<s>
Interpolation	B-Algorithm
sort	I-Algorithm
is	O
a	O
kind	O
of	O
bucket	B-Algorithm
sort	I-Algorithm
.	O
</s>
<s>
It	O
uses	O
an	O
interpolation	B-Algorithm
formula	O
to	O
assign	O
data	O
to	O
the	O
bucket	O
.	O
</s>
<s>
A	O
general	O
interpolation	B-Algorithm
formula	O
is	O
:	O
</s>
<s>
Interpolation	B-Algorithm
sort	I-Algorithm
(	O
or	O
histogram	B-Algorithm
sort	I-Algorithm
)	O
.	O
</s>
<s>
It	O
is	O
a	O
sorting	B-Algorithm
algorithm	I-Algorithm
that	O
uses	O
the	O
interpolation	B-Algorithm
formula	O
to	O
disperse	O
data	O
divide	B-Algorithm
and	I-Algorithm
conquer	I-Algorithm
.	O
</s>
<s>
Interpolation	B-Algorithm
sort	I-Algorithm
is	O
also	O
a	O
variant	O
of	O
bucket	B-Algorithm
sort	I-Algorithm
algorithm	O
.	O
</s>
<s>
The	O
interpolation	B-Algorithm
sort	I-Algorithm
method	O
uses	O
an	O
array	O
of	O
record	O
bucket	O
lengths	O
corresponding	O
to	O
the	O
original	O
number	O
column	O
.	O
</s>
<s>
However	O
the	O
execution	O
complexity	O
can	O
still	O
be	O
maintained	O
as	O
an	O
efficient	O
sorting	B-Algorithm
method	O
of	O
.	O
</s>
<s>
Array	O
of	O
dynamically	O
allocated	O
memory	O
can	O
be	O
implemented	O
by	O
linked	B-Data_Structure
list	I-Data_Structure
,	O
stack	B-Application
,	O
queue	B-Application
,	O
associative	B-Application
array	I-Application
,	O
tree	B-Data_Structure
structure	I-Data_Structure
,	O
etc	O
.	O
</s>
<s>
An	O
array	O
object	O
such	O
as	O
JavaScript	B-Language
is	O
applicable	O
.	O
</s>
<s>
The	O
difference	O
in	O
data	B-General_Concept
structure	I-General_Concept
is	O
related	O
to	O
the	O
speed	O
of	O
data	O
access	O
and	O
thus	O
the	O
time	O
required	O
for	O
sorting.When	O
the	O
values	O
in	O
the	O
ordered	O
array	O
are	O
uniformly	O
distributed	O
approximately	O
the	O
arithmetic	O
progression	O
,	O
the	O
linear	O
time	O
of	O
interpolation	B-Algorithm
sort	I-Algorithm
ordering	O
is	O
.	O
</s>
<s>
If	O
the	O
maximum	O
value	O
is	O
equal	O
to	O
the	O
minimum	O
value	O
,	O
the	O
sorting	B-Algorithm
is	O
completed	O
to	O
stop	O
Divide	O
.	O
</s>
<s>
Divide	O
into	O
the	O
bucket	O
according	O
to	O
the	O
interpolation	B-Algorithm
number	O
.	O
</s>
<s>
The	O
NIST	O
definition	O
:	O
An	O
efficient	O
3-pass	O
refinement	O
of	O
a	O
bucket	B-Algorithm
sort	I-Algorithm
algorithm	O
.	O
</s>
<s>
JavaScript	B-Language
code	O
:	O
</s>
<s>
Interpolation	B-Algorithm
Tag	B-Algorithm
Sort	I-Algorithm
is	O
a	O
variant	O
of	O
Interpolation	B-Algorithm
Sort	I-Algorithm
.	O
</s>
<s>
Applying	O
the	O
bucket	B-Algorithm
sorting	I-Algorithm
and	O
dividing	O
method	O
,	O
the	O
array	O
data	O
is	O
distributed	O
into	O
a	O
limited	O
number	O
of	O
buckets	O
by	O
mathematical	O
interpolation	B-Algorithm
formula	O
,	O
and	O
the	O
bucket	O
then	O
recursively	O
the	O
original	O
processing	O
program	O
until	O
the	O
sorting	B-Algorithm
is	O
completed	O
.	O
</s>
<s>
Interpolation	B-Algorithm
tag	B-Algorithm
sort	I-Algorithm
is	O
a	O
recursive	O
sorting	B-Algorithm
method	O
for	O
interpolation	B-Algorithm
sorting	B-Algorithm
.	O
</s>
<s>
Stack	B-Application
,	O
queue	B-Application
,	O
associative	B-Application
array	I-Application
,	O
and	O
tree	B-Data_Structure
structure	I-Data_Structure
can	O
be	O
implemented	O
as	O
buckets	O
.	O
</s>
<s>
As	O
the	O
JavaScript	B-Language
array	O
object	O
is	O
suitable	O
for	O
this	O
sorting	B-Algorithm
method	O
,	O
the	O
difference	O
in	O
data	B-General_Concept
structure	I-General_Concept
is	O
related	O
to	O
the	O
speed	O
of	O
data	O
access	O
and	O
thus	O
the	O
time	O
required	O
for	O
sorting	B-Algorithm
.	O
</s>
<s>
The	O
bucket	B-Algorithm
sort	I-Algorithm
algorithm	O
does	O
not	O
limit	O
the	O
sorting	B-Algorithm
to	O
the	O
lower	O
limit	O
of	O
.	O
</s>
<s>
Interpolation	B-Algorithm
tag	B-Algorithm
sort	I-Algorithm
average	O
performance	O
complexity	O
is	O
.	O
</s>
<s>
If	O
the	O
sorting	B-Algorithm
is	O
not	O
completed	O
,	O
the	O
[	O
Divide	O
function ]	O
is	O
executed	O
.	O
</s>
<s>
If	O
the	O
maximum	O
value	O
is	O
equal	O
to	O
the	O
minimum	O
value	O
,	O
the	O
sorting	B-Algorithm
is	O
completed	O
and	O
the	O
division	O
is	O
stopped	O
.	O
</s>
<s>
Divide	O
into	O
the	O
bucket	O
according	O
to	O
the	O
interpolation	B-Algorithm
number	O
.	O
</s>
<s>
JavaScript	B-Language
code	O
:	O
</s>
<s>
The	O
in-place	B-Algorithm
interpolation	B-Algorithm
tag	B-Algorithm
sort	I-Algorithm
is	O
an	O
in-place	B-Algorithm
algorithm	I-Algorithm
of	O
interpolation	B-Algorithm
sort	I-Algorithm
.	O
</s>
<s>
In-place	B-Algorithm
Interpolation	B-Algorithm
Tag	B-Algorithm
Sort	I-Algorithm
can	O
achieve	O
sorting	B-Algorithm
by	O
only	O
N	O
times	O
of	O
swapping	O
by	O
maintaining	O
N	O
bit	O
tags	O
;	O
however	O
,	O
the	O
array	O
to	O
be	O
sorted	O
must	O
be	O
a	O
continuous	O
integer	O
sequence	O
and	O
not	O
repeated	O
,	O
or	O
the	O
series	O
is	O
completely	O
evenly	O
distributed	O
to	O
approximate	O
The	O
number	O
of	O
arithmetical	O
progression	O
.	O
</s>
<s>
For	O
example	O
,	O
sorting	B-Algorithm
0	O
~	O
100	O
can	O
be	O
sorted	O
in	O
one	O
step	O
.	O
</s>
<s>
If	O
the	O
characteristics	O
of	O
the	O
series	O
meet	O
the	O
conditional	O
requirements	O
of	O
this	O
sorting	B-Algorithm
method	O
:	O
"	O
The	O
array	O
is	O
a	O
continuous	O
integer	O
or	O
an	O
arithmetical	O
progression	O
that	O
does	O
not	O
repeat	O
"	O
,	O
the	O
in-place	B-Algorithm
interpolation	B-Algorithm
tag	B-Algorithm
sort	I-Algorithm
will	O
be	O
an	O
excellent	O
sorting	B-Algorithm
method	O
that	O
is	O
extremely	O
fast	O
and	O
saves	O
memory	O
space	O
.	O
</s>
<s>
In-place	B-Algorithm
Interpolation	B-Algorithm
Tag	B-Algorithm
Sort	I-Algorithm
sorts	O
non-repeating	O
consecutive	O
integer	O
series	O
,	O
only	O
one	O
Boolean	O
data	O
type	O
tag	O
array	O
with	O
the	O
same	O
length	O
as	O
the	O
original	O
array	O
,	O
the	O
array	O
calculates	O
the	O
interpolation	B-Algorithm
of	O
the	O
data	O
from	O
the	O
beginning	O
,	O
and	O
the	O
interpolation	B-Algorithm
points	O
to	O
a	O
new	O
position	O
of	O
the	O
array	O
.	O
</s>
<s>
Visit	O
the	O
array	O
when	O
tag[i]	O
is	O
false	O
,	O
calculate	O
the	O
position	O
corresponding	O
to	O
the	O
interpolation	B-Algorithm
=p	O
.	O
</s>
<s>
The	O
tour	O
array	O
is	O
completed	O
and	O
the	O
sorting	B-Algorithm
is	O
completed	O
.	O
</s>
<s>
JavaScript	B-Language
code	O
:	O
</s>
<s>
The	O
famous	O
American	O
computer	O
scientist	O
Donald	O
Knuth	O
in	O
the	O
mathematical	O
analysis	O
of	O
algorithms	O
pointed	O
out	O
that	O
:	O
"	O
With	O
respect	O
to	O
the	O
sorting	B-Algorithm
problem	I-Algorithm
,	O
Knuth	O
points	O
out	O
,	O
that	O
time	O
effective	O
in-situ	O
permutation	O
is	O
inherently	O
connected	O
with	O
the	O
problem	O
of	O
finding	O
the	O
cycle	O
leaders	O
,	O
and	O
in-situ	O
permutations	O
could	O
easily	O
be	O
performed	O
in	O
time	O
if	O
we	O
would	O
be	O
allowed	O
to	O
manipulate	O
n	O
extra	O
"	O
tag	O
"	O
bits	O
specifying	O
how	O
much	O
of	O
the	O
permutation	O
has	O
been	O
carried	O
out	O
at	O
any	O
time	O
.	O
</s>
<s>
The	O
In-place	B-Algorithm
Interpolation	B-Algorithm
Tag	B-Algorithm
Sort	I-Algorithm
is	O
one	O
of	O
the	O
sorting	B-Algorithm
algorithms	I-Algorithm
that	O
the	O
Donald	O
Knuth	O
professor	O
said	O
:	O
"	O
manipulate	O
n	O
extra	O
"	O
tag	O
"	O
bits	O
...	O
finding	O
the	O
cycle	O
leaders	O
,	O
and	O
in-situ	O
permutations	O
could	O
easily	O
be	O
performed	O
in	O
time	O
"	O
.	O
</s>
<s>
Bucket	B-Algorithm
sort	I-Algorithm
can	O
be	O
mixed	O
with	O
other	O
sorting	B-Algorithm
methods	O
to	O
complete	O
sorting	B-Algorithm
.	O
</s>
<s>
If	O
it	O
is	O
sorted	O
by	O
bucket	B-Algorithm
sort	I-Algorithm
and	O
insert	O
sort	O
,	O
also	O
is	O
a	O
fairly	O
efficient	O
sorting	B-Algorithm
method	O
.	O
</s>
<s>
The	O
second	O
sorting	B-Algorithm
method	O
uses	O
insert	O
sort	O
.	O
</s>
<s>
This	O
has	O
lost	O
the	O
meaning	O
and	O
high-speed	O
performance	O
of	O
using	O
bucket	B-Algorithm
sort	I-Algorithm
.	O
</s>
<s>
Interpolation	B-Algorithm
sort	I-Algorithm
is	O
a	O
way	O
of	O
recursively	O
using	O
bucket	B-Algorithm
sort	I-Algorithm
.	O
</s>
<s>
After	O
performing	O
recursion	O
,	O
still	O
use	O
bucket	B-Algorithm
sort	I-Algorithm
to	O
disperse	O
the	O
series	O
.	O
</s>
<s>
If	O
you	O
want	O
to	O
make	O
the	O
recursive	O
interpolation	B-Algorithm
sort	I-Algorithm
execution	O
complexity	O
fall	O
into	O
,	O
it	O
is	O
necessary	O
to	O
present	O
a	O
factorial	O
amplification	O
in	O
the	O
entire	O
series	O
.	O
</s>
