libstdc++-v3/include/bits/stl_tree.h

   1 // RB tree implementation -*- C++ -*-
   2
   3 // Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007
   4 // Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 2, or (at your option)
  10 // any later version.
  11
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16
  17 // You should have received a copy of the GNU General Public License along
  18 // with this library; see the file COPYING.  If not, write to the Free
  19 // Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
  20 // USA.
  21
  22 // As a special exception, you may use this file as part of a free software
  23 // library without restriction.  Specifically, if other files instantiate
  24 // templates or use macros or inline functions from this file, or you compile
  25 // this file and link it with other files to produce an executable, this
  26 // file does not by itself cause the resulting executable to be covered by
  27 // the GNU General Public License.  This exception does not however
  28 // invalidate any other reasons why the executable file might be covered by
  29 // the GNU General Public License.
  30
  31 /*
  32  *
  33  * Copyright (c) 1996,1997
  34  * Silicon Graphics Computer Systems, Inc.
  35  *
  36  * Permission to use, copy, modify, distribute and sell this software
  37  * and its documentation for any purpose is hereby granted without fee,
  38  * provided that the above copyright notice appear in all copies and
  39  * that both that copyright notice and this permission notice appear
  40  * in supporting documentation.  Silicon Graphics makes no
  41  * representations about the suitability of this software for any
  42  * purpose.  It is provided "as is" without express or implied warranty.
  43  *
  44  *
  45  * Copyright (c) 1994
  46  * Hewlett-Packard Company
  47  *
  48  * Permission to use, copy, modify, distribute and sell this software
  49  * and its documentation for any purpose is hereby granted without fee,
  50  * provided that the above copyright notice appear in all copies and
  51  * that both that copyright notice and this permission notice appear
  52  * in supporting documentation.  Hewlett-Packard Company makes no
  53  * representations about the suitability of this software for any
  54  * purpose.  It is provided "as is" without express or implied warranty.
  55  *
  56  *
  57  */
  58
  59 /** @file stl_tree.h
  60  *  This is an internal header file, included by other library headers.
  61  *  You should not attempt to use it directly.
  62  */
  63
  64 #ifndef _TREE_H
  65 #define _TREE_H 1
  66
  67 #include <bits/stl_algobase.h>
  68 #include <bits/allocator.h>
  69 #include <bits/stl_function.h>
  70 #include <bits/cpp_type_traits.h>
  71
  72 _GLIBCXX_BEGIN_NAMESPACE(std)
  73
  74   // Red-black tree class, designed for use in implementing STL
  75   // associative containers (set, multiset, map, and multimap). The
  76   // insertion and deletion algorithms are based on those in Cormen,
  77   // Leiserson, and Rivest, Introduction to Algorithms (MIT Press,
  78   // 1990), except that
  79   //
  80   // (1) the header cell is maintained with links not only to the root
  81   // but also to the leftmost node of the tree, to enable constant
  82   // time begin(), and to the rightmost node of the tree, to enable
  83   // linear time performance when used with the generic set algorithms
  84   // (set_union, etc.)
  85   //
  86   // (2) when a node being deleted has two children its successor node
  87   // is relinked into its place, rather than copied, so that the only
  88   // iterators invalidated are those referring to the deleted node.
  89
  90   enum _Rb_tree_color { _S_red = false, _S_black = true };
  91
  92   struct _Rb_tree_node_base
  93   {
  94     typedef _Rb_tree_node_base* _Base_ptr;
  95     typedef const _Rb_tree_node_base* _Const_Base_ptr;
  96
  97     _Rb_tree_color      _M_color;
  98     _Base_ptr           _M_parent;
  99     _Base_ptr           _M_left;
 100     _Base_ptr           _M_right;
 101
 102     static _Base_ptr
 103     _S_minimum(_Base_ptr __x)
 104     {
 105       while (__x->_M_left != 0) __x = __x->_M_left;
 106       return __x;
 107     }
 108
 109     static _Const_Base_ptr
 110     _S_minimum(_Const_Base_ptr __x)
 111     {
 112       while (__x->_M_left != 0) __x = __x->_M_left;
 113       return __x;
 114     }
 115
 116     static _Base_ptr
 117     _S_maximum(_Base_ptr __x)
 118     {
 119       while (__x->_M_right != 0) __x = __x->_M_right;
 120       return __x;
 121     }
 122
 123     static _Const_Base_ptr
 124     _S_maximum(_Const_Base_ptr __x)
 125     {
 126       while (__x->_M_right != 0) __x = __x->_M_right;
 127       return __x;
 128     }
 129   };
 130
 131   template<typename _Val>
 132     struct _Rb_tree_node : public _Rb_tree_node_base
 133     {
 134       typedef _Rb_tree_node<_Val>* _Link_type;
 135       _Val _M_value_field;
 136     };
 137
 138   _Rb_tree_node_base*
 139   _Rb_tree_increment(_Rb_tree_node_base* __x);
 140
 141   const _Rb_tree_node_base*
 142   _Rb_tree_increment(const _Rb_tree_node_base* __x);
 143
 144   _Rb_tree_node_base*
 145   _Rb_tree_decrement(_Rb_tree_node_base* __x);
 146
 147   const _Rb_tree_node_base*
 148   _Rb_tree_decrement(const _Rb_tree_node_base* __x);
 149
 150   template<typename _Tp>
 151     struct _Rb_tree_iterator
 152     {
 153       typedef _Tp  value_type;
 154       typedef _Tp& reference;
 155       typedef _Tp* pointer;
 156
 157       typedef bidirectional_iterator_tag iterator_category;
 158       typedef ptrdiff_t                  difference_type;
 159
 160       typedef _Rb_tree_iterator<_Tp>        _Self;
 161       typedef _Rb_tree_node_base::_Base_ptr _Base_ptr;
 162       typedef _Rb_tree_node<_Tp>*           _Link_type;
 163
 164       _Rb_tree_iterator()
 165       : _M_node() { }
 166
 167       explicit
 168       _Rb_tree_iterator(_Link_type __x)
 169       : _M_node(__x) { }
 170
 171       reference
 172       operator*() const
 173       { return static_cast<_Link_type>(_M_node)->_M_value_field; }
 174
 175       pointer
 176       operator->() const
 177       { return &static_cast<_Link_type>(_M_node)->_M_value_field; }
 178
 179       _Self&
 180       operator++()
 181       {
 182         _M_node = _Rb_tree_increment(_M_node);
 183         return *this;
 184       }
 185
 186       _Self
 187       operator++(int)
 188       {
 189         _Self __tmp = *this;
 190         _M_node = _Rb_tree_increment(_M_node);
 191         return __tmp;
 192       }
 193
 194       _Self&
 195       operator--()
 196       {
 197         _M_node = _Rb_tree_decrement(_M_node);
 198         return *this;
 199       }
 200
 201       _Self
 202       operator--(int)
 203       {
 204         _Self __tmp = *this;
 205         _M_node = _Rb_tree_decrement(_M_node);
 206         return __tmp;
 207       }
 208
 209       bool
 210       operator==(const _Self& __x) const
 211       { return _M_node == __x._M_node; }
 212
 213       bool
 214       operator!=(const _Self& __x) const
 215       { return _M_node != __x._M_node; }
 216
 217       _Base_ptr _M_node;
 218   };
 219
 220   template<typename _Tp>
 221     struct _Rb_tree_const_iterator
 222     {
 223       typedef _Tp        value_type;
 224       typedef const _Tp& reference;
 225       typedef const _Tp* pointer;
 226
 227       typedef _Rb_tree_iterator<_Tp> iterator;
 228
 229       typedef bidirectional_iterator_tag iterator_category;
 230       typedef ptrdiff_t                  difference_type;
 231
 232       typedef _Rb_tree_const_iterator<_Tp>        _Self;
 233       typedef _Rb_tree_node_base::_Const_Base_ptr _Base_ptr;
 234       typedef const _Rb_tree_node<_Tp>*           _Link_type;
 235
 236       _Rb_tree_const_iterator()
 237       : _M_node() { }
 238
 239       explicit
 240       _Rb_tree_const_iterator(_Link_type __x)
 241       : _M_node(__x) { }
 242
 243       _Rb_tree_const_iterator(const iterator& __it)
 244       : _M_node(__it._M_node) { }
 245
 246       reference
 247       operator*() const
 248       { return static_cast<_Link_type>(_M_node)->_M_value_field; }
 249
 250       pointer
 251       operator->() const
 252       { return &static_cast<_Link_type>(_M_node)->_M_value_field; }
 253
 254       _Self&
 255       operator++()
 256       {
 257         _M_node = _Rb_tree_increment(_M_node);
 258         return *this;
 259       }
 260
 261       _Self
 262       operator++(int)
 263       {
 264         _Self __tmp = *this;
 265         _M_node = _Rb_tree_increment(_M_node);
 266         return __tmp;
 267       }
 268
 269       _Self&
 270       operator--()
 271       {
 272         _M_node = _Rb_tree_decrement(_M_node);
 273         return *this;
 274       }
 275
 276       _Self
 277       operator--(int)
 278       {
 279         _Self __tmp = *this;
 280         _M_node = _Rb_tree_decrement(_M_node);
 281         return __tmp;
 282       }
 283
 284       bool
 285       operator==(const _Self& __x) const
 286       { return _M_node == __x._M_node; }
 287
 288       bool
 289       operator!=(const _Self& __x) const
 290       { return _M_node != __x._M_node; }
 291
 292       _Base_ptr _M_node;
 293     };
 294
 295   template<typename _Val>
 296     inline bool
 297     operator==(const _Rb_tree_iterator<_Val>& __x,
 298                const _Rb_tree_const_iterator<_Val>& __y)
 299     { return __x._M_node == __y._M_node; }
 300
 301   template<typename _Val>
 302     inline bool
 303     operator!=(const _Rb_tree_iterator<_Val>& __x,
 304                const _Rb_tree_const_iterator<_Val>& __y)
 305     { return __x._M_node != __y._M_node; }
 306
 307   void
 308   _Rb_tree_insert_and_rebalance(const bool __insert_left,
 309                                 _Rb_tree_node_base* __x,
 310                                 _Rb_tree_node_base* __p,
 311                                 _Rb_tree_node_base& __header);
 312
 313   _Rb_tree_node_base*
 314   _Rb_tree_rebalance_for_erase(_Rb_tree_node_base* const __z,
 315                                _Rb_tree_node_base& __header);
 316
 317
 318   template<typename _Key, typename _Val, typename _KeyOfValue,
 319            typename _Compare, typename _Alloc = allocator<_Val> >
 320     class _Rb_tree
 321     {
 322       typedef typename _Alloc::template rebind<_Rb_tree_node<_Val> >::other
 323               _Node_allocator;
 324
 325     protected:
 326       typedef _Rb_tree_node_base* _Base_ptr;
 327       typedef const _Rb_tree_node_base* _Const_Base_ptr;
 328
 329     public:
 330       typedef _Key key_type;
 331       typedef _Val value_type;
 332       typedef value_type* pointer;
 333       typedef const value_type* const_pointer;
 334       typedef value_type& reference;
 335       typedef const value_type& const_reference;
 336       typedef _Rb_tree_node<_Val>* _Link_type;
 337       typedef const _Rb_tree_node<_Val>* _Const_Link_type;
 338       typedef size_t size_type;
 339       typedef ptrdiff_t difference_type;
 340       typedef _Alloc allocator_type;
 341
 342       _Node_allocator&
 343       _M_get_Node_allocator()
 344       { return *static_cast<_Node_allocator*>(&this->_M_impl); }
 345
 346       const _Node_allocator&
 347       _M_get_Node_allocator() const
 348       { return *static_cast<const _Node_allocator*>(&this->_M_impl); }
 349
 350       allocator_type
 351       get_allocator() const
 352       { return allocator_type(_M_get_Node_allocator()); }
 353
 354     protected:
 355       _Link_type
 356       _M_get_node()
 357       { return _M_impl._Node_allocator::allocate(1); }
 358
 359       void
 360       _M_put_node(_Link_type __p)
 361       { _M_impl._Node_allocator::deallocate(__p, 1); }
 362
 363       _Link_type
 364       _M_create_node(const value_type& __x)
 365       {
 366         _Link_type __tmp = _M_get_node();
 367         try
 368           { get_allocator().construct(&__tmp->_M_value_field, __x); }
 369         catch(...)
 370           {
 371             _M_put_node(__tmp);
 372             __throw_exception_again;
 373           }
 374         return __tmp;
 375       }
 376
 377       _Link_type
 378       _M_clone_node(_Const_Link_type __x)
 379       {
 380         _Link_type __tmp = _M_create_node(__x->_M_value_field);
 381         __tmp->_M_color = __x->_M_color;
 382         __tmp->_M_left = 0;
 383         __tmp->_M_right = 0;
 384         return __tmp;
 385       }
 386
 387       void
 388       _M_destroy_node(_Link_type __p)
 389       {
 390         get_allocator().destroy(&__p->_M_value_field);
 391         _M_put_node(__p);
 392       }
 393
 394     protected:
 395       template<typename _Key_compare,
 396                bool _Is_pod_comparator = __is_pod(_Key_compare)>
 397         struct _Rb_tree_impl : public _Node_allocator
 398         {
 399           _Key_compare          _M_key_compare;
 400           _Rb_tree_node_base    _M_header;
 401           size_type             _M_node_count; // Keeps track of size of tree.
 402
 403           _Rb_tree_impl(const _Node_allocator& __a = _Node_allocator(),
 404                         const _Key_compare& __comp = _Key_compare())
 405           : _Node_allocator(__a), _M_key_compare(__comp), _M_header(),
 406             _M_node_count(0)
 407           {
 408             this->_M_header._M_color = _S_red;
 409             this->_M_header._M_parent = 0;
 410             this->_M_header._M_left = &this->_M_header;
 411             this->_M_header._M_right = &this->_M_header;
 412           }
 413         };
 414
 415       // Specialization for _Comparison types that are not capable of
 416       // being base classes / super classes.
 417       template<typename _Key_compare>
 418         struct _Rb_tree_impl<_Key_compare, true> : public _Node_allocator
 419         {
 420           _Key_compare          _M_key_compare;
 421           _Rb_tree_node_base    _M_header;
 422           size_type             _M_node_count; // Keeps track of size of tree.
 423
 424           _Rb_tree_impl(const _Node_allocator& __a = _Node_allocator(),
 425                         const _Key_compare& __comp = _Key_compare())
 426           : _Node_allocator(__a), _M_key_compare(__comp), _M_header(),
 427             _M_node_count(0)
 428           {
 429             this->_M_header._M_color = _S_red;
 430             this->_M_header._M_parent = 0;
 431             this->_M_header._M_left = &this->_M_header;
 432             this->_M_header._M_right = &this->_M_header;
 433           }
 434         };
 435
 436       _Rb_tree_impl<_Compare> _M_impl;
 437
 438     protected:
 439       _Base_ptr&
 440       _M_root()
 441       { return this->_M_impl._M_header._M_parent; }
 442
 443       _Const_Base_ptr
 444       _M_root() const
 445       { return this->_M_impl._M_header._M_parent; }
 446
 447       _Base_ptr&
 448       _M_leftmost()
 449       { return this->_M_impl._M_header._M_left; }
 450
 451       _Const_Base_ptr
 452       _M_leftmost() const
 453       { return this->_M_impl._M_header._M_left; }
 454
 455       _Base_ptr&
 456       _M_rightmost()
 457       { return this->_M_impl._M_header._M_right; }
 458
 459       _Const_Base_ptr
 460       _M_rightmost() const
 461       { return this->_M_impl._M_header._M_right; }
 462
 463       _Link_type
 464       _M_begin()
 465       { return static_cast<_Link_type>(this->_M_impl._M_header._M_parent); }
 466
 467       _Const_Link_type
 468       _M_begin() const
 469       {
 470         return static_cast<_Const_Link_type>
 471           (this->_M_impl._M_header._M_parent);
 472       }
 473
 474       _Link_type
 475       _M_end()
 476       { return static_cast<_Link_type>(&this->_M_impl._M_header); }
 477
 478       _Const_Link_type
 479       _M_end() const
 480       { return static_cast<_Const_Link_type>(&this->_M_impl._M_header); }
 481
 482       static const_reference
 483       _S_value(_Const_Link_type __x)
 484       { return __x->_M_value_field; }
 485
 486       static const _Key&
 487       _S_key(_Const_Link_type __x)
 488       { return _KeyOfValue()(_S_value(__x)); }
 489
 490       static _Link_type
 491       _S_left(_Base_ptr __x)
 492       { return static_cast<_Link_type>(__x->_M_left); }
 493
 494       static _Const_Link_type
 495       _S_left(_Const_Base_ptr __x)
 496       { return static_cast<_Const_Link_type>(__x->_M_left); }
 497
 498       static _Link_type
 499       _S_right(_Base_ptr __x)
 500       { return static_cast<_Link_type>(__x->_M_right); }
 501
 502       static _Const_Link_type
 503       _S_right(_Const_Base_ptr __x)
 504       { return static_cast<_Const_Link_type>(__x->_M_right); }
 505
 506       static const_reference
 507       _S_value(_Const_Base_ptr __x)
 508       { return static_cast<_Const_Link_type>(__x)->_M_value_field; }
 509
 510       static const _Key&
 511       _S_key(_Const_Base_ptr __x)
 512       { return _KeyOfValue()(_S_value(__x)); }
 513
 514       static _Base_ptr
 515       _S_minimum(_Base_ptr __x)
 516       { return _Rb_tree_node_base::_S_minimum(__x); }
 517
 518       static _Const_Base_ptr
 519       _S_minimum(_Const_Base_ptr __x)
 520       { return _Rb_tree_node_base::_S_minimum(__x); }
 521
 522       static _Base_ptr
 523       _S_maximum(_Base_ptr __x)
 524       { return _Rb_tree_node_base::_S_maximum(__x); }
 525
 526       static _Const_Base_ptr
 527       _S_maximum(_Const_Base_ptr __x)
 528       { return _Rb_tree_node_base::_S_maximum(__x); }
 529
 530     public:
 531       typedef _Rb_tree_iterator<value_type>       iterator;
 532       typedef _Rb_tree_const_iterator<value_type> const_iterator;
 533
 534       typedef std::reverse_iterator<iterator>       reverse_iterator;
 535       typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
 536
 537     private:
 538       iterator
 539       _M_insert_(_Const_Base_ptr __x, _Const_Base_ptr __y,
 540                  const value_type& __v);
 541
 542       // _GLIBCXX_RESOLVE_LIB_DEFECTS
 543       // 233. Insertion hints in associative containers.
 544       iterator
 545       _M_insert_lower(_Base_ptr __x, _Base_ptr __y, const value_type& __v);
 546
 547       iterator
 548       _M_insert_equal_lower(const value_type& __x);
 549
 550       _Link_type
 551       _M_copy(_Const_Link_type __x, _Link_type __p);
 552
 553       void
 554       _M_erase(_Link_type __x);
 555
 556       iterator
 557       _M_lower_bound(_Const_Link_type __x, _Const_Link_type __y,
 558                      const _Key& __k) const;
 559
 560       iterator
 561       _M_upper_bound(_Const_Link_type __x, _Const_Link_type __y,
 562                      const _Key& __k) const;
 563
 564       pair<iterator, iterator>
 565       _M_equal_range(const _Key& __k) const;
 566
 567     public:
 568       // allocation/deallocation
 569       _Rb_tree()
 570       { }
 571
 572       _Rb_tree(const _Compare& __comp)
 573       : _M_impl(allocator_type(), __comp)
 574       { }
 575
 576       _Rb_tree(const _Compare& __comp, const allocator_type& __a)
 577       : _M_impl(__a, __comp)
 578       { }
 579
 580       _Rb_tree(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x)
 581       : _M_impl(__x._M_get_Node_allocator(), __x._M_impl._M_key_compare)
 582       {
 583         if (__x._M_root() != 0)
 584           {
 585             _M_root() = _M_copy(__x._M_begin(), _M_end());
 586             _M_leftmost() = _S_minimum(_M_root());
 587             _M_rightmost() = _S_maximum(_M_root());
 588             _M_impl._M_node_count = __x._M_impl._M_node_count;
 589           }
 590       }
 591
 592       ~_Rb_tree()
 593       { _M_erase(_M_begin()); }
 594
 595       _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>&
 596       operator=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x);
 597
 598       // Accessors.
 599       _Compare
 600       key_comp() const
 601       { return _M_impl._M_key_compare; }
 602
 603       iterator
 604       begin()
 605       {
 606         return iterator(static_cast<_Link_type>
 607                         (this->_M_impl._M_header._M_left));
 608       }
 609
 610       const_iterator
 611       begin() const
 612       {
 613         return const_iterator(static_cast<_Const_Link_type>
 614                               (this->_M_impl._M_header._M_left));
 615       }
 616
 617       iterator
 618       end()
 619       { return iterator(static_cast<_Link_type>(&this->_M_impl._M_header)); }
 620
 621       const_iterator
 622       end() const
 623       {
 624         return const_iterator(static_cast<_Const_Link_type>
 625                               (&this->_M_impl._M_header));
 626       }
 627
 628       reverse_iterator
 629       rbegin()
 630       { return reverse_iterator(end()); }
 631
 632       const_reverse_iterator
 633       rbegin() const
 634       { return const_reverse_iterator(end()); }
 635
 636       reverse_iterator
 637       rend()
 638       { return reverse_iterator(begin()); }
 639
 640       const_reverse_iterator
 641       rend() const
 642       { return const_reverse_iterator(begin()); }
 643
 644       bool
 645       empty() const
 646       { return _M_impl._M_node_count == 0; }
 647
 648       size_type
 649       size() const
 650       { return _M_impl._M_node_count; }
 651
 652       size_type
 653       max_size() const
 654       { return get_allocator().max_size(); }
 655
 656       void
 657       swap(_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __t);
 658
 659       // Insert/erase.
 660       pair<iterator, bool>
 661       _M_insert_unique(const value_type& __x);
 662
 663       iterator
 664       _M_insert_equal(const value_type& __x);
 665
 666       iterator
 667       _M_insert_unique_(const_iterator __position, const value_type& __x);
 668
 669       iterator
 670       _M_insert_equal_(const_iterator __position, const value_type& __x);
 671
 672       template<typename _InputIterator>
 673         void
 674         _M_insert_unique(_InputIterator __first, _InputIterator __last);
 675
 676       template<typename _InputIterator>
 677         void
 678         _M_insert_equal(_InputIterator __first, _InputIterator __last);
 679
 680       void
 681       erase(iterator __position);
 682
 683       void
 684       erase(const_iterator __position);
 685
 686       size_type
 687       erase(const key_type& __x);
 688
 689       void
 690       erase(iterator __first, iterator __last);
 691
 692       void
 693       erase(const_iterator __first, const_iterator __last);
 694
 695       void
 696       erase(const key_type* __first, const key_type* __last);
 697
 698       void
 699       clear()
 700       {
 701         _M_erase(_M_begin());
 702         _M_leftmost() = _M_end();
 703         _M_root() = 0;
 704         _M_rightmost() = _M_end();
 705         _M_impl._M_node_count = 0;
 706       }
 707
 708       // Set operations.
 709       iterator
 710       find(const key_type& __k);
 711
 712       const_iterator
 713       find(const key_type& __k) const;
 714
 715       size_type
 716       count(const key_type& __k) const;
 717
 718       iterator
 719       lower_bound(const key_type& __k)
 720       { return iterator(_M_lower_bound(_M_begin(), _M_end(), __k)); }
 721
 722       const_iterator
 723       lower_bound(const key_type& __k) const
 724       { return const_iterator(_M_lower_bound(_M_begin(), _M_end(), __k)); }
 725
 726       iterator
 727       upper_bound(const key_type& __k)
 728       { return iterator(_M_upper_bound(_M_begin(), _M_end(), __k)); }
 729
 730       const_iterator
 731       upper_bound(const key_type& __k) const
 732       { return const_iterator(_M_upper_bound(_M_begin(), _M_end(), __k)); }
 733
 734       pair<iterator, iterator>
 735       equal_range(const key_type& __k)
 736       { return pair<iterator, iterator>(_M_equal_range(__k)); }
 737
 738       pair<const_iterator, const_iterator>
 739       equal_range(const key_type& __k) const
 740       { return pair<const_iterator, const_iterator>(_M_equal_range(__k)); }
 741
 742       // Debugging.
 743       bool
 744       __rb_verify() const;
 745     };
 746
 747   template<typename _Key, typename _Val, typename _KeyOfValue,
 748            typename _Compare, typename _Alloc>
 749     inline bool
 750     operator==(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
 751                const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
 752     {
 753       return __x.size() == __y.size()
 754              && std::equal(__x.begin(), __x.end(), __y.begin());
 755     }
 756
 757   template<typename _Key, typename _Val, typename _KeyOfValue,
 758            typename _Compare, typename _Alloc>
 759     inline bool
 760     operator<(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
 761               const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
 762     {
 763       return std::lexicographical_compare(__x.begin(), __x.end(),
 764                                           __y.begin(), __y.end());
 765     }
 766
 767   template<typename _Key, typename _Val, typename _KeyOfValue,
 768            typename _Compare, typename _Alloc>
 769     inline bool
 770     operator!=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
 771                const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
 772     { return !(__x == __y); }
 773
 774   template<typename _Key, typename _Val, typename _KeyOfValue,
 775            typename _Compare, typename _Alloc>
 776     inline bool
 777     operator>(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
 778               const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
 779     { return __y < __x; }
 780
 781   template<typename _Key, typename _Val, typename _KeyOfValue,
 782            typename _Compare, typename _Alloc>
 783     inline bool
 784     operator<=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
 785                const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
 786     { return !(__y < __x); }
 787
 788   template<typename _Key, typename _Val, typename _KeyOfValue,
 789            typename _Compare, typename _Alloc>
 790     inline bool
 791     operator>=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
 792                const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
 793     { return !(__x < __y); }
 794
 795   template<typename _Key, typename _Val, typename _KeyOfValue,
 796            typename _Compare, typename _Alloc>
 797     inline void
 798     swap(_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
 799          _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
 800     { __x.swap(__y); }
 801
 802   template<typename _Key, typename _Val, typename _KeyOfValue,
 803            typename _Compare, typename _Alloc>
 804     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>&
 805     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 806     operator=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x)
 807     {
 808       if (this != &__x)
 809         {
 810           // Note that _Key may be a constant type.
 811           clear();
 812           _M_impl._M_key_compare = __x._M_impl._M_key_compare;
 813           if (__x._M_root() != 0)
 814             {
 815               _M_root() = _M_copy(__x._M_begin(), _M_end());
 816               _M_leftmost() = _S_minimum(_M_root());
 817               _M_rightmost() = _S_maximum(_M_root());
 818               _M_impl._M_node_count = __x._M_impl._M_node_count;
 819             }
 820         }
 821       return *this;
 822     }
 823
 824   template<typename _Key, typename _Val, typename _KeyOfValue,
 825            typename _Compare, typename _Alloc>
 826     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
 827     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 828     _M_insert_(_Const_Base_ptr __x, _Const_Base_ptr __p, const _Val& __v)
 829     {
 830       bool __insert_left = (__x != 0 || __p == _M_end()
 831                             || _M_impl._M_key_compare(_KeyOfValue()(__v),
 832                                                       _S_key(__p)));
 833
 834       _Link_type __z = _M_create_node(__v);
 835
 836       _Rb_tree_insert_and_rebalance(__insert_left, __z,
 837                                     const_cast<_Base_ptr>(__p),
 838                                     this->_M_impl._M_header);
 839       ++_M_impl._M_node_count;
 840       return iterator(__z);
 841     }
 842
 843   template<typename _Key, typename _Val, typename _KeyOfValue,
 844            typename _Compare, typename _Alloc>
 845     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
 846     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 847     _M_insert_lower(_Base_ptr __x, _Base_ptr __p, const _Val& __v)
 848     {
 849       bool __insert_left = (__x != 0 || __p == _M_end()
 850                             || !_M_impl._M_key_compare(_S_key(__p),
 851                                                        _KeyOfValue()(__v)));
 852
 853       _Link_type __z = _M_create_node(__v);
 854
 855       _Rb_tree_insert_and_rebalance(__insert_left, __z, __p,
 856                                     this->_M_impl._M_header);
 857       ++_M_impl._M_node_count;
 858       return iterator(__z);
 859     }
 860
 861   template<typename _Key, typename _Val, typename _KeyOfValue,
 862            typename _Compare, typename _Alloc>
 863     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
 864     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 865     _M_insert_equal_lower(const _Val& __v)
 866     {
 867       _Link_type __x = _M_begin();
 868       _Link_type __y = _M_end();
 869       while (__x != 0)
 870         {
 871           __y = __x;
 872           __x = !_M_impl._M_key_compare(_S_key(__x), _KeyOfValue()(__v)) ?
 873                 _S_left(__x) : _S_right(__x);
 874         }
 875       return _M_insert_lower(__x, __y, __v);
 876     }
 877
 878   template<typename _Key, typename _Val, typename _KoV,
 879            typename _Compare, typename _Alloc>
 880     typename _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::_Link_type
 881     _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::
 882     _M_copy(_Const_Link_type __x, _Link_type __p)
 883     {
 884       // Structural copy.  __x and __p must be non-null.
 885       _Link_type __top = _M_clone_node(__x);
 886       __top->_M_parent = __p;
 887
 888       try
 889         {
 890           if (__x->_M_right)
 891             __top->_M_right = _M_copy(_S_right(__x), __top);
 892           __p = __top;
 893           __x = _S_left(__x);
 894
 895           while (__x != 0)
 896             {
 897               _Link_type __y = _M_clone_node(__x);
 898               __p->_M_left = __y;
 899               __y->_M_parent = __p;
 900               if (__x->_M_right)
 901                 __y->_M_right = _M_copy(_S_right(__x), __y);
 902               __p = __y;
 903               __x = _S_left(__x);
 904             }
 905         }
 906       catch(...)
 907         {
 908           _M_erase(__top);
 909           __throw_exception_again;
 910         }
 911       return __top;
 912     }
 913
 914   template<typename _Key, typename _Val, typename _KeyOfValue,
 915            typename _Compare, typename _Alloc>
 916     void
 917     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 918     _M_erase(_Link_type __x)
 919     {
 920       // Erase without rebalancing.
 921       while (__x != 0)
 922         {
 923           _M_erase(_S_right(__x));
 924           _Link_type __y = _S_left(__x);
 925           _M_destroy_node(__x);
 926           __x = __y;
 927         }
 928     }
 929
 930   template<typename _Key, typename _Val, typename _KeyOfValue,
 931            typename _Compare, typename _Alloc>
 932     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
 933     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 934     _M_lower_bound(_Const_Link_type __x, _Const_Link_type __y,
 935                    const _Key& __k) const
 936     {
 937       while (__x != 0)
 938         if (!_M_impl._M_key_compare(_S_key(__x), __k))
 939           __y = __x, __x = _S_left(__x);
 940         else
 941           __x = _S_right(__x);
 942       return iterator(const_cast<_Link_type>(__y));
 943     }
 944
 945   template<typename _Key, typename _Val, typename _KeyOfValue,
 946            typename _Compare, typename _Alloc>
 947     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
 948     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 949     _M_upper_bound(_Const_Link_type __x, _Const_Link_type __y,
 950                    const _Key& __k) const
 951     {
 952       while (__x != 0)
 953         if (_M_impl._M_key_compare(__k, _S_key(__x)))
 954           __y = __x, __x = _S_left(__x);
 955         else
 956           __x = _S_right(__x);
 957       return iterator(const_cast<_Link_type>(__y));
 958     }
 959
 960   template<typename _Key, typename _Val, typename _KeyOfValue,
 961            typename _Compare, typename _Alloc>
 962     pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
 963                            _Compare, _Alloc>::iterator,
 964          typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator>
 965     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 966     _M_equal_range(const _Key& __k) const
 967     {
 968       _Const_Link_type __x = _M_begin();
 969       _Const_Link_type __y = _M_end();
 970       while (__x != 0)
 971         {
 972           if (_M_impl._M_key_compare(_S_key(__x), __k))
 973             __x = _S_right(__x);
 974           else if (_M_impl._M_key_compare(__k, _S_key(__x)))
 975             __y = __x, __x = _S_left(__x);
 976           else
 977             {
 978               _Const_Link_type __xu(__x), __yu(__y);
 979               __y = __x, __x = _S_left(__x);
 980               __xu = _S_right(__xu);
 981               return pair<iterator, iterator>(_M_lower_bound(__x, __y, __k),
 982                                               _M_upper_bound(__xu, __yu, __k));
 983             }
 984         }
 985       return pair<iterator, iterator>(iterator(const_cast<_Link_type>(__y)),
 986                                       iterator(const_cast<_Link_type>(__y)));
 987     }
 988
 989   template<typename _Key, typename _Val, typename _KeyOfValue,
 990            typename _Compare, typename _Alloc>
 991     void
 992     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
 993     swap(_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __t)
 994     {
 995       if (_M_root() == 0)
 996         {
 997           if (__t._M_root() != 0)
 998             {
 999               _M_root() = __t._M_root();
1000               _M_leftmost() = __t._M_leftmost();
1001               _M_rightmost() = __t._M_rightmost();
1002               _M_root()->_M_parent = _M_end();
1003
1004               __t._M_root() = 0;
1005               __t._M_leftmost() = __t._M_end();
1006               __t._M_rightmost() = __t._M_end();
1007             }
1008         }
1009       else if (__t._M_root() == 0)
1010         {
1011           __t._M_root() = _M_root();
1012           __t._M_leftmost() = _M_leftmost();
1013           __t._M_rightmost() = _M_rightmost();
1014           __t._M_root()->_M_parent = __t._M_end();
1015
1016           _M_root() = 0;
1017           _M_leftmost() = _M_end();
1018           _M_rightmost() = _M_end();
1019         }
1020       else
1021         {
1022           std::swap(_M_root(),__t._M_root());
1023           std::swap(_M_leftmost(),__t._M_leftmost());
1024           std::swap(_M_rightmost(),__t._M_rightmost());
1025
1026           _M_root()->_M_parent = _M_end();
1027           __t._M_root()->_M_parent = __t._M_end();
1028         }
1029       // No need to swap header's color as it does not change.
1030       std::swap(this->_M_impl._M_node_count, __t._M_impl._M_node_count);
1031       std::swap(this->_M_impl._M_key_compare, __t._M_impl._M_key_compare);
1032
1033       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1034       // 431. Swapping containers with unequal allocators.
1035       std::__alloc_swap<_Node_allocator>::
1036         _S_do_it(_M_get_Node_allocator(), __t._M_get_Node_allocator());
1037     }
1038
1039   template<typename _Key, typename _Val, typename _KeyOfValue,
1040            typename _Compare, typename _Alloc>
1041     pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
1042                            _Compare, _Alloc>::iterator, bool>
1043     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1044     _M_insert_unique(const _Val& __v)
1045     {
1046       _Link_type __x = _M_begin();
1047       _Link_type __y = _M_end();
1048       bool __comp = true;
1049       while (__x != 0)
1050         {
1051           __y = __x;
1052           __comp = _M_impl._M_key_compare(_KeyOfValue()(__v), _S_key(__x));
1053           __x = __comp ? _S_left(__x) : _S_right(__x);
1054         }
1055       iterator __j = iterator(__y);
1056       if (__comp)
1057         {
1058           if (__j == begin())
1059             return pair<iterator, bool>(_M_insert_(__x, __y, __v), true);
1060           else
1061             --__j;
1062         }
1063       if (_M_impl._M_key_compare(_S_key(__j._M_node), _KeyOfValue()(__v)))
1064         return pair<iterator, bool>(_M_insert_(__x, __y, __v), true);
1065       return pair<iterator, bool>(__j, false);
1066     }
1067
1068   template<typename _Key, typename _Val, typename _KeyOfValue,
1069            typename _Compare, typename _Alloc>
1070     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
1071     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1072     _M_insert_equal(const _Val& __v)
1073     {
1074       _Link_type __x = _M_begin();
1075       _Link_type __y = _M_end();
1076       while (__x != 0)
1077         {
1078           __y = __x;
1079           __x = _M_impl._M_key_compare(_KeyOfValue()(__v), _S_key(__x)) ?
1080                 _S_left(__x) : _S_right(__x);
1081         }
1082       return _M_insert_(__x, __y, __v);
1083     }
1084
1085   template<typename _Key, typename _Val, typename _KeyOfValue,
1086            typename _Compare, typename _Alloc>
1087     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
1088     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1089     _M_insert_unique_(const_iterator __position, const _Val& __v)
1090     {
1091       // end()
1092       if (__position._M_node == _M_end())
1093         {
1094           if (size() > 0
1095               && _M_impl._M_key_compare(_S_key(_M_rightmost()),
1096                                         _KeyOfValue()(__v)))
1097             return _M_insert_(0, _M_rightmost(), __v);
1098           else
1099             return _M_insert_unique(__v).first;
1100         }
1101       else if (_M_impl._M_key_compare(_KeyOfValue()(__v),
1102                                       _S_key(__position._M_node)))
1103         {
1104           // First, try before...
1105           const_iterator __before = __position;
1106           if (__position._M_node == _M_leftmost()) // begin()
1107             return _M_insert_(_M_leftmost(), _M_leftmost(), __v);
1108           else if (_M_impl._M_key_compare(_S_key((--__before)._M_node),
1109                                           _KeyOfValue()(__v)))
1110             {
1111               if (_S_right(__before._M_node) == 0)
1112                 return _M_insert_(0, __before._M_node, __v);
1113               else
1114                 return _M_insert_(__position._M_node,
1115                                   __position._M_node, __v);
1116             }
1117           else
1118             return _M_insert_unique(__v).first;
1119         }
1120       else if (_M_impl._M_key_compare(_S_key(__position._M_node),
1121                                       _KeyOfValue()(__v)))
1122         {
1123           // ... then try after.
1124           const_iterator __after = __position;
1125           if (__position._M_node == _M_rightmost())
1126             return _M_insert_(0, _M_rightmost(), __v);
1127           else if (_M_impl._M_key_compare(_KeyOfValue()(__v),
1128                                           _S_key((++__after)._M_node)))
1129             {
1130               if (_S_right(__position._M_node) == 0)
1131                 return _M_insert_(0, __position._M_node, __v);
1132               else
1133                 return _M_insert_(__after._M_node, __after._M_node, __v);
1134             }
1135           else
1136             return _M_insert_unique(__v).first;
1137         }
1138       else
1139         // Equivalent keys.
1140         return iterator(static_cast<_Link_type>
1141                         (const_cast<_Base_ptr>(__position._M_node)));
1142     }
1143
1144   template<typename _Key, typename _Val, typename _KeyOfValue,
1145            typename _Compare, typename _Alloc>
1146     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
1147     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1148     _M_insert_equal_(const_iterator __position, const _Val& __v)
1149     {
1150       // end()
1151       if (__position._M_node == _M_end())
1152         {
1153           if (size() > 0
1154               && !_M_impl._M_key_compare(_KeyOfValue()(__v),
1155                                          _S_key(_M_rightmost())))
1156             return _M_insert_(0, _M_rightmost(), __v);
1157           else
1158             return _M_insert_equal(__v);
1159         }
1160       else if (!_M_impl._M_key_compare(_S_key(__position._M_node),
1161                                        _KeyOfValue()(__v)))
1162         {
1163           // First, try before...
1164           const_iterator __before = __position;
1165           if (__position._M_node == _M_leftmost()) // begin()
1166             return _M_insert_(_M_leftmost(), _M_leftmost(), __v);
1167           else if (!_M_impl._M_key_compare(_KeyOfValue()(__v),
1168                                            _S_key((--__before)._M_node)))
1169             {
1170               if (_S_right(__before._M_node) == 0)
1171                 return _M_insert_(0, __before._M_node, __v);
1172               else
1173                 return _M_insert_(__position._M_node,
1174                                   __position._M_node, __v);
1175             }
1176           else
1177             return _M_insert_equal(__v);
1178         }
1179       else
1180         {
1181           // ... then try after.
1182           const_iterator __after = __position;
1183           if (__position._M_node == _M_rightmost())
1184             return _M_insert_(0, _M_rightmost(), __v);
1185           else if (!_M_impl._M_key_compare(_S_key((++__after)._M_node),
1186                                            _KeyOfValue()(__v)))
1187             {
1188               if (_S_right(__position._M_node) == 0)
1189                 return _M_insert_(0, __position._M_node, __v);
1190               else
1191                 return _M_insert_(__after._M_node, __after._M_node, __v);
1192             }
1193           else
1194             return _M_insert_equal_lower(__v);
1195         }
1196     }
1197
1198   template<typename _Key, typename _Val, typename _KoV,
1199            typename _Cmp, typename _Alloc>
1200     template<class _II>
1201       void
1202       _Rb_tree<_Key, _Val, _KoV, _Cmp, _Alloc>::
1203       _M_insert_unique(_II __first, _II __last)
1204       {
1205         for (; __first != __last; ++__first)
1206           _M_insert_unique_(end(), *__first);
1207       }
1208
1209   template<typename _Key, typename _Val, typename _KoV,
1210            typename _Cmp, typename _Alloc>
1211     template<class _II>
1212       void
1213       _Rb_tree<_Key, _Val, _KoV, _Cmp, _Alloc>::
1214       _M_insert_equal(_II __first, _II __last)
1215       {
1216         for (; __first != __last; ++__first)
1217           _M_insert_equal_(end(), *__first);
1218       }
1219
1220   template<typename _Key, typename _Val, typename _KeyOfValue,
1221            typename _Compare, typename _Alloc>
1222     inline void
1223     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1224     erase(iterator __position)
1225     {
1226       _Link_type __y =
1227         static_cast<_Link_type>(_Rb_tree_rebalance_for_erase
1228                                 (__position._M_node,
1229                                  this->_M_impl._M_header));
1230       _M_destroy_node(__y);
1231       --_M_impl._M_node_count;
1232     }
1233
1234   template<typename _Key, typename _Val, typename _KeyOfValue,
1235            typename _Compare, typename _Alloc>
1236     inline void
1237     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1238     erase(const_iterator __position)
1239     {
1240       _Link_type __y =
1241         static_cast<_Link_type>(_Rb_tree_rebalance_for_erase
1242                                 (const_cast<_Base_ptr>(__position._M_node),
1243                                  this->_M_impl._M_header));
1244       _M_destroy_node(__y);
1245       --_M_impl._M_node_count;
1246     }
1247
1248   template<typename _Key, typename _Val, typename _KeyOfValue,
1249            typename _Compare, typename _Alloc>
1250     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::size_type
1251     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1252     erase(const _Key& __x)
1253     {
1254       pair<iterator, iterator> __p = equal_range(__x);
1255       const size_type __old_size = size();
1256       erase(__p.first, __p.second);
1257       return __old_size - size();
1258     }
1259
1260   template<typename _Key, typename _Val, typename _KeyOfValue,
1261            typename _Compare, typename _Alloc>
1262     void
1263     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1264     erase(iterator __first, iterator __last)
1265     {
1266       if (__first == begin() && __last == end())
1267         clear();
1268       else
1269         while (__first != __last)
1270           erase(__first++);
1271     }
1272
1273   template<typename _Key, typename _Val, typename _KeyOfValue,
1274            typename _Compare, typename _Alloc>
1275     void
1276     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1277     erase(const_iterator __first, const_iterator __last)
1278     {
1279       if (__first == begin() && __last == end())
1280         clear();
1281       else
1282         while (__first != __last)
1283           erase(__first++);
1284     }
1285
1286   template<typename _Key, typename _Val, typename _KeyOfValue,
1287            typename _Compare, typename _Alloc>
1288     void
1289     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1290     erase(const _Key* __first, const _Key* __last)
1291     {
1292       while (__first != __last)
1293         erase(*__first++);
1294     }
1295
1296   template<typename _Key, typename _Val, typename _KeyOfValue,
1297            typename _Compare, typename _Alloc>
1298     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
1299     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1300     find(const _Key& __k)
1301     {
1302       iterator __j = iterator(_M_lower_bound(_M_begin(), _M_end(), __k));
1303       return (__j == end()
1304               || _M_impl._M_key_compare(__k,
1305                                         _S_key(__j._M_node))) ? end() : __j;
1306     }
1307
1308   template<typename _Key, typename _Val, typename _KeyOfValue,
1309            typename _Compare, typename _Alloc>
1310     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::const_iterator
1311     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1312     find(const _Key& __k) const
1313     {
1314       const_iterator __j = const_iterator(_M_lower_bound(_M_begin(),
1315                                                          _M_end(), __k));
1316       return (__j == end()
1317               || _M_impl._M_key_compare(__k,
1318                                         _S_key(__j._M_node))) ? end() : __j;
1319     }
1320
1321   template<typename _Key, typename _Val, typename _KeyOfValue,
1322            typename _Compare, typename _Alloc>
1323     typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::size_type
1324     _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
1325     count(const _Key& __k) const
1326     {
1327       pair<const_iterator, const_iterator> __p = equal_range(__k);
1328       const size_type __n = std::distance(__p.first, __p.second);
1329       return __n;
1330     }
1331
1332   unsigned int
1333   _Rb_tree_black_count(const _Rb_tree_node_base* __node,
1334                        const _Rb_tree_node_base* __root);
1335
1336   template<typename _Key, typename _Val, typename _KeyOfValue,
1337            typename _Compare, typename _Alloc>
1338     bool
1339     _Rb_tree<_Key,_Val,_KeyOfValue,_Compare,_Alloc>::__rb_verify() const
1340     {
1341       if (_M_impl._M_node_count == 0 || begin() == end())
1342         return _M_impl._M_node_count == 0 && begin() == end()
1343                && this->_M_impl._M_header._M_left == _M_end()
1344                && this->_M_impl._M_header._M_right == _M_end();
1345
1346       unsigned int __len = _Rb_tree_black_count(_M_leftmost(), _M_root());
1347       for (const_iterator __it = begin(); __it != end(); ++__it)
1348         {
1349           _Const_Link_type __x = static_cast<_Const_Link_type>(__it._M_node);
1350           _Const_Link_type __L = _S_left(__x);
1351           _Const_Link_type __R = _S_right(__x);
1352
1353           if (__x->_M_color == _S_red)
1354             if ((__L && __L->_M_color == _S_red)
1355                 || (__R && __R->_M_color == _S_red))
1356               return false;
1357
1358           if (__L && _M_impl._M_key_compare(_S_key(__x), _S_key(__L)))
1359             return false;
1360           if (__R && _M_impl._M_key_compare(_S_key(__R), _S_key(__x)))
1361             return false;
1362
1363           if (!__L && !__R && _Rb_tree_black_count(__x, _M_root()) != __len)
1364             return false;
1365         }
1366
1367       if (_M_leftmost() != _Rb_tree_node_base::_S_minimum(_M_root()))
1368         return false;
1369       if (_M_rightmost() != _Rb_tree_node_base::_S_maximum(_M_root()))
1370         return false;
1371       return true;
1372     }
1373
1374 _GLIBCXX_END_NAMESPACE
1375
1376 #endif