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Submission #1083688

# Submission time Handle Problem Language Result Execution time Memory
1083688 2024-09-03T20:26:32 Z vjudge1 Mobile (BOI12_mobile) C++17
90 / 100
 1000 ms 35152 KB 
#include <iostream>
#include <vector>
#include <cmath>
#include <iomanip>

using namespace std;

// Function to check if all points on the highway [0, L] can be covered with distance R
bool canCoverAllPoints(const vector<pair<double, double>>& stations, double R, double L) {
    double currentCoverage = 0.0;
    
    for (const auto& station : stations) {
        double xi = station.first;
        double yi = station.second;
        
        if (yi > R) continue; // This base station cannot help at this R
        
        double reach = sqrt(R * R - yi * yi);
        double startCoverage = max(0.0, xi - reach);
        double endCoverage = xi + reach;
        
        // If this base station can extend the coverage
        if (startCoverage <= currentCoverage) {
            currentCoverage = max(currentCoverage, endCoverage);
        }
        
        if (currentCoverage >= L) return true;
    }
    
    return currentCoverage >= L;
}

int main() {
    int N;
    double L;
    cin >> N >> L;

    vector<pair<double, double>> stations(N);
    for (int i = 0; i < N; ++i) {
        double xi, yi;
        cin >> xi >> yi;
        stations[i] = {xi, yi};
    }

    // Binary search for the smallest possible R
    double low = 0.0;
    double high = 1e9;
    double epsilon = 1e-7; // Tighten the precision for better performance

    while (high - low > epsilon) {
        double mid = (low + high) / 2.0;
        if (canCoverAllPoints(stations, mid, L)) {
            high = mid; // Try smaller radius
        } else {
            low = mid; // Increase radius
        }
    }

    cout << fixed << setprecision(6) << high << endl;
    return 0;
}

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct

Subtask #2
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct

Subtask #3
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 348 KB Output is correct
2 Correct 2 ms 348 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 2 ms 348 KB Output is correct

Subtask #4
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 348 KB Output is correct
2 Correct 4 ms 452 KB Output is correct
3 Correct 3 ms 344 KB Output is correct
4 Correct 4 ms 348 KB Output is correct

Subtask #5
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 348 KB Output is correct
2 Correct 4 ms 348 KB Output is correct
3 Correct 3 ms 348 KB Output is correct
4 Correct 4 ms 344 KB Output is correct

Subtask #6
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 348 KB Output is correct
2 Correct 4 ms 344 KB Output is correct
3 Correct 3 ms 344 KB Output is correct
4 Correct 4 ms 348 KB Output is correct
5 Correct 3 ms 348 KB Output is correct

Subtask #7
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 48 ms 2388 KB Output is correct
2 Correct 52 ms 2636 KB Output is correct
3 Correct 31 ms 1884 KB Output is correct
4 Correct 67 ms 2768 KB Output is correct
5 Correct 25 ms 1372 KB Output is correct

Subtask #8
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 46 ms 2396 KB Output is correct
2 Correct 56 ms 2140 KB Output is correct
3 Correct 63 ms 2592 KB Output is correct
4 Correct 70 ms 2644 KB Output is correct
5 Correct 84 ms 3188 KB Output is correct

Subtask #9
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 47 ms 2392 KB Output is correct
2 Correct 52 ms 2640 KB Output is correct
3 Correct 47 ms 2644 KB Output is correct
4 Correct 104 ms 3884 KB Output is correct
5 Correct 59 ms 2744 KB Output is correct

Subtask #10
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 72 ms 3372 KB Output is correct
2 Correct 65 ms 3152 KB Output is correct
3 Correct 54 ms 3016 KB Output is correct
4 Correct 108 ms 3920 KB Output is correct
5 Correct 77 ms 3156 KB Output is correct

Subtask #11
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 72 ms 3412 KB Output is correct
2 Correct 67 ms 3152 KB Output is correct
3 Correct 54 ms 3008 KB Output is correct
4 Correct 104 ms 3920 KB Output is correct
5 Correct 79 ms 3264 KB Output is correct

Subtask #12
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 290 ms 12372 KB Output is correct
2 Correct 360 ms 15912 KB Output is correct
3 Correct 311 ms 15444 KB Output is correct
4 Correct 516 ms 18000 KB Output is correct
5 Correct 416 ms 14912 KB Output is correct

Subtask #13
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 377 ms 16464 KB Output is correct
2 Correct 382 ms 14676 KB Output is correct
3 Correct 280 ms 13864 KB Output is correct
4 Correct 508 ms 17576 KB Output is correct
5 Correct 481 ms 15444 KB Output is correct

Subtask #14
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 347 ms 14928 KB Output is correct
2 Correct 421 ms 19012 KB Output is correct
3 Correct 369 ms 18256 KB Output is correct
4 Correct 630 ms 21464 KB Output is correct
5 Correct 535 ms 17740 KB Output is correct

Subtask #15
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 443 ms 19656 KB Output is correct
2 Correct 487 ms 17496 KB Output is correct
3 Correct 341 ms 16464 KB Output is correct
4 Correct 628 ms 21448 KB Output is correct
5 Correct 518 ms 18384 KB Output is correct

Subtask #16
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 408 ms 17248 KB Output is correct
2 Correct 479 ms 22100 KB Output is correct
3 Correct 455 ms 21316 KB Output is correct
4 Correct 721 ms 25168 KB Output is correct
5 Correct 564 ms 20404 KB Output is correct

Subtask #17
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 498 ms 22756 KB Output is correct
2 Correct 516 ms 20692 KB Output is correct
3 Correct 419 ms 19540 KB Output is correct
4 Correct 735 ms 24656 KB Output is correct
5 Correct 607 ms 21472 KB Output is correct

Subtask #18
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 467 ms 19976 KB Output is correct
2 Correct 561 ms 25172 KB Output is correct
3 Correct 500 ms 24404 KB Output is correct
4 Correct 866 ms 28496 KB Output is correct
5 Correct 708 ms 23936 KB Output is correct

Subtask #19
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 661 ms 26192 KB Output is correct
2 Correct 592 ms 23636 KB Output is correct
3 Correct 450 ms 22352 KB Output is correct
4 Correct 838 ms 28180 KB Output is correct
5 Correct 713 ms 24404 KB Output is correct

Subtask #20
0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 591 ms 24768 KB Output is correct
2 Correct 659 ms 31572 KB Output is correct
3 Correct 677 ms 30420 KB Output is correct
4 Execution timed out 1041 ms 35004 KB Time limit exceeded
5 Halted 0 ms 0 KB -

Subtask #21
0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 735 ms 32568 KB Output is correct
2 Correct 754 ms 29272 KB Output is correct
3 Correct 592 ms 28356 KB Output is correct
4 Execution timed out 1056 ms 35152 KB Time limit exceeded
5 Halted 0 ms 0 KB -