<s>
A	O
sorted	B-Data_Structure
array	I-Data_Structure
is	O
an	O
array	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
in	O
which	O
each	O
element	O
is	O
sorted	O
in	O
numerical	O
,	O
alphabetical	O
,	O
or	O
some	O
other	O
order	O
,	O
and	O
placed	O
at	O
equally	O
spaced	O
addresses	O
in	O
computer	O
memory	O
.	O
</s>
<s>
It	O
is	O
typically	O
used	O
in	O
computer	B-General_Concept
science	I-General_Concept
to	O
implement	O
static	B-General_Concept
lookup	B-Data_Structure
tables	I-Data_Structure
to	O
hold	O
multiple	O
values	O
which	O
have	O
the	O
same	O
data	O
type	O
.	O
</s>
<s>
Sorting	B-Algorithm
an	O
array	O
is	O
useful	O
in	O
organising	O
data	O
in	O
ordered	O
form	O
and	O
recovering	O
them	O
rapidly	O
.	O
</s>
<s>
Sorted	B-Data_Structure
arrays	I-Data_Structure
are	O
the	O
most	O
space-efficient	O
data	B-General_Concept
structure	I-General_Concept
with	O
the	O
best	O
locality	B-General_Concept
of	I-General_Concept
reference	I-General_Concept
for	O
sequentially	O
stored	O
data	O
.	O
</s>
<s>
Elements	O
within	O
a	O
sorted	B-Data_Structure
array	I-Data_Structure
are	O
found	O
using	O
a	O
binary	O
search	O
,	O
in	O
O(log n )	O
;	O
thus	O
sorted	B-Data_Structure
arrays	I-Data_Structure
are	O
suited	O
for	O
cases	O
when	O
one	O
needs	O
to	O
be	O
able	O
to	O
look	O
up	O
elements	O
quickly	O
,	O
e.g.	O
</s>
<s>
as	O
a	O
set	O
or	O
multiset	O
data	B-General_Concept
structure	I-General_Concept
.	O
</s>
<s>
This	O
complexity	O
for	O
lookups	B-Data_Structure
is	O
the	O
same	O
as	O
for	O
self-balancing	B-Data_Structure
binary	I-Data_Structure
search	I-Data_Structure
trees	I-Data_Structure
.	O
</s>
<s>
In	O
some	O
data	B-General_Concept
structures	I-General_Concept
,	O
an	O
array	O
of	O
structures	O
is	O
used	O
.	O
</s>
<s>
In	O
such	O
cases	O
,	O
the	O
same	O
sorting	B-Algorithm
methods	O
can	O
be	O
used	O
to	O
sort	O
the	O
structures	O
according	O
to	O
some	O
key	O
as	O
a	O
structure	O
element	O
;	O
for	O
example	O
,	O
sorting	B-Algorithm
records	O
of	O
students	O
according	O
to	O
roll	O
numbers	O
or	O
names	O
or	O
grades	O
.	O
</s>
<s>
If	O
one	O
is	O
using	O
a	O
sorted	O
dynamic	B-Data_Structure
array	I-Data_Structure
,	O
then	O
it	O
is	O
possible	O
to	O
insert	O
and	O
delete	O
elements	O
.	O
</s>
<s>
The	O
insertion	O
and	O
deletion	O
of	O
elements	O
in	O
a	O
sorted	B-Data_Structure
array	I-Data_Structure
executes	O
at	O
O(n )	O
,	O
due	O
to	O
the	O
need	O
to	O
shift	O
all	O
the	O
elements	O
following	O
the	O
element	O
to	O
be	O
inserted	O
or	O
deleted	O
;	O
in	O
comparison	O
a	O
self-balancing	B-Data_Structure
binary	I-Data_Structure
search	I-Data_Structure
tree	I-Data_Structure
inserts	O
and	O
deletes	O
at	O
O(log n )	O
.	O
</s>
<s>
In	O
the	O
case	O
where	O
elements	O
are	O
deleted	O
or	O
inserted	O
at	O
the	O
end	O
,	O
a	O
sorted	O
dynamic	B-Data_Structure
array	I-Data_Structure
can	O
do	O
this	O
in	O
amortized	B-General_Concept
O(1 )	O
time	O
while	O
a	O
self-balancing	B-Data_Structure
binary	I-Data_Structure
search	I-Data_Structure
tree	I-Data_Structure
always	O
operates	O
at	O
O(log n )	O
.	O
</s>
<s>
Elements	O
in	O
a	O
sorted	B-Data_Structure
array	I-Data_Structure
can	O
be	O
looked	O
up	O
by	O
their	O
index	O
(	O
random	B-General_Concept
access	I-General_Concept
)	O
at	O
O(1 )	O
time	O
,	O
an	O
operation	O
taking	O
O(log n )	O
or	O
O(n )	O
time	O
for	O
more	O
complex	O
data	B-General_Concept
structures	I-General_Concept
.	O
</s>
<s>
John	O
von	O
Neumann	O
wrote	O
the	O
first	O
array	O
sorting	B-Algorithm
program	O
(	O
merge	B-Algorithm
sort	I-Algorithm
)	O
in	O
1945	O
,	O
when	O
the	O
first	B-Device
stored-program	I-Device
computer	I-Device
was	O
still	O
being	O
built	O
.	O
</s>
