Submission #1097990

#	Time	Username	Problem	Language	Result	Execution time	Memory
1097990		0x34c	Mobile (BOI12_mobile)	C++17	0 / 100	1093 ms	121524 KiB

mobile

#include <bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define endl '\n'
#define int ll
#define ld long double
#define pdd pair<ld, ld>

using namespace std;

int dist2(pii a, pii b)
{
    return (a.first - b.first) * (a.first - b.first) + (a.second - b.second) * (a.second - b.second);
}

ld dist(pii a, ld x)
{
    return sqrt((((ld)a.first) - x) * (((ld)a.first) - x) + (ld)(a.second * a.second));
}

const int INF = 1e9 + 1;
const int INF2 = 1e12;
ld eps = 1e-4;

signed main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int N, L;
    cin >> N >> L;

    vector<pii> inp(N);
    map<int, int> closest;
    for (int i = 0; i < N; i++)
    {
        int x, y;
        cin >> x >> y;

        inp[i] = {x, y};

        if (!closest.count(x))
            closest[x] = abs(y);
        else
            closest[x] = min(closest[x], abs(y));
    }

    vector<pii> pts;
    for (pii p : closest)
        pts.push_back(p);

    N = pts.size();
    vector<ld> bp(N);
    for (int i = 0; i < N - 1; i++)
    {
        ld l = -INF, r = INF;
        while ((r - l) > eps)
        {
            ld m = l + (r - l) / 2;

            ld d1 = dist(pts[i], m), d2 = dist(pts[i + 1], m);
            if (d1 < d2)
                l = m;
            else
                r = m;
        }

        bp[i] = l + (r - l) / 2;
    }

    ld mx_dist = 0;
    for (int i = 0; i < N - 1; i++)
    {
        if (bp[i] < 0 || bp[i] > L)
            continue;
        mx_dist = max(mx_dist, dist(pts[i], bp[i]));
    }

    ld mn_start = INF2, mn_end = INF2;
    for (int i = 0; i < N; i++)
    {
        mn_start = min(mn_start, dist(pts[i], 0));
        mn_end = min(mn_end, dist(pts[i], L));
    }

    mx_dist = max({mx_dist, mn_start, mn_end});
    cout << setprecision(4) << fixed << mx_dist << endl;
}

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