test/mytest/stern_brocot.test.cpp

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• Last update: 2023-11-09 02:18:09+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• my_template.hpp
• nt/stern_brocot_tree.hpp
• random/base.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "random/base.hpp"
#include "nt/stern_brocot_tree.hpp"

void test() {
  using SBT = Stern_Brocot_Tree;
  // get_path
  assert(SBT::get_path({1, 1}) == vi());
  assert(SBT::get_path({1, 2}) == vi({0, 1}));
  assert(SBT::get_path({2, 1}) == vi({1}));
  assert(SBT::get_path({1, 3}) == vi({0, 2}));
  assert(SBT::get_path({2, 3}) == vi({0, 1, 1}));
  assert(SBT::get_path({3, 2}) == vi({1, 1}));
  assert(SBT::get_path({3, 1}) == vi({2}));
  assert(SBT::get_path({1, 4}) == vi({0, 3}));
  assert(SBT::get_path({2, 5}) == vi({0, 2, 1}));
  assert(SBT::get_path({3, 5}) == vi({0, 1, 1, 1}));
  assert(SBT::get_path({3, 4}) == vi({0, 1, 2}));
  assert(SBT::get_path({4, 3}) == vi({1, 2}));
  assert(SBT::get_path({5, 3}) == vi({1, 1, 1}));
  assert(SBT::get_path({5, 2}) == vi({2, 1}));
  assert(SBT::get_path({4, 1}) == vi({3}));
  // range
  assert(SBT::range({1, 1}) == mp(pi{0, 1}, pi{1, 0}));
  assert(SBT::range({1, 2}) == mp(pi{0, 1}, pi{1, 1}));
  assert(SBT::range({2, 1}) == mp(pi{1, 1}, pi{1, 0}));
  assert(SBT::range({1, 3}) == mp(pi{0, 1}, pi{1, 2}));
  assert(SBT::range({2, 3}) == mp(pi{1, 2}, pi{1, 1}));
  assert(SBT::range({3, 2}) == mp(pi{1, 1}, pi{2, 1}));
  assert(SBT::range({3, 1}) == mp(pi{2, 1}, pi{1, 0}));
  assert(SBT::range({1, 4}) == mp(pi{0, 1}, pi{1, 3}));
  assert(SBT::range({2, 5}) == mp(pi{1, 3}, pi{1, 2}));
  assert(SBT::range({3, 5}) == mp(pi{1, 2}, pi{2, 3}));
  assert(SBT::range({3, 4}) == mp(pi{2, 3}, pi{1, 1}));
  assert(SBT::range({4, 3}) == mp(pi{1, 1}, pi{3, 2}));
  assert(SBT::range({5, 3}) == mp(pi{3, 2}, pi{2, 1}));
  assert(SBT::range({5, 2}) == mp(pi{2, 1}, pi{3, 1}));
  assert(SBT::range({4, 1}) == mp(pi{3, 1}, pi{1, 0}));
  // child
  assert(SBT::child({1, 1}) == mp(pi{1, 2}, pi{2, 1}));
  assert(SBT::child({1, 2}) == mp(pi{1, 3}, pi{2, 3}));
  assert(SBT::child({2, 1}) == mp(pi{3, 2}, pi{3, 1}));
  assert(SBT::child({1, 3}) == mp(pi{1, 4}, pi{2, 5}));
  assert(SBT::child({2, 3}) == mp(pi{3, 5}, pi{3, 4}));
  assert(SBT::child({3, 2}) == mp(pi{4, 3}, pi{5, 3}));
  assert(SBT::child({3, 1}) == mp(pi{5, 2}, pi{4, 1}));
  // la
  pi NG = {-1, -1};
  assert(SBT::LA({1, 1}, 0) == pi({1, 1}));
  assert(SBT::LA({1, 1}, 1) == NG);
  assert(SBT::LA({3, 4}, 0) == pi({1, 1}));
  assert(SBT::LA({3, 4}, 1) == pi({1, 2}));
  assert(SBT::LA({3, 4}, 2) == pi({2, 3}));
  assert(SBT::LA({3, 4}, 3) == pi({3, 4}));
  assert(SBT::LA({3, 4}, 4) == NG);
  assert(SBT::LA({3, 5}, 0) == pi({1, 1}));
  assert(SBT::LA({3, 5}, 1) == pi({1, 2}));
  assert(SBT::LA({3, 5}, 2) == pi({2, 3}));
  assert(SBT::LA({3, 5}, 3) == pi({3, 5}));
  assert(SBT::LA({3, 5}, 4) == NG);

  auto get_random = [&]() -> pi {
    while (1) {
      ll x = RNG(1, 1LL << 60);
      ll y = RNG(1, 1LL << 60);
      if (gcd(x, y) > 1) continue;
      return {x, y};
    }
  };

  FOR(10000) {
    pi x = get_random();
    auto [l, r] = SBT::range(x);
    assert(i128(x.fi) * l.se - i128(x.se) * l.fi == 1);
    assert(i128(r.fi) * x.se - i128(r.se) * x.fi == 1);
    assert(l.fi + r.fi == x.fi && l.se + r.se == x.se);
    tie(l, r) = SBT::child(x);
    assert(i128(x.fi) * l.se - i128(x.se) * l.fi == 1);
    assert(i128(r.fi) * x.se - i128(r.se) * x.fi == 1);
    auto P = SBT::get_path(x);
    assert(SBT::from_path<ll>(P) == x);
    pi y = get_random();
    pi z = SBT::LCA(x, y);
    assert(SBT::in_subtree(x, z));
    assert(SBT::in_subtree(y, z));
    tie(l, r) = SBT::child(z);
    assert(!SBT::in_subtree(x, l) || !SBT::in_subtree(y, l));
    assert(!SBT::in_subtree(x, r) || !SBT::in_subtree(y, r));
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test();
  solve();

  return 0;
}

#line 1 "test/mytest/stern_brocot.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 2 "random/base.hpp"

u64 RNG_64() {
  static uint64_t x_
      = uint64_t(chrono::duration_cast<chrono::nanoseconds>(
                     chrono::high_resolution_clock::now().time_since_epoch())
                     .count())
        * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 1 "nt/stern_brocot_tree.hpp"

struct Stern_Brocot_Tree {
  using PATH = vi; // はじめは R

  static tuple<PATH, pi, pi> get_path_and_range(pi x) {
    PATH path;
    pi l = {0, 1}, r = {1, 0};
    pi m = {1, 1};
    ll det_l = l.fi * x.se - l.se * x.fi;
    ll det_r = r.fi * x.se - r.se * x.fi;
    ll det_m = det_l + det_r;
    while (1) {
      if (det_m == 0) break;
      ll k = ceil(-det_m, det_r);
      path.eb(k);
      l = {l.fi + k * r.fi, l.se + k * r.se};
      m = {l.fi + r.fi, l.se + r.se};
      det_l += k * det_r;
      det_m += k * det_r;
      if (det_m == 0) break;
      k = ceil(det_m, -det_l);
      path.eb(k);
      r = {r.fi + k * l.fi, r.se + k * l.se};
      m = {l.fi + r.fi, l.se + r.se};
      det_r += k * det_l;
      det_m += k * det_l;
    }
    return {path, l, r};
  }

  static PATH get_path(pi x) {
    auto [path, l, r] = get_path_and_range(x);
    return path;
  }

  static pair<pi, pi> range(pi x) {
    auto [path, l, r] = get_path_and_range(x);
    return {l, r};
  }

  // x in range(y)
  static bool in_subtree(pi x, pi y) {
    auto [l, r] = range(y);
    bool ok_l = i128(x.fi) * l.se - i128(x.se) * l.fi > 0;
    bool ok_r = i128(r.fi) * x.se - i128(r.se) * x.fi > 0;
    return ok_l && ok_r;
  }

  template <typename T = ll>
  static pair<T, T> from_path(PATH& p) {
    using P = pair<T, T>;
    P l = {0, 1}, r = {1, 0};
    FOR(i, len(p)) {
      ll k = p[i];
      if (i % 2 == 0) {
        l.fi += T(k) * r.fi;
        l.se += T(k) * r.se;
      }
      if (i % 2 == 1) {
        r.fi += T(k) * l.fi;
        r.se += T(k) * l.se;
      }
    }
    return {l.fi + r.fi, l.se + r.se};
  }

  static pair<pi, pi> child(pi x) {
    auto [l, r] = range(x);
    pi lc = {l.fi + x.fi, l.se + x.se};
    pi rc = {x.fi + r.fi, x.se + r.se};
    return {lc, rc};
  }

  static pi LCA(pi x, pi y) {
    auto Px = get_path(x);
    auto Py = get_path(y);
    vi P;
    FOR(i, min(len(Px), len(Py))) {
      ll k = min(Px[i], Py[i]);
      P.eb(k);
      if (k < Px[i] || k < Py[i]) break;
    }
    return from_path(P);
  }

  static pi LA(pi x, ll dep) {
    pi l = {0, 1}, r = {1, 0};
    pi m = {1, 1};
    ll det_l = l.fi * x.se - l.se * x.fi;
    ll det_r = r.fi * x.se - r.se * x.fi;
    ll det_m = det_l + det_r;
    while (1) {
      if (det_m == 0 || dep == 0) break;
      ll k = min(dep, ceil(-det_m, det_r));
      l = {l.fi + k * r.fi, l.se + k * r.se};
      m = {l.fi + r.fi, l.se + r.se};
      det_l += k * det_r;
      det_m += k * det_r;
      dep -= k;
      if (det_m == 0 || dep == 0) break;
      k = min(dep, ceil(det_m, -det_l));
      r = {r.fi + k * l.fi, r.se + k * l.se};
      m = {l.fi + r.fi, l.se + r.se};
      det_r += k * det_l;
      det_m += k * det_l;
      dep -= k;
    }
    if (dep == 0) return m;
    return {-1, -1};
  }

  static string to_string(PATH& p) {
    string res;
    char c = 'L';
    for (auto&& x: p) {
      c = 'L' + 'R' - c;
      if (x == 0) continue;
      res += c;
      res += " " + std::to_string(x);
    }
    return res;
  }
};
#line 5 "test/mytest/stern_brocot.test.cpp"

void test() {
  using SBT = Stern_Brocot_Tree;
  // get_path
  assert(SBT::get_path({1, 1}) == vi());
  assert(SBT::get_path({1, 2}) == vi({0, 1}));
  assert(SBT::get_path({2, 1}) == vi({1}));
  assert(SBT::get_path({1, 3}) == vi({0, 2}));
  assert(SBT::get_path({2, 3}) == vi({0, 1, 1}));
  assert(SBT::get_path({3, 2}) == vi({1, 1}));
  assert(SBT::get_path({3, 1}) == vi({2}));
  assert(SBT::get_path({1, 4}) == vi({0, 3}));
  assert(SBT::get_path({2, 5}) == vi({0, 2, 1}));
  assert(SBT::get_path({3, 5}) == vi({0, 1, 1, 1}));
  assert(SBT::get_path({3, 4}) == vi({0, 1, 2}));
  assert(SBT::get_path({4, 3}) == vi({1, 2}));
  assert(SBT::get_path({5, 3}) == vi({1, 1, 1}));
  assert(SBT::get_path({5, 2}) == vi({2, 1}));
  assert(SBT::get_path({4, 1}) == vi({3}));
  // range
  assert(SBT::range({1, 1}) == mp(pi{0, 1}, pi{1, 0}));
  assert(SBT::range({1, 2}) == mp(pi{0, 1}, pi{1, 1}));
  assert(SBT::range({2, 1}) == mp(pi{1, 1}, pi{1, 0}));
  assert(SBT::range({1, 3}) == mp(pi{0, 1}, pi{1, 2}));
  assert(SBT::range({2, 3}) == mp(pi{1, 2}, pi{1, 1}));
  assert(SBT::range({3, 2}) == mp(pi{1, 1}, pi{2, 1}));
  assert(SBT::range({3, 1}) == mp(pi{2, 1}, pi{1, 0}));
  assert(SBT::range({1, 4}) == mp(pi{0, 1}, pi{1, 3}));
  assert(SBT::range({2, 5}) == mp(pi{1, 3}, pi{1, 2}));
  assert(SBT::range({3, 5}) == mp(pi{1, 2}, pi{2, 3}));
  assert(SBT::range({3, 4}) == mp(pi{2, 3}, pi{1, 1}));
  assert(SBT::range({4, 3}) == mp(pi{1, 1}, pi{3, 2}));
  assert(SBT::range({5, 3}) == mp(pi{3, 2}, pi{2, 1}));
  assert(SBT::range({5, 2}) == mp(pi{2, 1}, pi{3, 1}));
  assert(SBT::range({4, 1}) == mp(pi{3, 1}, pi{1, 0}));
  // child
  assert(SBT::child({1, 1}) == mp(pi{1, 2}, pi{2, 1}));
  assert(SBT::child({1, 2}) == mp(pi{1, 3}, pi{2, 3}));
  assert(SBT::child({2, 1}) == mp(pi{3, 2}, pi{3, 1}));
  assert(SBT::child({1, 3}) == mp(pi{1, 4}, pi{2, 5}));
  assert(SBT::child({2, 3}) == mp(pi{3, 5}, pi{3, 4}));
  assert(SBT::child({3, 2}) == mp(pi{4, 3}, pi{5, 3}));
  assert(SBT::child({3, 1}) == mp(pi{5, 2}, pi{4, 1}));
  // la
  pi NG = {-1, -1};
  assert(SBT::LA({1, 1}, 0) == pi({1, 1}));
  assert(SBT::LA({1, 1}, 1) == NG);
  assert(SBT::LA({3, 4}, 0) == pi({1, 1}));
  assert(SBT::LA({3, 4}, 1) == pi({1, 2}));
  assert(SBT::LA({3, 4}, 2) == pi({2, 3}));
  assert(SBT::LA({3, 4}, 3) == pi({3, 4}));
  assert(SBT::LA({3, 4}, 4) == NG);
  assert(SBT::LA({3, 5}, 0) == pi({1, 1}));
  assert(SBT::LA({3, 5}, 1) == pi({1, 2}));
  assert(SBT::LA({3, 5}, 2) == pi({2, 3}));
  assert(SBT::LA({3, 5}, 3) == pi({3, 5}));
  assert(SBT::LA({3, 5}, 4) == NG);

  auto get_random = [&]() -> pi {
    while (1) {
      ll x = RNG(1, 1LL << 60);
      ll y = RNG(1, 1LL << 60);
      if (gcd(x, y) > 1) continue;
      return {x, y};
    }
  };

  FOR(10000) {
    pi x = get_random();
    auto [l, r] = SBT::range(x);
    assert(i128(x.fi) * l.se - i128(x.se) * l.fi == 1);
    assert(i128(r.fi) * x.se - i128(r.se) * x.fi == 1);
    assert(l.fi + r.fi == x.fi && l.se + r.se == x.se);
    tie(l, r) = SBT::child(x);
    assert(i128(x.fi) * l.se - i128(x.se) * l.fi == 1);
    assert(i128(r.fi) * x.se - i128(r.se) * x.fi == 1);
    auto P = SBT::get_path(x);
    assert(SBT::from_path<ll>(P) == x);
    pi y = get_random();
    pi z = SBT::LCA(x, y);
    assert(SBT::in_subtree(x, z));
    assert(SBT::in_subtree(y, z));
    tie(l, r) = SBT::child(z);
    assert(!SBT::in_subtree(x, l) || !SBT::in_subtree(y, l));
    assert(!SBT::in_subtree(x, r) || !SBT::in_subtree(y, r));
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test();
  solve();

  return 0;
}

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