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Submission #956886

# Submission time Handle Problem Language Result Execution time Memory
956886 2024-04-02T15:48:57 Z dzzz Balloons (CEOI11_bal) C++17
100 / 100
 274 ms 7204 KB 
#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
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB 10 numbers

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB 2 numbers

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB 505 numbers

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 504 KB 2000 numbers

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 26 ms 600 KB 20000 numbers

Subtask #6
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 60 ms 1368 KB 50000 numbers
2 Correct 67 ms 1876 KB 49912 numbers

Subtask #7
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 120 ms 2132 KB 100000 numbers

Subtask #8
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 142 ms 2284 KB 115362 numbers
2 Correct 156 ms 4316 KB 119971 numbers

Subtask #9
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 199 ms 3028 KB 154271 numbers
2 Correct 274 ms 7204 KB 200000 numbers

Subtask #10
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 243 ms 3412 KB 200000 numbers
2 Correct 255 ms 6988 KB 199945 numbers