Match polygons

// clang-format off
#include <bits/stdc++.h>
#include <cmath>
using namespace std;
#ifndef DO_DBG
#define dbg(...)
#endif
template <typename... Args> void read(Args&... args) { ((cin >> args), ...); }
template <typename T> using v = vector<T>; typedef long long ll; typedef long double ld; typedef v<ll> vi; typedef pair<ll, ll> pii; typedef complex<ll> Pi; typedef complex<ld> Pr;
#define ios ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin.exceptions(cin.failbit);
#define rep(i,a,b) for (ll i = a; i < b; i++)
#define rp(n) for (ll i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define sq(x) ((x)*(x))
#define d(...) ll __VA_ARGS__; read(__VA_ARGS__);
#define df(...) ld __VA_ARGS__; read(__VA_ARGS__);
#define dv(x, n) vi x(n); for (size_t i = 0; i < n; i++) cin >> x[i];
#define even(x) ((x)%2==0)
#define sz(s) ((ll)s.size())
#define dist(v,it) distance(v.begin(),it)
#define X real()
#define Y imag()
#define cross(a,b) (conj(a)*(b)).imag()
#define dot(a,b) (conj(a)*(b)).real()
#define idxof(a, elem) dist(a, find(all(a), elem))
// clang-format on

// // law of cosines / kosinilause
// // c^2 = a^2 + b^2 - 2ab * cos(gamma)
// // cos(gamma) = (a^2 + b^2 - c^2) / 2ab
// // gamma = acos((a^2 + b^2 - c^2) / 2ab)
// // where gamma is the angle opposite side c
//
// ld gamma(ld a, ld b, ld c) {
//   return acos((sq(a) + sq(b) - sq(c)) / (2.0L * a * b));
// }

// actually we can use the complex trick to get the angles
// or abs(remainder(arg(a-b) - arg(c-b), 2.0 * M_PI))
// except we remove the abs

constexpr ld EPS = 1e-9L;

int main() {
  ios;
  d(n);
  v<Pr> p1(n), p2(n);
  v<ld> angles1(n), angles2(n);
  rp(n) {
    df(x, y);
    p1[i] = {x, y};
  }
  rp(n) {
    angles1[i] = remainder(arg(p1[(i + 1) % n] - p1[i]) -
                               arg(p1[(i - 1 + n) % n] - p1[i]),
                           2.0L * M_PI);
    dbg(angles1[i]);
  }

  rp(n) {
    df(x, y);
    p2[i] = {x, y};
  }
  ll start = -1;
  rp(n) {
    angles2[i] = remainder(arg(p2[(i + 1) % n] - p2[i]) -
                               arg(p2[(i - 1 + n) % n] - p2[i]),
                           2.0L * M_PI);
    dbg(angles2[i]);
  }
  rp(n) {
    if (abs(angles1[0] - angles2[i]) < EPS) {
      // check the two angles around it also
      if (abs(angles1[1] - angles2[(i + 1) % n]) < EPS &&
          abs(angles1[n - 1] - angles2[(i - 1 + n) % n]) < EPS) {
        start = i;
        break;
      }
    }
  }

  dbg(start);

  rp(n) {
    if (start == -1 || abs(angles1[i] - angles2[(start + i) % n]) >= EPS)
      goto no;
  }

  cout << "Yes\n";
  return 0;
no:
  cout << "No\n";
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: WRONG ANSWER

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: WRONG ANSWER

Test 8

Verdict: ACCEPTED

Test 9

Verdict: WRONG ANSWER

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: WRONG ANSWER

Test 13

Verdict: WRONG ANSWER

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: WRONG ANSWER

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: WRONG ANSWER

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: WRONG ANSWER

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: WRONG ANSWER

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: WRONG ANSWER

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: WRONG ANSWER

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: WRONG ANSWER

Test 53

Verdict: ACCEPTED

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: WRONG ANSWER

Test 57

Verdict: ACCEPTED

Test 58

Verdict: WRONG ANSWER

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

Test 63

Verdict: WRONG ANSWER

Test 64

Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

Test 66

Verdict: ACCEPTED

Test 67

Verdict: ACCEPTED

Test 68

Verdict: WRONG ANSWER

Test 69

Verdict: ACCEPTED

Test 70

Verdict: WRONG ANSWER

Test 71

Verdict: ACCEPTED

Test 72

Verdict: WRONG ANSWER

Test 73

Verdict: WRONG ANSWER

Test 74

Verdict: ACCEPTED

Test 75

Verdict: ACCEPTED