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Submission #481865

# Submission time Handle Problem Language Result Execution time Memory
481865 2021-10-22T04:13:17 Z sberens Mobile (BOI12_mobile) C++17
70 / 100
 1000 ms 47512 KB 
#pragma GCC optimize ("O3,fast-math,inline")

#include <bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template <typename K> using hset = gp_hash_table<K, null_type>;
template <typename K, typename V> using hmap = gp_hash_table<K, V>;


using namespace std;

#define all(x) (x).begin(), (x).end()
#define pb push_back
#define eb emplace_back
#define smax(x, y) (x = max(x, y))
#define smin(x, y) (x = min(x, y))

using ld = long double;
using ll = long long;

template <typename T>
using vv = vector<vector<T>>;

using vi = vector<int>;
using ii = array<int, 2>;
using vii = vector<ii>;
using vvi = vv<int>;

using vll = vector<ll>;
using l2 = array<int, 2>;
using vl2 = vector<l2>;
using vvll = vv<ll>;

template <typename T>
using minq = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxq = priority_queue<T>;

const ll M = 1000000007;

#ifndef REFERENCE_DISCRETE_BINARY_SEARCH_H
#define REFERENCE_DISCRETE_BINARY_SEARCH_H


#include <iostream>
#include <functional>


template<typename IN>
IN discrete_binary_search(function<bool(IN)> predicate, IN low = 0, IN high = numeric_limits<IN>::max()) {
    while (fabs(high - low) > 1e-4) {
        IN middle = low + (high - low) / 2; // todo std::midpoint in cpp 2020
        if (predicate(middle))
            high = middle;
        else low = middle;
    }
    return low;
}

#endif //REFERENCE_DISCRETE_BINARY_SEARCH_H

inline bool a_contains_b(array<ld, 2> a,  array<ld, 2> b) {
    return a[0] <= b[0] && b[1] <= a[1];
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n, l;
    cin >> n >> l;
    vll x(n), y(n);
    for (int i = 0; i < n; ++i) {
        cin >> x[i] >> y[i];
    }

    cout << fixed << setprecision(4) <<  discrete_binary_search<ld>([&](ld d) -> bool {
        // is there a point with min distance > d
        // equivalently, is every point within distance d

        vector<array<ld, 2>> intervals;
        intervals.reserve(n);
        // add to intervals
        for (int i = 0; i < n; ++i) {
            if (abs(y[i]) > d) continue;
            ld dx = sqrt(d * d - y[i] * y[i]);
            // get rid of nested intervals
            array<ld, 2> new_interval{x[i] - dx, x[i] + dx};
            while (!intervals.empty() && a_contains_b(new_interval, intervals.back())) {
                intervals.pop_back();
            }
            if (!(!intervals.empty() && a_contains_b(intervals.back(), new_interval)))
                intervals.pb(new_interval);
        }

        // merge intervals
        vector<array<ld, 2>> merged;
        merged.reserve(n);
        for (auto [s, e] : intervals) {
            if (!merged.empty() && s <= merged.back()[1]) smax(merged.back()[1], e);
            else merged.pb({s, e});
        }
        // check interval spans whole highway
        array<ld, 2> highway{0, (ld) l};
        for (auto interval : merged) {
            if (a_contains_b(interval, highway)) return true;
        }
        return false;

    }, 0, sqrt(1e18 + 4 * 1e18 + 1e10)) << '\n';

}

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct

Subtask #2
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct

Subtask #3
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 540 KB Output is correct
2 Correct 4 ms 432 KB Output is correct
3 Correct 2 ms 332 KB Output is correct
4 Correct 4 ms 424 KB Output is correct

Subtask #4
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 472 KB Output is correct
2 Correct 8 ms 552 KB Output is correct
3 Correct 4 ms 416 KB Output is correct
4 Correct 4 ms 532 KB Output is correct

Subtask #5
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 492 KB Output is correct
2 Correct 7 ms 552 KB Output is correct
3 Correct 4 ms 416 KB Output is correct
4 Correct 5 ms 524 KB Output is correct

Subtask #6
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 556 KB Output is correct
2 Correct 8 ms 552 KB Output is correct
3 Correct 4 ms 428 KB Output is correct
4 Correct 3 ms 496 KB Output is correct
5 Correct 5 ms 548 KB Output is correct

Subtask #7
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 100 ms 3692 KB Output is correct
2 Correct 82 ms 3148 KB Output is correct
3 Correct 68 ms 2888 KB Output is correct
4 Correct 38 ms 2152 KB Output is correct
5 Correct 29 ms 1264 KB Output is correct

Subtask #8
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 59 ms 1900 KB Output is correct
2 Correct 49 ms 2508 KB Output is correct
3 Correct 49 ms 3276 KB Output is correct
4 Correct 40 ms 2252 KB Output is correct
5 Correct 39 ms 2144 KB Output is correct

Subtask #9
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 142 ms 4504 KB Output is correct
2 Correct 85 ms 3148 KB Output is correct
3 Correct 106 ms 3940 KB Output is correct
4 Correct 39 ms 2344 KB Output is correct
5 Correct 58 ms 2252 KB Output is correct

Subtask #10
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 117 ms 3036 KB Output is correct
2 Correct 90 ms 3168 KB Output is correct
3 Correct 81 ms 2428 KB Output is correct
4 Correct 39 ms 2368 KB Output is correct
5 Correct 60 ms 3944 KB Output is correct

Subtask #11
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 169 ms 5116 KB Output is correct
2 Correct 89 ms 3172 KB Output is correct
3 Correct 74 ms 2532 KB Output is correct
4 Correct 45 ms 2352 KB Output is correct
5 Correct 59 ms 3812 KB Output is correct

Subtask #12
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 864 ms 23936 KB Output is correct
2 Correct 384 ms 8428 KB Output is correct
3 Correct 380 ms 8408 KB Output is correct
4 Correct 190 ms 8660 KB Output is correct
5 Correct 254 ms 12736 KB Output is correct

Subtask #13
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 391 ms 8624 KB Output is correct
2 Correct 687 ms 23676 KB Output is correct
3 Correct 382 ms 11172 KB Output is correct
4 Correct 187 ms 8656 KB Output is correct
5 Correct 228 ms 10948 KB Output is correct

Subtask #14
0 / 5.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1035 ms 28640 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #15
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 468 ms 9992 KB Output is correct
2 Correct 818 ms 28456 KB Output is correct
3 Correct 434 ms 11792 KB Output is correct
4 Correct 228 ms 10212 KB Output is correct
5 Correct 270 ms 12896 KB Output is correct

Subtask #16
0 / 5.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1086 ms 33332 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #17
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 536 ms 11612 KB Output is correct
2 Correct 920 ms 32932 KB Output is correct
3 Correct 540 ms 15336 KB Output is correct
4 Correct 266 ms 11844 KB Output is correct
5 Correct 327 ms 15000 KB Output is correct

Subtask #18
0 / 5.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1090 ms 38064 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #19
0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 635 ms 13028 KB Output is correct
2 Execution timed out 1031 ms 37520 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #20
0 / 5.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1088 ms 47512 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #21
0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 760 ms 16240 KB Output is correct
2 Execution timed out 1101 ms 46716 KB Time limit exceeded
3 Halted 0 ms 0 KB -