Manhattan sightseeing

#include <iostream>
#include <cassert>

using namespace std;

const int N = 1e5 + 5;
const long long LLINF = 2e18;

int n;
int x[N], y[N];
long long xx, yy;

bool check(int mid) {
  long long r1 = -LLINF, c1 = -LLINF, r2 = LLINF, c2 = LLINF;
  for (int i = 1; i <= n; i++) {
    r1 = max(r1, 1LL * x[i] - y[i] - mid);
    c1 = max(c1, 1LL * x[i] + y[i] - mid);
    r2 = min(r2, 1LL * x[i] - y[i] + mid);
    c2 = min(c2, 1LL * x[i] + y[i] + mid);
  }
  xx = r1;
  yy = c1;
  if ((xx - yy) & 1) {
    if (r1 < r2) xx++;
    else yy++;
  }
  return (r1 <= r2 && c1 <= c2);
}

bool verify(long long xx, long long yy, long long ans) {
  bool f = true;
  long long zx = (xx + yy) / 2;
  long long zy = (yy - xx) / 2;
  for (int i = 1; i <= n; i++) {
    f &= (llabs(zx - x[i]) + llabs(zy - y[i]) <= ans);
  }
  return f;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> x[i] >> y[i];
  }
  long long lo = 0, hi = 20000000000LL, ans = -1;
  while (lo <= hi) {
    int mid = lo + (hi - lo) / 2;
    if (check(mid)) {
      ans = mid;
      hi = mid - 1;
    } else {
      lo = mid + 1;
    }
  }
  check(ans);
  cout << (xx + yy) / 2 << ' ' << (yy - xx) / 2 << '\n';
  return 0;
}

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: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

Test 41

Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: ACCEPTED

Test 53

Verdict: ACCEPTED

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: ACCEPTED

Test 57

Verdict: ACCEPTED

Test 58

Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

Test 63

Verdict: ACCEPTED

Test 64

Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

Test 66

Verdict: ACCEPTED

Test 67

Verdict: ACCEPTED

Test 68

Verdict: ACCEPTED

Test 69

Verdict: ACCEPTED

Test 70

Verdict: ACCEPTED

Test 71

Verdict: ACCEPTED

Test 72

Verdict: ACCEPTED

Test 73

Verdict: ACCEPTED

Test 74

Verdict: ACCEPTED

Test 75

Verdict: ACCEPTED

Test 76

Verdict: ACCEPTED

Test 77

Verdict: ACCEPTED