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1[/
2    Copyright (c) 2008-2010 Joachim Faulhaber
3
4    Distributed under the Boost Software License, Version 1.0.
5    (See accompanying file LICENSE_1_0.txt or copy at
6    http://www.boost.org/LICENSE_1_0.txt)
7]
8
9
10[/ //= Erasure ===================================================================]
11[section Erasure]
12
13[section Synopsis][/ Erasure]
14
15[table
16[[['*Erasure*]]                 [__ch_itv_sets__][__ch_itv_maps__][__ch_ele_sets__][__ch_ele_maps__]  ]
17[[`T& T::erase(const P&)`]              [__ei ]   [__ei __bp]     [__e]      [__bp]     ]
18[[`T& erase(T&, const P&)`]             [__eiS]  [__eiS __bpM]    [__es]     [__bm]     ]
19[[`void T::erase(iterator)`]               [1]        [1]         [1]        [1]        ]
20[[`void T::erase(iterator,iterator)`]      [1]        [1]         [1]        [1]        ]
21]
22
23[h5 Erasure]
24
25The effects of ['*erasure*] implemented by `erase` and ['*subtraction*]
26implemented by `subtract` and `operator -=` are identical for all Set-types of
27the *icl*.
28
29For Map-types, `erase` provides the *stl* semantics of erasure in
30contrast to `subtract` and `operator -=`, that implement a generalized subtraction,
31that performs inverse aggregations if key values collide or key intervals overlap.
32
33Using iterators it is possible to erase objects or ranges of
34objects the iterator is pointing at from icl Sets and Maps.
35
36[endsect][/ Synopsis Erasure]
37
38
39[section Erasure of Objects]
40
41
42``
43/* overload table for */       T\P| e i b p
44T& T::erase(const P&)          ---+--------
45T& erase(T&, const P&)          s | s
46                                m |     m
47                                S | S S
48                                M |     M M
49``
50
51The next table contains complexity characteristics for the `erase` function on elements and segments.
52
53[table Time Complexity for erasure of elements and segments on icl containers
54[[`T& T::erase(const P&)`\n
55  `T& erase(T&, const P&)`] [__ch_dom_t__][__ch_itv_t__][__ch_dom_mp_t__][__ch_itv_mp_t__]]
56[[__icl_set__]                 [__Olgn__]   []            []           []          ]
57[[__icl_map__]                 [__Olgn__]   []            [__Olgn__]   []          ]
58[[__itv_sets__]                [__Olgn__]   [__a_Olgn__]  []           []          ]
59[[__itv_maps__]                [__Olgn__]   [__On__]      [__Olgn__]   [__On__]    ]
60]
61
62
63As presented in the overload tables for inplace function `erase` below,
64more type combinations are available for /erasure/ than for
65/insertion/.
66
67``
68// overload tables for function    element containers:     interval containers:
69T& erase(T&, const P&)             T\P| e b s m            T\P| e i b p S M
70                                   ---+--------            ---+------------
71                                    s | s   s               S | S S     S
72                                    m | m m m m             M | M M M M M M
73``
74We can split up these overloads in two groups.
75The first group can be called /reverse insertion/.
76``
77/* (1) Reverse insertion */        T\P| e b s m            T\P| e i b p S M
78                                   ---+--------            ---+------------
79                                    s | s   s               S | S S     S
80                                    m |   m   m             M |     M M   M
81``
82The second group can be viewed as an /erasure by key objects/
83``
84/* (2) Erasure by key objects */   T\P| e b s m            T\P| e i b p S M
85                                   ---+--------            ---+------------
86                                    s | s   s               S | S S     S
87                                    m | m   m               M | M M     M
88``
89
90On Maps ['*reverse insertion (1)*] is different from
91*stl's* erase semantics, because value pairs are deleted only,
92if key ['*and*] data values are found. Only
93['*erasure by key objects (2)*] works like the erase function
94on *stl's* std::maps, that passes a ['*key value*] as argument.
95
96On Sets both function groups fall together
97as ['*set difference*].
98
99
100Complexity characteristics for inplace erasure operations are
101given by the next tables where
102``
103n = iterative_size(y);
104m = iterative_size(x); //if P is a container type
105``
106
107[table Time Complexity for inplace erasure on element containers
108[[`T& erase(T& y, const P& x)`][__ch_dom_t__][__ch_dom_mp_t__][__ch_icl_set__][__ch_icl_map__]]
109[[__icl_set__]                    [__Olgn__]    []               [__Omlgn__]     []              ]
110[[__icl_map__]                    [__Olgn__]    [__Olgn__]       [__Omlgn__]     [__Omlgn__]     ]
111]
112
113
114[table Time Complexity for inplace erasure on interval containers
115[[`T& erase(T& y, const P& x)`][__ch_dom_t__][__ch_itv_t__][__ch_dom_mp_t__][__ch_itv_mp_t__][__ch_itv_sets__][__ch_itv_maps__]]
116[[interval_sets]                  [__Olgn__]    [__a_Olgn__]  []               []               [__Omlgnpm__]    []               ]
117[[interval_maps]                  [__Olgn__]    [__a_Olgn__]  [__Olgn__]       [__On__]         [__Omlgnpm__]    [__Omlgnpm__]    ]
118]
119
120[endsect][/ Erasure of Objects]
121
122[section Erasure by Iterators]
123
124The next table shows the *icl* containers that erasure with iterators is
125available for. Erase on iterators erases always one `value` of `value_type`
126for an iterator pointing to it.
127So we erase
128
129* elements from __icl_sets__
130* element-value pairs from __icl_maps__
131* intervals from __itv_sets__ and
132* interval-value-pairs from __itv_maps__
133
134[table
135[[['*Erasure by iterators*]]                [__ch_itv_sets__][__ch_itv_maps__][__ch_ele_sets__][__ch_ele_maps__]  ]
136[[`void T::erase(iterator pos)`]                   [__aO1__]   [__aO1__]    [__aO1__]   [__aO1__]   ]
137[[`void T::erase(iterator first, iterator past)`]  [__Ok__]    [__Ok__]     [__Ok__]    [__Ok__]    ]
138]
139
140Erasing by a single iterator need only ['*amortized constant time*].
141Erasing via a range of iterators `[first, past)` is of ['*linear time*]
142in the number `k` of iterators in range `[first, past)`.
143
144[endsect][/ Erasure by Iterators]
145
146
147['*See also . . .*]
148[table
149[]
150[[[link boost_icl.function_reference.insertion   ['*Insertion*]]      ]]
151[[[link boost_icl.function_reference.subtraction ['*Subtraction*]]    ]]
152]
153
154['*Back to section . . .*]
155[table
156[]
157[[[link function_synopsis_table ['*Function Synopsis*]] ]]
158[[[link boost_icl.interface ['*Interface*]]             ]]
159]
160
161[endsect][/ Erasure]
162
163
164