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Submission #481872

# Submission time Handle Problem Language Result Execution time Memory
481872 2021-10-22T04:49:00 Z sberens Mobile (BOI12_mobile) C++17
70 / 100
 1000 ms 47364 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 1 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 1 ms 204 KB Output is correct

Subtask #3
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 368 KB Output is correct
2 Correct 4 ms 432 KB Output is correct
3 Correct 2 ms 332 KB Output is correct
4 Correct 3 ms 428 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 7 ms 552 KB Output is correct
3 Correct 4 ms 416 KB Output is correct
4 Correct 4 ms 540 KB Output is correct

Subtask #5
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 492 KB Output is correct
2 Correct 7 ms 552 KB Output is correct
3 Correct 4 ms 424 KB Output is correct
4 Correct 4 ms 532 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 7 ms 552 KB Output is correct
3 Correct 5 ms 428 KB Output is correct
4 Correct 4 ms 496 KB Output is correct
5 Correct 5 ms 416 KB Output is correct

Subtask #7
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 96 ms 3708 KB Output is correct
2 Correct 83 ms 3188 KB Output is correct
3 Correct 69 ms 2888 KB Output is correct
4 Correct 38 ms 2124 KB Output is correct
5 Correct 30 ms 1428 KB Output is correct

Subtask #8
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 46 ms 1900 KB Output is correct
2 Correct 49 ms 2528 KB Output is correct
3 Correct 49 ms 3256 KB Output is correct
4 Correct 49 ms 2208 KB Output is correct
5 Correct 39 ms 2112 KB Output is correct

Subtask #9
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 148 ms 4508 KB Output is correct
2 Correct 83 ms 3148 KB Output is correct
3 Correct 111 ms 4028 KB Output is correct
4 Correct 39 ms 2300 KB Output is correct
5 Correct 58 ms 2276 KB Output is correct

Subtask #10
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 118 ms 3044 KB Output is correct
2 Correct 90 ms 3148 KB Output is correct
3 Correct 78 ms 2528 KB Output is correct
4 Correct 40 ms 2376 KB Output is correct
5 Correct 60 ms 3812 KB Output is correct

Subtask #11
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 170 ms 5032 KB Output is correct
2 Correct 89 ms 3168 KB Output is correct
3 Correct 75 ms 2452 KB Output is correct
4 Correct 44 ms 2392 KB Output is correct
5 Correct 60 ms 3812 KB Output is correct

Subtask #12
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 868 ms 23996 KB Output is correct
2 Correct 398 ms 8412 KB Output is correct
3 Correct 383 ms 8416 KB Output is correct
4 Correct 198 ms 8648 KB Output is correct
5 Correct 253 ms 12740 KB Output is correct

Subtask #13
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 400 ms 8468 KB Output is correct
2 Correct 702 ms 23676 KB Output is correct
3 Correct 375 ms 11164 KB Output is correct
4 Correct 190 ms 8664 KB Output is correct
5 Correct 254 ms 10948 KB Output is correct

Subtask #14
0 / 5.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1046 ms 28672 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #15
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 464 ms 9976 KB Output is correct
2 Correct 818 ms 28296 KB Output is correct
3 Correct 414 ms 11788 KB Output is correct
4 Correct 219 ms 10208 KB Output is correct
5 Correct 286 ms 12868 KB Output is correct

Subtask #16
0 / 5.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1097 ms 33272 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #17
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 547 ms 11704 KB Output is correct
2 Correct 940 ms 32924 KB Output is correct
3 Correct 544 ms 15272 KB Output is correct
4 Correct 269 ms 11920 KB Output is correct
5 Correct 322 ms 14996 KB Output is correct

Subtask #18
0 / 5.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1089 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 616 ms 13032 KB Output is correct
2 Execution timed out 1034 ms 37544 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 1099 ms 47364 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #21
0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 775 ms 16232 KB Output is correct
2 Execution timed out 1097 ms 46700 KB Time limit exceeded
3 Halted 0 ms 0 KB -