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Equivalences and Orderings 
intervals 
interval 
interval 
element 
element 

Segment Ordering 






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Element Ordering 







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Distinct Equality 









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Types 




All common equality and compare operators are defined for all objects of
the icl. For all icl
containers equality and compare operators implement lexicographical equality
and lexicographical comparison, that depends on the equality of template
parameter Compare
. This
includes the less ordering on intervals, that can be perceived as the sequence
of elements between their lower and upper bound. This generalized lexicogrphical
comparison in intervals can also be specified this way:





The other operators can be deduced in the usual way 















Equality and compare operators are defined for all icl objects but there are no overloads between different types.
Containers of different segmentation are different, even if their elements are the same:
split_interval_set<time> w1, w2; //Pseudocode w1 = {[Mon .. Sun)}; //split_interval_set containing a week w2 = {[Mon .. Fri)[Sat .. Sun)}; //Same week split in work and week end parts. w1 == w2; //false: Different segmentation is_element_equal(w1,w2); //true: Same elements contained
Complexity is linear
in the iterative_size
of
the shorter container to compare.
The Sequential Element Ordering abstracts from the way in which elements of interval containers are clustered into intervals: it's segmentation.
So these equality and compare operations can be applied within interval container types. The admissible type combinations are summarized in the next overload table.
// overload tables for bool is_element_equal (const T&, const P&) bool is_element_less (const T&, const P&) bool is_element_greater(const T&, const P&) element containers: interval containers: T\P s m T\P S1 S2 S3 M1 M3 + + s  1 S1  1 1 1 m  1 S2  1 1 1 S3  1 1 1 M1  1 1 M3  1 1
For element containers lexicographical equality and sequential element equality are identical.
The complexity of sequential element comparison
functions is linear
in the iterative_size
of
the larger container.
Distinct Equality
is an equality predicate that is available for icl::maps
and interval_maps
.
It yields true, if two maps are sequential element equal except for value
pairs whose associated values are identity elements.
Complexity is linear in the iterative_size
of the larger container
to compare.
See also . . .
Back to section . . .