Submission #1131656

#	Time	Username	Problem	Language	Result	Execution time	Memory
1131656		monostack	Balloons (CEOI11_bal)	C++20	100 / 100	175 ms	3560 KiB

bal

#include <bits/stdc++.h>
using namespace std;

const int PRECISION = 3;

/*
 * how long can the radius of the new balloon at position bx be
 * so that it touches the ballon a, which is described by
 * its x position a.first and its radius a.second
 */
double calc_r(pair<double, double> a, double bx) {
	return (a.first - bx) * (a.first - bx) / (4 * a.second);
}

int main() {
	int n;
	cin >> n;

	// the radius of each balloon after inflating
	vector<double> final_radius(n);
	// the balloons we should check when we add a new one
	stack<pair<double, double>> to_check;

	for (int i = 0; i < n; i++) {
		double x, r;
		cin >> x >> r;

		// the maximum radius of the current balloon
		double max_r = r;
		/*
		 * as long as the stack is not empty, we want to check
		 * if the last balloon makes the radius of the current balloon smaller
		 */
		while (!to_check.empty()) {
			pair<double, double> last = to_check.top();
			// the radius if the current balloon touches the last balloon
			double to_last_r = calc_r(last, x);
			/*
			 * the maximum possible radius is the smaller one between current
			 * maximum and the maximum radius so that we touches the last
			 * balloon (by which we have to stop)
			 */
			max_r = min(max_r, to_last_r);

			/*
			 * if current maximum radius >= radius of the last balloon, we can
			 * remove the last balloon since it will never be touched by any
			 * new balloons other than the current one
			 */
			if (max_r >= last.second) {
				to_check.pop();
				// check the next balloon saved which will possibly reduce max_r
				continue;
			}
			/*
			 * otherwise, the current balloon is smaller than the last saved
			 * balloon and we can stop checking
			 */
			else {
				break;
			}
		}
		/*
		 * save the x coordinate and radius of the current balloon, so that
		 * it can be checked later when a new balloon being inflated
		 */
		to_check.push({x, max_r});

		final_radius[i] = max_r;
	}

	cout << fixed << setprecision(PRECISION);
	for (double &r : final_radius) { cout << r << "\n"; }
}

• Subtask 1: 10 / 10
• Subtask 2: 10 / 10
• Subtask 3: 10 / 10
• Subtask 4: 10 / 10
• Subtask 5: 10 / 10
• Subtask 6: 10 / 10
• Subtask 7: 10 / 10
• Subtask 8: 10 / 10
• Subtask 9: 10 / 10
• Subtask 10: 10 / 10