test/1_mytest/kdtree_nns.test.cpp

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• Last update: 2025-01-27 19:24:29+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• ds/kdtree/kdtree.hpp
• my_template.hpp
• random/base.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include "my_template.hpp"

#include "random/base.hpp"
#include "ds/kdtree/kdtree.hpp"

void test_random_points_nns_is_fast() {
  ll N = 100'000, Q = 100'000;
  vc<int> X(N), Y(N);
  ll LIM = 1'000'000'000;
  FOR(i, N) X[i] = RNG(0, LIM);
  FOR(i, N) Y[i] = RNG(0, LIM);
  KDTree<int> KDT(X, Y);
  FOR(Q) {
    ll x = RNG(0, LIM);
    ll y = RNG(0, LIM);
    KDT.nearest_neighbor_search<ll>(x, y);
  }
}

void test_nns_is_correct() {
  ll LIM = RNG(10, 1000);
  ll N = RNG(1, 100);
  ll Q = 1000;
  vc<int> X(N), Y(N);
  FOR(i, N) X[i] = RNG(0, LIM);
  FOR(i, N) Y[i] = RNG(0, LIM);

  KDTree<int> KDT(X, Y);
  FOR(Q) {
    ll x = RNG(0, LIM);
    ll y = RNG(0, LIM);
    ll min_d = 1'000'000'000;
    auto dist = [&](int i) -> ll {
      ll dx = X[i] - x, dy = Y[i] - y;
      return dx * dx + dy * dy;
    };
    FOR(i, N) chmin(min_d, dist(i));
    int k = KDT.nearest_neighbor_search<ll>(x, y);
    assert(min_d == dist(k));
  }
}

void test() {
  test_random_points_nns_is_fast();
  test_nns_is_correct();
}

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

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

  return 0;
}

#line 1 "test/1_mytest/kdtree_nns.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
// https://codeforces.com/blog/entry/126772?#comment-1154880
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
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 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_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (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 kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename UINT>
struct all_bit {
  struct iter {
    UINT s;
    iter(UINT s) : s(s) {}
    int operator*() const { return lowbit(s); }
    iter &operator++() {
      s &= s - 1;
      return *this;
    }
    bool operator!=(const iter) const { return s != 0; }
  };
  UINT s;
  all_bit(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename UINT>
struct all_subset {
  static_assert(is_unsigned<UINT>::value);
  struct iter {
    UINT s, t;
    bool ed;
    iter(UINT s) : s(s), t(s), ed(0) {}
    int operator*() const { return s ^ t; }
    iter &operator++() {
      (t == 0 ? ed = 1 : t = (t - 1) & s);
      return *this;
    }
    bool operator!=(const iter) const { return !ed; }
  };
  UINT s;
  all_subset(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

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;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 4 "test/1_mytest/kdtree_nns.test.cpp"

#line 2 "random/base.hpp"

u64 RNG_64() {
  static u64 x_ = u64(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 "ds/kdtree/kdtree.hpp"
template <typename XY>
struct KDTree {
  // 小数も考慮すると、閉で持つ設計方針になる。ただし、クエリはいつもの半開を使う
  vc<tuple<XY, XY, XY, XY>> closed_range;
  // 同じ座標の点も集約しないようにして、座標ごとに unique なデータを使う
  vc<int> dat;
  int n;

  KDTree(vc<XY> xs, vc<XY> ys) : n(len(xs)) {
    int log = 0;
    while ((1 << log) < n) ++log;
    dat.assign(1 << (log + 1), -1);
    closed_range.resize(1 << (log + 1));
    vc<int> vs(n);
    iota(all(vs), 0);
    if (n > 0) build(1, xs, ys, vs);
  }

  // [xl, xr) x [yl, yr)
  vc<int> collect_rect(XY xl, XY xr, XY yl, XY yr, int max_size = -1) {
    assert(xl <= xr && yl <= yr);
    if (max_size == -1) max_size = n;
    vc<int> res;
    rect_rec(1, xl, xr, yl, yr, res, max_size);
    return res;
  }

  // 計算量保証なし、点群がランダムなら O(logN)
  // N = Q = 10^5 で、約 1 秒
  // T は座標の 2 乗がオーバーフローしないものを使う。XY=int, T=long など。
  // return するのは index
  template <typename T>
  int nearest_neighbor_search(XY x, XY y) {
    if (n == 0) return -1;
    pair<int, T> res = {-1, -1};
    nns_rec(1, x, y, res);
    return res.fi;
  }

private:
  void build(int idx, vc<XY> xs, vc<XY> ys, vc<int> vs, bool divx = true) {
    int n = len(xs);
    auto& [xmin, xmax, ymin, ymax] = closed_range[idx];
    xmin = ymin = infty<XY>;
    xmax = ymax = -infty<XY>;

    FOR(i, n) {
      auto x = xs[i], y = ys[i];
      chmin(xmin, x), chmax(xmax, x), chmin(ymin, y), chmax(ymax, y);
    }
    if (n == 1) {
      dat[idx] = vs[0];
      return;
    }

    int m = n / 2;
    vc<int> I(n);
    iota(all(I), 0);
    if (divx) {
      nth_element(I.begin(), I.begin() + m, I.end(), [xs](int i, int j) { return xs[i] < xs[j]; });
    } else {
      nth_element(I.begin(), I.begin() + m, I.end(), [ys](int i, int j) { return ys[i] < ys[j]; });
    }
    xs = rearrange(xs, I), ys = rearrange(ys, I), vs = rearrange(vs, I);
    build(2 * idx + 0, {xs.begin(), xs.begin() + m}, {ys.begin(), ys.begin() + m}, {vs.begin(), vs.begin() + m}, !divx);
    build(2 * idx + 1, {xs.begin() + m, xs.end()}, {ys.begin() + m, ys.end()}, {vs.begin() + m, vs.end()}, !divx);
  }

  void rect_rec(int i, XY x1, XY x2, XY y1, XY y2, vc<int>& res, int ms) {
    if (len(res) == ms) return;
    auto& [xmin, xmax, ymin, ymax] = closed_range[i];
    if (x2 <= xmin || xmax < x1) return;
    if (y2 <= ymin || ymax < y1) return;
    if (dat[i] != -1) {
      res.eb(dat[i]);
      return;
    }
    rect_rec(2 * i + 0, x1, x2, y1, y2, res, ms);
    rect_rec(2 * i + 1, x1, x2, y1, y2, res, ms);
  }

  template <typename T>
  T best_dist_squared(int i, XY x, XY y) {
    auto& [xmin, xmax, ymin, ymax] = closed_range[i];
    T dx = x - clamp(x, xmin, xmax);
    T dy = y - clamp(y, ymin, ymax);
    return dx * dx + dy * dy;
  }

  template <typename T>
  void nns_rec(int i, XY x, XY y, pair<int, T>& res) {
    T d = best_dist_squared<T>(i, x, y);
    if (res.fi != -1 && d >= res.se) return;
    if (dat[i] != -1) {
      res = {dat[i], d};
      return;
    }
    T d0 = best_dist_squared<T>(2 * i + 0, x, y);
    T d1 = best_dist_squared<T>(2 * i + 1, x, y);
    if (d0 < d1) {
      nns_rec(2 * i + 0, x, y, res), nns_rec(2 * i + 1, x, y, res);
    } else {
      nns_rec(2 * i + 1, x, y, res), nns_rec(2 * i + 0, x, y, res);
    }
  }
};
#line 7 "test/1_mytest/kdtree_nns.test.cpp"

void test_random_points_nns_is_fast() {
  ll N = 100'000, Q = 100'000;
  vc<int> X(N), Y(N);
  ll LIM = 1'000'000'000;
  FOR(i, N) X[i] = RNG(0, LIM);
  FOR(i, N) Y[i] = RNG(0, LIM);
  KDTree<int> KDT(X, Y);
  FOR(Q) {
    ll x = RNG(0, LIM);
    ll y = RNG(0, LIM);
    KDT.nearest_neighbor_search<ll>(x, y);
  }
}

void test_nns_is_correct() {
  ll LIM = RNG(10, 1000);
  ll N = RNG(1, 100);
  ll Q = 1000;
  vc<int> X(N), Y(N);
  FOR(i, N) X[i] = RNG(0, LIM);
  FOR(i, N) Y[i] = RNG(0, LIM);

  KDTree<int> KDT(X, Y);
  FOR(Q) {
    ll x = RNG(0, LIM);
    ll y = RNG(0, LIM);
    ll min_d = 1'000'000'000;
    auto dist = [&](int i) -> ll {
      ll dx = X[i] - x, dy = Y[i] - y;
      return dx * dx + dy * dy;
    };
    FOR(i, N) chmin(min_d, dist(i));
    int k = KDT.nearest_neighbor_search<ll>(x, y);
    assert(min_d == dist(k));
  }
}

void test() {
  test_random_points_nns_is_fast();
  test_nns_is_correct();
}

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

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

  return 0;
}

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