claoj/cpp/prevoi19_robots.cpp

#include <iostream>
#include <vector>
#include <algorithm>
#include <climits>
using namespace std;

typedef long long ll;

struct Point {
    ll x, y;
};

ll manhattan(const Point &a, const Point &b) {
    return abs(a.x - b.x) + abs(a.y - b.y);
}

bool isPossible(ll D, const vector<Point> &chargers, const Point &start, ll N) {
    ll u0 = start.x + start.y;
    ll v0 = start.x - start.y;
    ll min_u = u0 - N;
    ll max_u = u0 + N;
    ll min_v = v0 - N;
    ll max_v = v0 + N;

    vector<ll> u_candidates = {min_u, max_u, u0};
    vector<ll> v_candidates = {min_v, max_v, v0};

    for (const Point &c: chargers) {
        ll cu = c.x + c.y;
        ll cv = c.x - c.y;
        u_candidates.push_back(cu - D);
        u_candidates.push_back(cu + D);
        v_candidates.push_back(cv - D);
        v_candidates.push_back(cv + D);
    }

    sort(u_candidates.begin(), u_candidates.end());
    u_candidates.erase(unique(u_candidates.begin(), u_candidates.end()), u_candidates.end());

    sort(v_candidates.begin(), v_candidates.end());
    v_candidates.erase(unique(v_candidates.begin(), v_candidates.end()), v_candidates.end());

    for (ll u: u_candidates) {
        for (ll v: v_candidates) {
            if (u < min_u || u > max_u || v < min_v || v > max_v) continue;

            ll x = (u + v) / 2;
            ll y = (u - v) / 2;

            if ((u + v) % 2 != 0) continue;

            Point p = {x, y};
            if (manhattan(p, start) > N) continue;

            bool valid = true;
            for (const Point &c: chargers) {
                if (manhattan(p, c) < D) {
                    valid = false;
                    break;
                }
            }
            if (valid) return true;
        }
    }
    return false;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int U;
    ll N;
    cin >> U >> N;

    vector<Point> chargers(U);
    for (int i = 0; i < U; i++) {
        cin >> chargers[i].x >> chargers[i].y;
    }

    Point start;
    cin >> start.x >> start.y;

    ll left = 0;
    ll right = 4e9;

    while (left <= right) {
        ll mid = left + (right - left) / 2;
        if (isPossible(mid, chargers, start, N)) {
            left = mid + 1;
        } else {
            right = mid - 1;
        }
    }

    cout << right << endl;

    return 0;
}