1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
|
/// \file
// Range v3 library
//
// Copyright Eric Niebler 2014-present
//
// Use, modification and distribution is subject to the
// Boost Software License, Version 1.0. (See accompanying
// file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//
// Project home: https://github.com/ericniebler/range-v3
//
//===----------------------------------------------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
#ifndef RANGES_V3_ALGORITHM_NTH_ELEMENT_HPP
#define RANGES_V3_ALGORITHM_NTH_ELEMENT_HPP
#include <utility>
#include <range/v3/range_fwd.hpp>
#include <range/v3/algorithm/min_element.hpp>
#include <range/v3/functional/comparisons.hpp>
#include <range/v3/functional/identity.hpp>
#include <range/v3/functional/invoke.hpp>
#include <range/v3/iterator/concepts.hpp>
#include <range/v3/iterator/operations.hpp>
#include <range/v3/iterator/traits.hpp>
#include <range/v3/range/access.hpp>
#include <range/v3/range/concepts.hpp>
#include <range/v3/range/dangling.hpp>
#include <range/v3/range/traits.hpp>
#include <range/v3/utility/optional.hpp>
#include <range/v3/utility/static_const.hpp>
#include <range/v3/utility/swap.hpp>
#include <range/v3/detail/prologue.hpp>
namespace ranges
{
/// \cond
namespace detail
{
// stable, 2-3 compares, 0-2 swaps
template(typename I, typename C, typename P)(
requires forward_iterator<I> AND indirect_relation<C, projected<I, P>>)
unsigned sort3(I x, I y, I z, C & pred, P & proj)
{
unsigned r = 0;
if(!invoke(pred, invoke(proj, *y), invoke(proj, *x))) // if x <= y
{
if(!invoke(pred, invoke(proj, *z), invoke(proj, *y))) // if y <= z
return r; // x <= y && y <= z
// x <= y && y > z
ranges::iter_swap(y, z); // x <= z && y < z
r = 1;
if(invoke(pred, invoke(proj, *y), invoke(proj, *x))) // if x > y
{
ranges::iter_swap(x, y); // x < y && y <= z
r = 2;
}
return r; // x <= y && y < z
}
if(invoke(pred, invoke(proj, *z), invoke(proj, *y))) // x > y, if y > z
{
ranges::iter_swap(x, z); // x < y && y < z
r = 1;
return r;
}
ranges::iter_swap(x, y); // x > y && y <= z
r = 1; // x < y && x <= z
if(invoke(pred, invoke(proj, *z), invoke(proj, *y))) // if y > z
{
ranges::iter_swap(y, z); // x <= y && y < z
r = 2;
}
return r;
} // x <= y && y <= z
template(typename I, typename C, typename P)(
requires bidirectional_iterator<I> AND indirect_relation<C, projected<I, P>>)
void selection_sort(I first, I last, C & pred, P & proj)
{
RANGES_EXPECT(first != last);
for(I lm1 = ranges::prev(last); first != lm1; ++first)
{
I i = ranges::min_element(first, last, std::ref(pred), std::ref(proj));
if(i != first)
ranges::iter_swap(first, i);
}
}
} // namespace detail
/// \endcond
/// \addtogroup group-algorithms
/// @{
RANGES_FUNC_BEGIN(nth_element)
/// \brief function template \c nth_element
template(typename I, typename S, typename C = less, typename P = identity)(
requires random_access_iterator<I> AND sortable<I, C, P>)
constexpr I RANGES_FUNC(nth_element)(
I first, I nth, S end_, C pred = C{}, P proj = P{}) //
{
I last = ranges::next(nth, end_), end_orig = last;
// C is known to be a reference type
using difference_type = iter_difference_t<I>;
difference_type const limit = 7;
while(true)
{
if(nth == last)
return end_orig;
difference_type len = last - first;
switch(len)
{
case 0:
case 1:
return end_orig;
case 2:
if(invoke(pred, invoke(proj, *--last), invoke(proj, *first)))
ranges::iter_swap(first, last);
return end_orig;
case 3:
{
I m = first;
detail::sort3(first, ++m, --last, pred, proj);
return end_orig;
}
}
if(len <= limit)
{
detail::selection_sort(first, last, pred, proj);
return end_orig;
}
// len > limit >= 3
I m = first + len / 2;
I lm1 = last;
unsigned n_swaps = detail::sort3(first, m, --lm1, pred, proj);
// *m is median
// partition [first, m) < *m and *m <= [m, last)
//(this inhibits tossing elements equivalent to m around unnecessarily)
I i = first;
I j = lm1;
// j points beyond range to be tested, *lm1 is known to be <= *m
// The search going up is known to be guarded but the search coming down
// isn't. Prime the downward search with a guard.
if(!invoke(pred, invoke(proj, *i), invoke(proj, *m))) // if *first == *m
{
// *first == *m, *first doesn't go in first part
// manually guard downward moving j against i
while(true)
{
if(i == --j)
{
// *first == *m, *m <= all other elements
// Parition instead into [first, i) == *first and *first < [i,
// last)
++i; // first + 1
j = last;
if(!invoke(
pred,
invoke(proj, *first),
invoke(
proj,
*--j))) // we need a guard if *first == *(last-1)
{
while(true)
{
if(i == j)
return end_orig; // [first, last) all equivalent
// elements
if(invoke(
pred, invoke(proj, *first), invoke(proj, *i)))
{
ranges::iter_swap(i, j);
++n_swaps;
++i;
break;
}
++i;
}
}
// [first, i) == *first and *first < [j, last) and j == last -
// 1
if(i == j)
return end_orig;
while(true)
{
while(
!invoke(pred, invoke(proj, *first), invoke(proj, *i)))
++i;
while(invoke(
pred, invoke(proj, *first), invoke(proj, *--j)))
;
if(i >= j)
break;
ranges::iter_swap(i, j);
++n_swaps;
++i;
}
// [first, i) == *first and *first < [i, last)
// The first part is sorted,
if(nth < i)
return end_orig;
// nth_element the second part
// nth_element<C>(i, nth, last, pred);
first = i;
continue;
}
if(invoke(pred, invoke(proj, *j), invoke(proj, *m)))
{
ranges::iter_swap(i, j);
++n_swaps;
break; // found guard for downward moving j, now use unguarded
// partition
}
}
}
++i;
// j points beyond range to be tested, *lm1 is known to be <= *m
// if not yet partitioned...
if(i < j)
{
// known that *(i - 1) < *m
while(true)
{
// m still guards upward moving i
while(invoke(pred, invoke(proj, *i), invoke(proj, *m)))
++i;
// It is now known that a guard exists for downward moving j
while(!invoke(pred, invoke(proj, *--j), invoke(proj, *m)))
;
if(i >= j)
break;
ranges::iter_swap(i, j);
++n_swaps;
// It is known that m != j
// If m just moved, follow it
if(m == i)
m = j;
++i;
}
}
// [first, i) < *m and *m <= [i, last)
if(i != m && invoke(pred, invoke(proj, *m), invoke(proj, *i)))
{
ranges::iter_swap(i, m);
++n_swaps;
}
// [first, i) < *i and *i <= [i+1, last)
if(nth == i)
return end_orig;
const auto optional_return = [&]() -> ranges::optional<I> {
if(n_swaps == 0)
{
// We were given a perfectly partitioned sequence. Coincidence?
if(nth < i)
{
// Check for [first, i) already sorted
j = m = first;
while(++j != i)
{
if(invoke(pred, invoke(proj, *j), invoke(proj, *m)))
// not yet sorted, so sort
return ranges::nullopt;
m = j;
}
// [first, i) sorted
return end_orig;
}
else
{
// Check for [i, last) already sorted
j = m = i;
while(++j != last)
{
if(invoke(pred, invoke(proj, *j), invoke(proj, *m)))
// not yet sorted, so sort
return ranges::nullopt;
m = j;
}
// [i, last) sorted
return end_orig;
}
}
return ranges::nullopt;
}();
if(optional_return)
{
return *optional_return;
}
// nth_element on range containing nth
if(nth < i)
{
// nth_element<C>(first, nth, i, pred);
last = i;
}
else
{
// nth_element<C>(i+1, nth, last, pred);
first = ++i;
}
}
return end_orig;
}
/// \overload
template(typename Rng, typename C = less, typename P = identity)(
requires random_access_range<Rng> AND sortable<iterator_t<Rng>, C, P>)
constexpr borrowed_iterator_t<Rng> RANGES_FUNC(nth_element)(
Rng && rng, iterator_t<Rng> nth, C pred = C{}, P proj = P{}) //
{
return (*this)(
begin(rng), std::move(nth), end(rng), std::move(pred), std::move(proj));
}
RANGES_FUNC_END(nth_element)
namespace cpp20
{
using ranges::nth_element;
}
/// @}
} // namespace ranges
#include <range/v3/detail/epilogue.hpp>
#endif
|
