 KB	Output is correct
5	Correct	19 ms	4956 KB	Output is correct

Subtask #8
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	37 ms	4696 KB	Output is correct
2	Correct	61 ms	5532 KB	Output is correct
3	Correct	73 ms	5720 KB	Output is correct
4	Correct	71 ms	5720 KB	Output is correct
5	Correct	80 ms	5952 KB	Output is correct

Subtask #9
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	28 ms	4700 KB	Output is correct
2	Correct	30 ms	4700 KB	Output is correct
3	Correct	26 ms	4700 KB	Output is correct
4	Correct	95 ms	7040 KB	Output is correct
5	Correct	61 ms	5448 KB	Output is correct

Subtask #10
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	41 ms	6748 KB	Output is correct
2	Correct	50 ms	6792 KB	Output is correct
3	Correct	29 ms	6748 KB	Output is correct
4	Correct	105 ms	6748 KB	Output is correct
5	Correct	101 ms	7932 KB	Output is correct

Subtask #11
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	43 ms	6780 KB	Output is correct
2	Correct	37 ms	8184 KB	Output is correct
3	Correct	30 ms	7816 KB	Output is correct
4	Correct	98 ms	8540 KB	Output is correct
5	Correct	89 ms	8052 KB	Output is correct

Subtask #12
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	168 ms	6772 KB	Output is correct
2	Correct	223 ms	14328 KB	Output is correct
3	Correct	174 ms	13780 KB	Output is correct
4	Correct	484 ms	16208 KB	Output is correct
5	Correct	458 ms	13392 KB	Output is correct

Subtask #13
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	186 ms	6776 KB	Output is correct
2	Correct	309 ms	13388 KB	Output is correct
3	Correct	143 ms	12372 KB	Output is correct
4	Correct	478 ms	15956 KB	Output is correct
5	Correct	452 ms	13908 KB	Output is correct

Subtask #14
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	196 ms	6744 KB	Output is correct
2	Correct	239 ms	15996 KB	Output is correct
3	Correct	208 ms	15360 KB	Output is correct
4	Correct	601 ms	18688 KB	Output is correct
5	Correct	541 ms	14676 KB	Output is correct

Subtask #15
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	210 ms	6748 KB	Output is correct
2	Correct	353 ms	14708 KB	Output is correct
3	Correct	169 ms	13396 KB	Output is correct
4	Correct	616 ms	18516 KB	Output is correct
5	Correct	531 ms	15508 KB	Output is correct

Subtask #16
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	225 ms	6996 KB	Output is correct
2	Correct	241 ms	17744 KB	Output is correct
3	Correct	242 ms	17236 KB	Output is correct
4	Correct	664 ms	20564 KB	Output is correct
5	Correct	655 ms	15956 KB	Output is correct

Subtask #17
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	248 ms	7088 KB	Output is correct
2	Correct	384 ms	16352 KB	Output is correct
3	Correct	206 ms	15444 KB	Output is correct
4	Correct	672 ms	20348 KB	Output is correct
5	Correct	630 ms	17240 KB	Output is correct

Subtask #18
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	261 ms	7480 KB	Output is correct
2	Correct	306 ms	20048 KB	Output is correct
3	Correct	281 ms	18940 KB	Output is correct
4	Correct	772 ms	22916 KB	Output is correct
5	Correct	725 ms	18648 KB	Output is correct

Subtask #19
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	293 ms	7400 KB	Output is correct
2	Correct	405 ms	18256 KB	Output is correct
3	Correct	238 ms	17232 KB	Output is correct
4	Correct	789 ms	22776 KB	Output is correct
5	Correct	736 ms	19280 KB	Output is correct

Subtask #20
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	357 ms	8020 KB	Output is correct
2	Correct	349 ms	23636 KB	Output is correct
3	Correct	344 ms	22688 KB	Output is correct
4	Correct	960 ms	27488 KB	Output is correct
5	Correct	854 ms	21848 KB	Output is correct

Subtask #21
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	348 ms	8024 KB	Output is correct
2	Correct	492 ms	21584 KB	Output is correct
3	Correct	289 ms	20560 KB	Output is correct
4	Correct	960 ms	27628 KB	Output is correct
5	Correct	916 ms	23028 KB	Output is correct

Submission #1056877

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