Submission #1045674

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
1045674	2024-08-06T06:53:22 Z	VectorLi	Mobile (BOI12_mobile)	C++14	100 / 100	964 ms	27512 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	2396 KB	Output is correct
2	Correct	2512 KB	Output is correct
3	Correct	2396 KB	Output is correct
4	Correct	2436 KB	Output is correct

Subtask #2
4.0 / 4.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	2392 KB	Output is correct
2	Correct	0 ms	2396 KB	Output is correct
3	Correct	1 ms	2508 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	1 ms	2396 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	2480 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	2528 KB	Output is correct
3	Correct	2 ms	2396 KB	Output is correct
4	Correct	3 ms	2596 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	2 ms	2392 KB	Output is correct
3	Correct	3 ms	2392 KB	Output is correct
4	Correct	3 ms	2396 KB	Output is correct

Subtask #6
5.0 / 5.0

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

Subtask #7
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	45 ms	4700 KB	Output is correct
2	Correct	27 ms	5724 KB	Output is correct
3	Correct	17 ms	5208 KB	Output is correct
4	Correct	70 ms	5896 KB	Output is correct
5	Correct	33 ms	5068 KB	Output is correct

Subtask #8
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	37 ms	4700 KB	Output is correct
2	Correct	59 ms	5464 KB	Output is correct
3	Correct	89 ms	5720 KB	Output is correct
4	Correct	72 ms	5720 KB	Output is correct
5	Correct	79 ms	5976 KB	Output is correct

Subtask #9
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	30 ms	4700 KB	Output is correct
2	Correct	28 ms	4744 KB	Output is correct
3	Correct	24 ms	4752 KB	Output is correct
4	Correct	100 ms	8540 KB	Output is correct
5	Correct	65 ms	5628 KB	Output is correct

Subtask #10
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	35 ms	6748 KB	Output is correct
2	Correct	37 ms	6748 KB	Output is correct
3	Correct	28 ms	6748 KB	Output is correct
4	Correct	98 ms	8736 KB	Output is correct
5	Correct	87 ms	8036 KB	Output is correct

Subtask #11
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	35 ms	6744 KB	Output is correct
2	Correct	43 ms	6744 KB	Output is correct
3	Correct	41 ms	6748 KB	Output is correct
4	Correct	99 ms	8720 KB	Output is correct
5	Correct	86 ms	8028 KB	Output is correct

Subtask #12
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	167 ms	6772 KB	Output is correct
2	Correct	179 ms	6780 KB	Output is correct
3	Correct	177 ms	6748 KB	Output is correct
4	Correct	477 ms	6792 KB	Output is correct
5	Correct	469 ms	13396 KB	Output is correct

Subtask #13
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	182 ms	6744 KB	Output is correct
2	Correct	304 ms	6780 KB	Output is correct
3	Correct	142 ms	12368 KB	Output is correct
4	Correct	477 ms	15956 KB	Output is correct
5	Correct	442 ms	14080 KB	Output is correct

Subtask #14
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	194 ms	6748 KB	Output is correct
2	Correct	208 ms	6784 KB	Output is correct
3	Correct	209 ms	6748 KB	Output is correct
4	Correct	575 ms	6776 KB	Output is correct
5	Correct	521 ms	14680 KB	Output is correct

Subtask #15
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	212 ms	6776 KB	Output is correct
2	Correct	346 ms	6744 KB	Output is correct
3	Correct	183 ms	13568 KB	Output is correct
4	Correct	573 ms	18612 KB	Output is correct
5	Correct	570 ms	15504 KB	Output is correct

Subtask #16
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	249 ms	7088 KB	Output is correct
2	Correct	254 ms	7036 KB	Output is correct
3	Correct	266 ms	6996 KB	Output is correct
4	Correct	671 ms	6996 KB	Output is correct
5	Correct	581 ms	16112 KB	Output is correct

Subtask #17
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	251 ms	6992 KB	Output is correct
2	Correct	370 ms	7028 KB	Output is correct
3	Correct	200 ms	15456 KB	Output is correct
4	Correct	684 ms	20480 KB	Output is correct
5	Correct	625 ms	17240 KB	Output is correct

Subtask #18
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	258 ms	7484 KB	Output is correct
2	Correct	271 ms	7508 KB	Output is correct
3	Correct	270 ms	7252 KB	Output is correct
4	Correct	811 ms	7252 KB	Output is correct
5	Correct	696 ms	18512 KB	Output is correct

Subtask #19
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	277 ms	7248 KB	Output is correct
2	Correct	409 ms	7508 KB	Output is correct
3	Correct	230 ms	16896 KB	Output is correct
4	Correct	765 ms	22976 KB	Output is correct
5	Correct	721 ms	19280 KB	Output is correct

Subtask #20
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	321 ms	8252 KB	Output is correct
2	Correct	350 ms	8172 KB	Output is correct
3	Correct	347 ms	8016 KB	Output is correct
4	Correct	952 ms	8260 KB	Output is correct
5	Correct	857 ms	21740 KB	Output is correct

Subtask #21
5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	353 ms	8060 KB	Output is correct
2	Correct	483 ms	8260 KB	Output is correct
3	Correct	294 ms	20308 KB	Output is correct
4	Correct	964 ms	27512 KB	Output is correct
5	Correct	902 ms	22900 KB	Output is correct

Submission #1045674

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