Submission #88187

#	Time	Username	Problem	Language	Result	Execution time	Memory
88187		JustInCase	Mobile (BOI12_mobile)	C++17	25 / 100	1078 ms	71208 KiB

mobile

#include <bits/stdc++.h>

const int32_t MAX_N = 1e6;
const double EPS = 1e-6;

int32_t n, l;
std::pair< int32_t, int32_t > points[MAX_N + 5];

bool Check(long double r) {
	std::vector< std::pair< long double, bool > > events(2 * n);

	for(int32_t i = 0; i < n; i++) {
		if(r * r < (int64_t) points[i].second * points[i].second) {
			events[2 * i] = { -2.0, 0 };
			events[2 * i + 1] = { -1.0, 1 };
			continue;
		}

		long double x1 = points[i].first - sqrt(r * r - (int64_t) points[i].second * points[i].second);
		long double x2 = points[i].first + sqrt(r * r - (int64_t) points[i].second * points[i].second);

		events[2 * i] = { x1, 0 };
		events[2 * i + 1] = { x2, 1 };
	}

	std::sort(events.begin(), events.end());

	int32_t currCnt = 0;
	for(int32_t i = 0; i < 2 * n; i++) {
		if(events[i].first > 0 && currCnt == 0) {
			return false;
		}

		if(events[i].first > l) {
			break;
		}

		if(events[i].second == 0) {
			currCnt++;
		}
		else {
			currCnt--;
		}

		if(!(events[i].first < 0.0) && currCnt == 0) {
			return false;
		}
	}

	if(events.back().first < 0) {
		return false;
	}

	return true;
}

int main() {
	std::ios_base::sync_with_stdio(false);
	std::cin.tie(nullptr);

	std::cin >> n >> l;

	for(int32_t i = 0; i < n; i++) {
		std::cin >> points[i].first >> points[i].second;
	}

	int64_t low = 1, high = 1e16;
	long double ans;
	while(low <= high) {
		int64_t mid = (low + high) / 2;

		if(Check(mid / 1000.0)) {
			ans = mid / 1000.0;
			high = mid - 1;
		}
		else {
			low = mid + 1;
		}
	}

	std::cout << std::fixed << std::setprecision(7);
	std::cout << ans << '\n';
}

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