#pragma once
#include "../../../util/alias/num/lib.hpp"
namespace tifa_libs {
// Copyright Malte Skarupke 2020.
// Distributed under the Boost Software License, Version 1.0.
// (See http://www.boost.org/LICENSE_1_0.txt)
namespace d_ary_heap_impl_ {
template <int D>
CEXP u32 ch1idx_(u32 i) NE { return i * D + 1; }
template <int D>
CEXP u32 chls_idx_(u32 i) NE { return i * D + D; }
template <int D>
CEXP u32 gchls_idx_(u32 i) NE { return i * (D * D) + (D * D + D); }
template <int D>
CEXP u32 pidx_(u32 i) NE { return (i - 1) / D; }
template <int D>
CEXP u32 gpidx_(u32 i) NE { return (i - (D + 1)) / (D * D); }
template <int D>
CEXP u32 idx_ngch_(u32 l) NE { return gpidx_<D>(l - 1) + 1; }
template <int D, class I, class C>
CEXP I l_ch_(I it_ch1, C&& c) NE {
if CEXP (D == 1) return it_ch1;
else if CEXP (D == 2) return it_ch1 + !!c(it_ch1[0], it_ch1[1]);
else {
I hl1 = l_ch_<D / 2>(it_ch1, c), hl2 = l_ch_<D - D / 2>(it_ch1 + D / 2, c);
retif_((c(*hl1, *hl2)), hl2, hl1);
}
}
template <int D, class I, class C>
CEXP I l_ch_(I it_ch1, int num_ch, C&& c) NE {
if CEXP (D == 2) return it_ch1;
else if CEXP (D == 3) {
if (num_ch == 1) return it_ch1;
return it_ch1 + !!c(it_ch1[0], it_ch1[1]);
} else if CEXP (D == 4) {
switch (num_ch) {
case 1: return it_ch1;
case 2: return it_ch1 + !!c(it_ch1[0], it_ch1[1]);
default:
I largest = it_ch1 + !!c(it_ch1[0], it_ch1[1]);
retif_((c(*largest, it_ch1[2])), it_ch1 + 2, largest);
}
} else {
switch (num_ch) {
case 1: return it_ch1;
case 2: return it_ch1 + !!c(it_ch1[0], it_ch1[1]);
case 3: {
I l = it_ch1 + !!c(it_ch1[0], it_ch1[1]);
retif_((c(*l, it_ch1[2])), it_ch1 + 2, l);
}
case 4: {
I hl1 = it_ch1 + !!c(it_ch1[0], it_ch1[1]),
hl2 = it_ch1 + 2 + !!c(it_ch1[2], it_ch1[3]);
retif_((c(*hl1, *hl2)), hl2, hl1);
}
default:
int h = num_ch / 2;
I hl1 = l_ch_<D>(it_ch1, h, c), hl2 = l_ch_<D>(it_ch1 + h, num_ch - h, c);
retif_((c(*hl1, *hl2)), hl2, hl1);
}
}
}
} // namespace d_ary_heap_impl_
template <int D, class I, class C = std::less<>>
CEXP void make_dary_heap(I begin, I end, C&& comp = C{}) NE {
u32 len = u32(end - begin);
if (len <= 1) return;
u32 idx = (len - 2) / D;
if (int num_ch_end = (len - 1) % D; num_ch_end) {
I chl = d_ary_heap_impl_::l_ch_<D>(begin + d_ary_heap_impl_::ch1idx_<D>(idx), num_ch_end, comp);
if (comp(begin[idx], *chl)) swap(begin[idx], *chl);
if (idx == 0) return;
--idx;
}
if (idx > 0)
for (u32 lidx_ngcd = d_ary_heap_impl_::idx_ngch_<D>(len);;) {
I ch = d_ary_heap_impl_::l_ch_<D>(begin + d_ary_heap_impl_::ch1idx_<D>(idx), comp);
if (comp(begin[idx], *ch)) swap(begin[idx], *ch);
if (idx-- == lidx_ngcd) break;
}
for (;; --idx) {
TPN std::iterator_traits<I>::value_type value = std::move(begin[idx]);
u32 mdidx = idx;
for (;;) {
u32 idx_ch = d_ary_heap_impl_::chls_idx_<D>(mdidx), idx_ch1 = idx_ch - (D - 1);
I ch = begin;
if (idx_ch < len) ch = d_ary_heap_impl_::l_ch_<D>(begin + idx_ch1, comp);
else if (idx_ch1 >= len) break;
else ch = d_ary_heap_impl_::l_ch_<D>(begin + idx_ch1, int(len - idx_ch1), comp);
if (!comp(value, *ch)) break;
begin[mdidx] = std::move(*ch), mdidx = u32(ch - begin);
}
if (begin[mdidx] = std::move(value); idx == 0) break;
}
}
template <int D, common_range R, class C = std::less<>>
CEXP void make_dary_heap(R CR r, C&& comp = C{}) NE { return make_dary_heap<D>(begin(r), end(r), std::forward<C>(comp)); }
template <int D, class I, class C = std::less<>>
CEXP bool is_dary_heap(I begin, I end, C&& comp = C{}) NE {
flt_ (u32, i, 1, u32(end - begin))
if (u32 p = d_ary_heap_impl_::pidx_<D>(i); comp(begin[p], begin[i])) return false;
return true;
}
template <int D, common_range R, class C = std::less<>>
CEXP void is_dary_heap(R CR r, C&& comp = C{}) NE { return is_dary_heap<D>(begin(r), end(r), std::forward<C>(comp)); }
template <int D, class I, class C = std::less<>>
CEXP void push_dary_heap(I begin, I end, C&& comp = C{}) NE {
TPN std::iterator_traits<I>::value_type val = std::move(end[-1]);
u32 idx = u32(end - begin) - 1;
while (idx > 0) {
u32 p = d_ary_heap_impl_::pidx_<D>(idx);
if (!comp(begin[p], val)) break;
begin[idx] = std::move(begin[p]), idx = p;
}
begin[idx] = std::move(val);
}
template <int D, common_range R, class C = std::less<>>
CEXP void push_dary_heap(R CR r, C&& comp = C{}) NE { return push_dary_heap<D>(begin(r), end(r), std::forward<C>(comp)); }
template <int D, class I, class C = std::less<>>
CEXP void pop_dary_heap(I begin, I end, C&& comp = C{}) NE {
u32 len = u32(end - begin) - 1;
TPN std::iterator_traits<I>::value_type val = std::move(end[-1]);
u32 idx = 0;
for (end[-1] = std::move(begin[0]);;) {
if (u32 chls = d_ary_heap_impl_::chls_idx_<D>(idx), ch1 = chls - (D - 1); chls < len) {
I ch = d_ary_heap_impl_::l_ch_<D>(begin + ch1, comp);
if (!comp(val, *ch)) break;
begin[idx] = std::move(*ch), idx = u32(ch - begin);
} else if (ch1 < len) {
I ch = d_ary_heap_impl_::l_ch_<D>(begin + ch1, int(len - ch1), comp);
if (comp(val, *ch)) begin[idx] = std::move(*ch), idx = u32(ch - begin);
break;
} else break;
}
begin[idx] = std::move(val);
}
template <int D, common_range R, class C = std::less<>>
CEXP void pop_dary_heap(R CR r, C&& comp = C{}) NE { return pop_dary_heap<D>(begin(r), end(r), std::forward<C>(comp)); }
} // namespace tifa_libs
#line 2 "src/ds/heap/d_ary/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/ds/heap/d_ary/lib.hpp"
namespace tifa_libs {
// Copyright Malte Skarupke 2020.
// Distributed under the Boost Software License, Version 1.0.
// (See http://www.boost.org/LICENSE_1_0.txt)
namespace d_ary_heap_impl_ {
template <int D>
CEXP u32 ch1idx_(u32 i) NE { return i * D + 1; }
template <int D>
CEXP u32 chls_idx_(u32 i) NE { return i * D + D; }
template <int D>
CEXP u32 gchls_idx_(u32 i) NE { return i * (D * D) + (D * D + D); }
template <int D>
CEXP u32 pidx_(u32 i) NE { return (i - 1) / D; }
template <int D>
CEXP u32 gpidx_(u32 i) NE { return (i - (D + 1)) / (D * D); }
template <int D>
CEXP u32 idx_ngch_(u32 l) NE { return gpidx_<D>(l - 1) + 1; }
template <int D, class I, class C>
CEXP I l_ch_(I it_ch1, C&& c) NE {
if CEXP (D == 1) return it_ch1;
else if CEXP (D == 2) return it_ch1 + !!c(it_ch1[0], it_ch1[1]);
else {
I hl1 = l_ch_<D / 2>(it_ch1, c), hl2 = l_ch_<D - D / 2>(it_ch1 + D / 2, c);
retif_((c(*hl1, *hl2)), hl2, hl1);
}
}
template <int D, class I, class C>
CEXP I l_ch_(I it_ch1, int num_ch, C&& c) NE {
if CEXP (D == 2) return it_ch1;
else if CEXP (D == 3) {
if (num_ch == 1) return it_ch1;
return it_ch1 + !!c(it_ch1[0], it_ch1[1]);
} else if CEXP (D == 4) {
switch (num_ch) {
case 1: return it_ch1;
case 2: return it_ch1 + !!c(it_ch1[0], it_ch1[1]);
default:
I largest = it_ch1 + !!c(it_ch1[0], it_ch1[1]);
retif_((c(*largest, it_ch1[2])), it_ch1 + 2, largest);
}
} else {
switch (num_ch) {
case 1: return it_ch1;
case 2: return it_ch1 + !!c(it_ch1[0], it_ch1[1]);
case 3: {
I l = it_ch1 + !!c(it_ch1[0], it_ch1[1]);
retif_((c(*l, it_ch1[2])), it_ch1 + 2, l);
}
case 4: {
I hl1 = it_ch1 + !!c(it_ch1[0], it_ch1[1]),
hl2 = it_ch1 + 2 + !!c(it_ch1[2], it_ch1[3]);
retif_((c(*hl1, *hl2)), hl2, hl1);
}
default:
int h = num_ch / 2;
I hl1 = l_ch_<D>(it_ch1, h, c), hl2 = l_ch_<D>(it_ch1 + h, num_ch - h, c);
retif_((c(*hl1, *hl2)), hl2, hl1);
}
}
}
} // namespace d_ary_heap_impl_
template <int D, class I, class C = std::less<>>
CEXP void make_dary_heap(I begin, I end, C&& comp = C{}) NE {
u32 len = u32(end - begin);
if (len <= 1) return;
u32 idx = (len - 2) / D;
if (int num_ch_end = (len - 1) % D; num_ch_end) {
I chl = d_ary_heap_impl_::l_ch_<D>(begin + d_ary_heap_impl_::ch1idx_<D>(idx), num_ch_end, comp);
if (comp(begin[idx], *chl)) swap(begin[idx], *chl);
if (idx == 0) return;
--idx;
}
if (idx > 0)
for (u32 lidx_ngcd = d_ary_heap_impl_::idx_ngch_<D>(len);;) {
I ch = d_ary_heap_impl_::l_ch_<D>(begin + d_ary_heap_impl_::ch1idx_<D>(idx), comp);
if (comp(begin[idx], *ch)) swap(begin[idx], *ch);
if (idx-- == lidx_ngcd) break;
}
for (;; --idx) {
TPN std::iterator_traits<I>::value_type value = std::move(begin[idx]);
u32 mdidx = idx;
for (;;) {
u32 idx_ch = d_ary_heap_impl_::chls_idx_<D>(mdidx), idx_ch1 = idx_ch - (D - 1);
I ch = begin;
if (idx_ch < len) ch = d_ary_heap_impl_::l_ch_<D>(begin + idx_ch1, comp);
else if (idx_ch1 >= len) break;
else ch = d_ary_heap_impl_::l_ch_<D>(begin + idx_ch1, int(len - idx_ch1), comp);
if (!comp(value, *ch)) break;
begin[mdidx] = std::move(*ch), mdidx = u32(ch - begin);
}
if (begin[mdidx] = std::move(value); idx == 0) break;
}
}
template <int D, common_range R, class C = std::less<>>
CEXP void make_dary_heap(R CR r, C&& comp = C{}) NE { return make_dary_heap<D>(begin(r), end(r), std::forward<C>(comp)); }
template <int D, class I, class C = std::less<>>
CEXP bool is_dary_heap(I begin, I end, C&& comp = C{}) NE {
flt_ (u32, i, 1, u32(end - begin))
if (u32 p = d_ary_heap_impl_::pidx_<D>(i); comp(begin[p], begin[i])) return false;
return true;
}
template <int D, common_range R, class C = std::less<>>
CEXP void is_dary_heap(R CR r, C&& comp = C{}) NE { return is_dary_heap<D>(begin(r), end(r), std::forward<C>(comp)); }
template <int D, class I, class C = std::less<>>
CEXP void push_dary_heap(I begin, I end, C&& comp = C{}) NE {
TPN std::iterator_traits<I>::value_type val = std::move(end[-1]);
u32 idx = u32(end - begin) - 1;
while (idx > 0) {
u32 p = d_ary_heap_impl_::pidx_<D>(idx);
if (!comp(begin[p], val)) break;
begin[idx] = std::move(begin[p]), idx = p;
}
begin[idx] = std::move(val);
}
template <int D, common_range R, class C = std::less<>>
CEXP void push_dary_heap(R CR r, C&& comp = C{}) NE { return push_dary_heap<D>(begin(r), end(r), std::forward<C>(comp)); }
template <int D, class I, class C = std::less<>>
CEXP void pop_dary_heap(I begin, I end, C&& comp = C{}) NE {
u32 len = u32(end - begin) - 1;
TPN std::iterator_traits<I>::value_type val = std::move(end[-1]);
u32 idx = 0;
for (end[-1] = std::move(begin[0]);;) {
if (u32 chls = d_ary_heap_impl_::chls_idx_<D>(idx), ch1 = chls - (D - 1); chls < len) {
I ch = d_ary_heap_impl_::l_ch_<D>(begin + ch1, comp);
if (!comp(val, *ch)) break;
begin[idx] = std::move(*ch), idx = u32(ch - begin);
} else if (ch1 < len) {
I ch = d_ary_heap_impl_::l_ch_<D>(begin + ch1, int(len - ch1), comp);
if (comp(val, *ch)) begin[idx] = std::move(*ch), idx = u32(ch - begin);
break;
} else break;
}
begin[idx] = std::move(val);
}
template <int D, common_range R, class C = std::less<>>
CEXP void pop_dary_heap(R CR r, C&& comp = C{}) NE { return pop_dary_heap<D>(begin(r), end(r), std::forward<C>(comp)); }
} // namespace tifa_libs
src/ds/heap/d_ary/lib.hpp