Tifa's CP Library

:heavy_check_mark: lichao_segtree (src/code/ds/lichao_segtree.hpp)

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#ifndef TIFALIBS_DS_LICHAO_SEGTREE
#define TIFALIBS_DS_LICHAO_SEGTREE

#include "../util/util.hpp"

namespace tifa_libs::ds {

template <class T, T (*op)(T, T)>
class lichao_segtree {
  struct seg {
    u32 id;
    T a, b, l, r;  // y = ax + b(where x in [l, r])
    CEXP T w(T x) const { return a * x + b; }
  };
  u32 sz;
  vec<T> lsh;
  vec<seg> t;

 public:
  CEXPE lichao_segtree(spn<T> LSH) : lsh(LSH.begin(), LSH.end()), t(LSH.size() * 4) { sz = (u32)lsh.size(); }

  CEXP void add(T a, T b, T l, T r, u32 id = 1) {
    seg k = {id, a, b, l, r};
    add(1, 0, sz - 1, u32(std::ranges::lower_bound(lsh, l) - lsh.begin()), u32(std::ranges::lower_bound(lsh, r) - lsh.begin()), k);
  }
  T query(T pos) { return query(1, 0, sz - 1, pos); }

 private:
  // min: <=   max: >=
  CEXP bool pd(T a, T b) const { return op(a, b) == a; }
  CEXP void add(u32 x, u32 l, u32 r, u32 L, u32 R, cT_(seg) k) {
    u32 mid = l + (r - l) / 2;
    if (L <= l && R >= r) {
      if (!t[x].id) return void(t[x] = k);
      T tl = t[x].w(lsh[l]), tr = t[x].w(lsh[r]), kl = k.w(lsh[l]), kr = k.w(lsh[r]);
      if (pd(tl, kl) && pd(tr, kr)) return;
      if (!pd(tl, kl) && !pd(tr, kr)) return void(t[x] = k);
      if (T in = (t[x].b - k.b) / (k.a - t[x].a); pd(kl, tl)) {
        if (in <= lsh[mid]) add(x << 1, l, mid, L, R, k);
        else add(x << 1 | 1, mid + 1, r, L, R, t[x]), t[x] = k;
      } else if (in > lsh[mid]) add(x << 1 | 1, mid + 1, r, L, R, k);
      else add(x << 1, l, mid, L, R, t[x]), t[x] = k;
      return;
    }
    if (L <= mid) add(x << 1, l, mid, L, R, k);
    if (R > mid) add(x << 1 | 1, mid + 1, r, L, R, k);
  }
  CEXP T query(u32 x, u32 l, u32 r, T pos) {
    T MIN = std::numeric_limits<T>::lowest(), MAX = std::numeric_limits<T>::max();
    T ret = t[x].id ? t[x].w(pos) : (pd(MIN, MAX) ? MAX : MIN);
    if (l == r) return ret;
    if (u32 mid = l + (r - l) / 2; pos <= lsh[mid]) return op(ret, query(x << 1, l, mid, pos));
    else return op(ret, query(x << 1 | 1, mid + 1, r, pos));
  }
};
}  // namespace tifa_libs::ds

#endif
#line 1 "src/code/ds/lichao_segtree.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/extc++.h>

#define CEXP constexpr
#define CEXPE constexpr explicit
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;
using f32 = float;
using f64 = double;
using f128 = long double;
using strn = std::string;
using strnv = std::string_view;

// clang-format off
template <class T, T v> using ic = std::integral_constant<T, v>;
template <class T> using ptt = std::pair<T, T>;
template <class T> struct edge_t {
  T w; u32 u, v;
  CEXP auto operator<=>(edge_t CR) const = default;
};
template <class T> struct pt3 {
  T _0, _1, _2;
  CEXP auto operator<=>(pt3 CR) const = default;
};
template <class T> struct pt4 {
  T _0, _1, _2, _3;
  CEXP auto operator<=>(pt4 CR) const = default;
};
template <class E> using itl = std::initializer_list<E>;
template <class T> using vec = std::vector<T>;
template <class T> using vvec = vec<vec<T>>;
template <class T> using v3ec = vec<vvec<T>>;
template <class T> using vecpt = vec<ptt<T>>;
template <class T> using vvecpt = vvec<ptt<T>>;
template <class T> using ptvec = ptt<vec<T>>;
template <class T> using ptvvec = ptt<vvec<T>>;

template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>;

template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
template <class T> using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;
// clang-format on

#define mk_(V, A, T) using V##A = V<T>;
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk_(spn, A, T) mk_(itl, A, T)
mk(b, bool) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64);
#undef mk
#undef mk_

using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) { eps_v<FP> = v; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


#line 5 "src/code/ds/lichao_segtree.hpp"

namespace tifa_libs::ds {

template <class T, T (*op)(T, T)>
class lichao_segtree {
  struct seg {
    u32 id;
    T a, b, l, r;  // y = ax + b(where x in [l, r])
    CEXP T w(T x) const { return a * x + b; }
  };
  u32 sz;
  vec<T> lsh;
  vec<seg> t;

 public:
  CEXPE lichao_segtree(spn<T> LSH) : lsh(LSH.begin(), LSH.end()), t(LSH.size() * 4) { sz = (u32)lsh.size(); }

  CEXP void add(T a, T b, T l, T r, u32 id = 1) {
    seg k = {id, a, b, l, r};
    add(1, 0, sz - 1, u32(std::ranges::lower_bound(lsh, l) - lsh.begin()), u32(std::ranges::lower_bound(lsh, r) - lsh.begin()), k);
  }
  T query(T pos) { return query(1, 0, sz - 1, pos); }

 private:
  // min: <=   max: >=
  CEXP bool pd(T a, T b) const { return op(a, b) == a; }
  CEXP void add(u32 x, u32 l, u32 r, u32 L, u32 R, cT_(seg) k) {
    u32 mid = l + (r - l) / 2;
    if (L <= l && R >= r) {
      if (!t[x].id) return void(t[x] = k);
      T tl = t[x].w(lsh[l]), tr = t[x].w(lsh[r]), kl = k.w(lsh[l]), kr = k.w(lsh[r]);
      if (pd(tl, kl) && pd(tr, kr)) return;
      if (!pd(tl, kl) && !pd(tr, kr)) return void(t[x] = k);
      if (T in = (t[x].b - k.b) / (k.a - t[x].a); pd(kl, tl)) {
        if (in <= lsh[mid]) add(x << 1, l, mid, L, R, k);
        else add(x << 1 | 1, mid + 1, r, L, R, t[x]), t[x] = k;
      } else if (in > lsh[mid]) add(x << 1 | 1, mid + 1, r, L, R, k);
      else add(x << 1, l, mid, L, R, t[x]), t[x] = k;
      return;
    }
    if (L <= mid) add(x << 1, l, mid, L, R, k);
    if (R > mid) add(x << 1 | 1, mid + 1, r, L, R, k);
  }
  CEXP T query(u32 x, u32 l, u32 r, T pos) {
    T MIN = std::numeric_limits<T>::lowest(), MAX = std::numeric_limits<T>::max();
    T ret = t[x].id ? t[x].w(pos) : (pd(MIN, MAX) ? MAX : MIN);
    if (l == r) return ret;
    if (u32 mid = l + (r - l) / 2; pos <= lsh[mid]) return op(ret, query(x << 1, l, mid, pos));
    else return op(ret, query(x << 1 | 1, mid + 1, r, pos));
  }
};
}  // namespace tifa_libs::ds


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