test/1_mytest/kdtree_monoid.test.cpp

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• Last update: 2024-11-16 23:01:41+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• alg/monoid/summax.hpp
• ds/kdtree/kdtree_monoid.hpp
• my_template.hpp
• random/base.hpp

Code

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

#include "ds/kdtree/kdtree_monoid.hpp"
#include "alg/monoid/summax.hpp"
#include "random/base.hpp"

void test() {
  ll LIM = RNG(1, 100);
  int N = RNG(1, 100);
  using MX = Monoid_SumMax<int>;

  vc<int> dat[100][100];

  vc<int> X, Y;
  vc<typename MX::value_type> val;
  FOR(i, N) {
    int x = RNG(0, LIM);
    int y = RNG(0, LIM);
    int v = RNG(0, 100);
    dat[x][y].eb(v);
    X.eb(x), Y.eb(y), val.eb(v, v);
  }
  KDTree_Monoid<MX, int> KDT(X, Y, val);

  int Q = 100;
  FOR(Q) {
    int t = RNG(0, 3);
    int xl = RNG(0, LIM), xr = RNG(0, LIM), yl = RNG(0, LIM), yr = RNG(0, LIM);
    if (xl > xr) swap(xl, xr);
    if (yl > yr) swap(yl, yr);
    if (t == 0) {
      // multiply
      int k = RNG(0, N);
      int x = X[k], y = Y[k];
      int v = RNG(0, 100);
      dat[x][y].eb(v);
      KDT.multiply(x, y, {v, v});
    }
    if (t == 1) {
      // prod
      int sm = 0, mx = MX::unit().se;
      FOR(i, xl, xr) FOR(j, yl, yr) {
        for (auto&& x: dat[i][j]) sm += x, chmax(mx, x);
      }
      auto res = KDT.prod(xl, xr, yl, yr);
      assert(res.fi == sm && res.se == mx);
    }
    if (t == 2) {
      // prod all
      int sm = 0, mx = MX::unit().se;
      FOR(i, LIM) FOR(j, LIM) {
        for (auto&& x: dat[i][j]) sm += x, chmax(mx, x);
      }
      auto res = KDT.prod_all();
      assert(res.fi == sm && res.se == mx);
    }
  }
}

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

signed main() {
  FOR(100) test();
  solve();

  return 0;
}

#line 1 "test/1_mytest/kdtree_monoid.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
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #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 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_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parity(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 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 3 "test/1_mytest/kdtree_monoid.test.cpp"

#line 1 "ds/kdtree/kdtree_monoid.hpp"
template <class Monoid, typename XY>
struct KDTree_Monoid {
  using MX = Monoid;
  using X = typename MX::value_type;
  static_assert(MX::commute);

  // 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;
  vc<X> dat;
  int n;

  KDTree_Monoid(vc<XY> xs, vc<XY> ys, vc<X> vs) : n(len(xs)) {
    assert(n > 0);
    int log = 0;
    while ((1 << log) < n) ++log;
    dat.resize(1 << (log + 1));
    closed_range.resize(1 << (log + 1));
    build(1, xs, ys, vs);
  }

  void multiply(XY x, XY y, const X& v) { multiply_rec(1, x, y, v); }

  // [xl, xr) x [yl, yr)

  X prod(XY xl, XY xr, XY yl, XY yr) {
    assert(xl <= xr && yl <= yr);
    return prod_rec(1, xl, xr, yl, yr);
  }

  X prod_all() { return dat[1]; }

private:
  void build(int idx, vc<XY> xs, vc<XY> ys, vc<X> 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 (xmin == xmax && ymin == ymax) {
      X x = MX::unit();
      for (auto&& v: vs) x = MX::op(x, v);
      dat[idx] = x;
      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);
    dat[idx] = MX::op(dat[2 * idx + 0], dat[2 * idx + 1]);
  }

  inline bool is_leaf(int idx) {
    auto& [xmin, xmax, ymin, ymax] = closed_range[idx];
    return xmin == xmax && ymin == ymax;
  }

  inline bool isin(XY x, XY y, int idx) {
    auto& [xmin, xmax, ymin, ymax] = closed_range[idx];
    return (xmin <= x && x <= xmax && ymin <= y && y <= ymax);
  }

  bool multiply_rec(int idx, XY x, XY y, X v) {
    if (!isin(x, y, idx)) return false;
    if (is_leaf(idx)) {
      dat[idx] = MX::op(dat[idx], v);
      return true;
    }
    bool done = 0;
    if (multiply_rec(2 * idx + 0, x, y, v)) done = 1;
    if (!done && multiply_rec(2 * idx + 1, x, y, v)) done = 1;
    if (done) { dat[idx] = MX::op(dat[2 * idx + 0], dat[2 * idx + 1]); }
    return done;
  }

  X prod_rec(int idx, XY x1, XY x2, XY y1, XY y2) {
    auto& [xmin, xmax, ymin, ymax] = closed_range[idx];
    if (x2 <= xmin || xmax < x1) return MX::unit();
    if (y2 <= ymin || ymax < y1) return MX::unit();
    if (x1 <= xmin && xmax < x2 && y1 <= ymin && ymax < y2) { return dat[idx]; }
    return MX::op(prod_rec(2 * idx + 0, x1, x2, y1, y2),
                  prod_rec(2 * idx + 1, x1, x2, y1, y2));
  }
};
#line 2 "alg/monoid/summax.hpp"

template <typename E>
struct Monoid_SumMax {
  using value_type = pair<E, E>;
  using X = value_type;
  static X op(X x, X y) { return {x.fi + y.fi, max(x.se, y.se)}; }
  static X from_element(E e) { return {e, e}; }
  static constexpr X unit() { return {E(0), -infty<E>}; }
  static constexpr bool commute = 1;
};
#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 7 "test/1_mytest/kdtree_monoid.test.cpp"

void test() {
  ll LIM = RNG(1, 100);
  int N = RNG(1, 100);
  using MX = Monoid_SumMax<int>;

  vc<int> dat[100][100];

  vc<int> X, Y;
  vc<typename MX::value_type> val;
  FOR(i, N) {
    int x = RNG(0, LIM);
    int y = RNG(0, LIM);
    int v = RNG(0, 100);
    dat[x][y].eb(v);
    X.eb(x), Y.eb(y), val.eb(v, v);
  }
  KDTree_Monoid<MX, int> KDT(X, Y, val);

  int Q = 100;
  FOR(Q) {
    int t = RNG(0, 3);
    int xl = RNG(0, LIM), xr = RNG(0, LIM), yl = RNG(0, LIM), yr = RNG(0, LIM);
    if (xl > xr) swap(xl, xr);
    if (yl > yr) swap(yl, yr);
    if (t == 0) {
      // multiply
      int k = RNG(0, N);
      int x = X[k], y = Y[k];
      int v = RNG(0, 100);
      dat[x][y].eb(v);
      KDT.multiply(x, y, {v, v});
    }
    if (t == 1) {
      // prod
      int sm = 0, mx = MX::unit().se;
      FOR(i, xl, xr) FOR(j, yl, yr) {
        for (auto&& x: dat[i][j]) sm += x, chmax(mx, x);
      }
      auto res = KDT.prod(xl, xr, yl, yr);
      assert(res.fi == sm && res.se == mx);
    }
    if (t == 2) {
      // prod all
      int sm = 0, mx = MX::unit().se;
      FOR(i, LIM) FOR(j, LIM) {
        for (auto&& x: dat[i][j]) sm += x, chmax(mx, x);
      }
      auto res = KDT.prod_all();
      assert(res.fi == sm && res.se == mx);
    }
  }
}

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

signed main() {
  FOR(100) test();
  solve();

  return 0;
}

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