Erasure

Synopsis

Erasure	interval sets	interval maps	itl::set	itl::map
`T& T::erase(const P&)`	e i	e i b p	e	b p
`T& erase(T&, const P&)`	e i S	e i S b p M	e s	b m
`void T::erase(iterator)`	1	1	1	1
`void T::erase(iterator,iterator)`	1	1	1	1

Erasure

The effects of erasure implemented by erase and subtraction implemented by subtract and operator -= are identical for all Set-types of the itl.

For Map-types, erase provides the stl semantics of erasure in contrast to subtract and operator -=, that implement a generalized subtraction, that performs inverse aggregations if key values collide or key intervals overlap.

Using iterators it is possible to erase objects or ranges of objects the iterator is pointing at from itl Sets and Maps.

Erasure of Objects

// overload table for
T& T::erase(const P&)

erase | e i b p    
------+--------
  s   | s
  m   |     m
  S   | S S         
  M   |     M M

The next table contains complexity characteristics for member function erase.

Table 1.28. Time Complexity for member function erase on itl containers

`T& T::erase(const P&)`	domain type	interval type	domain mapping type	interval mapping type
`itl::set`	O(log n)
`itl::map`	O(log n)		O(log n)
`interval_sets`	O(log n)	amortized O(log n)
`interval_maps`	O(log n)	O(n)	O(log n)	O(n)

As presented in the overload tables for inplace function erase below, more type combinations are available for erasure than for insertion.

// overload tables for inplace function
T& operator erase(T&, const P&)

element containers:     interval containers:  
erase | e b s m         erase | e i b p S M    
------+--------         ------+------------    
   s  | s   s              S  | S S     S       
   m  | m m m m            M  | M M M M M M

We can split up these overloads in two groups. The first group can be called reverse insertion.

// (1) Reverse insertion
erase | e b s m         erase | e i b p S M    
   ---+--------            ---+------------    
   s  | s   s              S  | S S     S       
   m  |   m   m            M  |     M M   M

The second group can be viewed as an erasure by key objects

// (2) Erasure by key objects
erase | e b s m         erase | e i b p S M    
   ---+--------            ---+------------    
   s  | s   s              S  | S S     S       
   m  | m   m              M  | M M     M

On Maps reverse insertion (1) is different from stl's erase semantics, because value pairs are deleted only, if key and data values are found. Only erasure by key objects (2) works like the erase function on stl's std::maps, that passes a key value as argument.

On Sets both function groups fall together as set difference.

Complexity characteristics for inplace erasure operations are given by the next tables where

n = y.iterative_size();
m = x.iterative_size(); //if P is a container type

Table 1.29. Time Complexity for inplace erasure on element containers

`T& erase(T& y, const P& x)`	domain type	domain mapping type	interval sets	interval maps
`itl::set`	O(log n)		O(m log n)
`itl::map`	O(log n)	O(log n)	O(m log n)	O(m log n)

Table 1.30. Time Complexity for inplace erasure on interval containers

`T& erase(T& y, const P& x)`	domain type	interval type	domain mapping type	interval mapping type	interval sets	interval maps
interval_sets	O(log n)	amortized O(log n)			O(m log(n+m))
interval_maps	O(log n)	amortized O(log n)	O(log n)	O(n)	O(m log(n+m))	O(m log(n+m))

Erasure by Iterators

The next table shows the itl containers that erasure with iterators is available for. Erase on iterators erases always one value of value_type for an iterator pointing to it. So we erase

elements from itl::sets
element-value pairs from itl::maps
intervals from interval_sets and
interval-value-pairs from interval_maps

Erasure by iterators	interval sets	interval maps	itl::set	itl::map
`void T::erase(iterator pos)`	amortized O(1)	amortized O(1)	amortized O(1)	amortized O(1)
`void T::erase(iterator first, iterator past)`	O(k)	O(k)	O(k)	O(k)

Erasing by a single iterator need only amortized constant time. Erasing via a range of iterators [first, past) is of linear time in the number k of iterators in range [first, past).