Manhattan sightseeing

#include <algorithm>
#include <bits/stdc++.h>
#include <string>
using namespace std;
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define int long long

string to_string(string s) {
    return '"' + s + '"';
}
 
string to_string(const char* s) {
    return to_string((string) s);
}
 
string to_string(bool b) {
    return (b ? "true" : "false");
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A>
string to_string(A v) {
    bool first = true;
    string res = "{";
    for (const auto &x : v) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(x);
    }
    res += "}";
    return res;
}
 
void debug_out() {
    cerr << endl;
}
 
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}
 
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

const int N = 1e5 + 5;
const int INF = 1e9;

int n, x[N], y[N];

void solve() {
    cin >> n;
    int mxx = 0, mnx = INF, mxy = 0, mny = INF;    
    for (int i = 1; i <= n; i++) {
        cin >> x[i] >> y[i];
        mxx = max(mxx, x[i]);
        mxy = max(mxy, y[i]);
        mnx = min(mnx, x[i]);
        mny = min(mny, x[i]);
    }

    int cx = x[1], cy = y[1];
    for (int i = 2; i <= n; i++) {
        cx = (cx + x[i]) / 2;
        cy = (cy + y[i]) / 2;
    }

    auto mxdist = [&](int posx, int posy) -> int {
        int ans = 0;
        for (int i = 1; i <= n; i++) {
            ans = max(ans, abs(posx - x[i]) + abs(posy - y[i]));
        }
        return ans;
    };

    int best = mxdist(cx, cy), ansx = cx, ansy = cy;
    for (int xx = cx - 5; xx <= cx + 5; xx++) {
        for (int yy = cy - 5; yy <= cy + 5; yy++) {
            int cur = mxdist(xx, yy);
            if (cur < best) {
                best = cur;
                ansx = xx;
                ansy = yy;
            }
        }   
    }

    cout << ansx << ' ' << ansy << '\n';

    

    // auto calc = [&](int posx) -> int {
    //     int low = mny, high = mxy, ans = -1;
    //     while (low <= high) {
    //         int mid = (low + high) / 2;
    //         if (mxdist(posx, mid) >= mxdist(posx, mid + 1)) {
    //             low = mid + 1;
    //             ans = mid + 1;
    //         } else {
    //             high = mid - 1;
    //             ans = mid;
    //         }
    //     } 
    //     return mxdist(posx, ans);
    // };

    // auto findcalc = [&](int posx) -> int {
    //     int low = mny, high = mxy, ans = -1;
    //     while (low <= high) {
    //         int mid = (low + high) / 2;
    //         if (mxdist(posx, mid) >= mxdist(posx, mid + 1)) {
    //             low = mid + 1;
    //             ans = mid + 1;
    //         } else {
    //             high = mid - 1;
    //             ans = mid;
    //         }
    //     } 
    //     return ans;
    // };

    // int lowx = mnx, highx = mxx, ansx = -1;
    // while (lowx <= highx) {
    //     int midx = (lowx + highx) / 2;
    //     if (calc(midx) >= calc(midx + 1)) {
    //         lowx = midx + 1;
    //         ansx = midx + 1;
    //     } else {
    //         highx = midx - 1;
    //         ansx = midx;
    //     }
    // } 

    // cout << ansx << ' ' << findcalc(ansx) << '\n';
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);
            
    int t = 1;
    // cin >> t;

    while (t--) {
        solve();
    }
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: ACCEPTED

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: WRONG ANSWER

Test 39

Verdict: WRONG ANSWER

Test 40

Verdict: WRONG ANSWER

Test 41

Verdict: WRONG ANSWER

Test 42

Verdict: WRONG ANSWER

Test 43

Verdict: WRONG ANSWER

Test 44

Verdict: WRONG ANSWER

Test 45

Verdict: WRONG ANSWER

Test 46

Verdict: WRONG ANSWER

Test 47

Verdict: WRONG ANSWER

Test 48

Verdict: WRONG ANSWER

Test 49

Verdict: WRONG ANSWER

Test 50

Verdict: WRONG ANSWER

Test 51

Verdict: WRONG ANSWER

Test 52

Verdict: WRONG ANSWER

Test 53

Verdict: WRONG ANSWER

Test 54

Verdict: WRONG ANSWER

Test 55

Verdict: WRONG ANSWER

Test 56

Verdict: WRONG ANSWER

Test 57

Verdict: WRONG ANSWER

Test 58

Verdict: WRONG ANSWER

Test 59

Verdict: WRONG ANSWER

Test 60

Verdict: WRONG ANSWER

Test 61

Verdict: WRONG ANSWER

Test 62

Verdict: WRONG ANSWER

Test 63

Verdict: WRONG ANSWER

Test 64

Verdict: WRONG ANSWER

Test 65

Verdict: WRONG ANSWER

Test 66

Verdict: WRONG ANSWER

Test 67

Verdict: WRONG ANSWER

Test 68

Verdict: WRONG ANSWER

Test 69

Verdict: WRONG ANSWER

Test 70

Verdict: WRONG ANSWER

Test 71

Verdict: WRONG ANSWER

Test 72

Verdict: WRONG ANSWER

Test 73

Verdict: WRONG ANSWER

Test 74

Verdict: WRONG ANSWER

Test 75

Verdict: WRONG ANSWER

Test 76

Verdict: WRONG ANSWER

Test 77

Verdict: WRONG ANSWER