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/**
*
@function
Introsort (As implemented in STD C++ Lib)
* The function performs introsort which is used in
* C++ Standard LIbrary, the implementation is inspired from]
* library routine itself.
* ALGORITHM:
* 1) It performs quicksort on array until the recursion depth
* exceeds a pre determined limit.
* 2) If the limit is reached it switches to heapsort
* 3) For array size less than a threshold(16) directly
* does insertion sort on array
*
@param
{
Array
} array the array to be sorted
*
@param
{
Function
} compare the comparison function
*
*
@see
[Introsort](https://en.wikipedia.org/wiki/Introsort)
*
@author
[Lakhan Nad](https://github.com/Lakhan-Nad)
*/
function
introsort
(
array
,
compare
)
{
/**
*
@function
Default Comparison Function
* This function is same as implemented by
* Array.sort method
*
@see
[StackOverflow](https://stackoverflow.com/questions/47334234/how-to-implement-array-prototype-sort-default-compare-function)
*
@param
{
*
} a variable 1
*
@param
{
*
} b variable 2
*
@returns
{
Number
}
* -1 if a is less than b
* 0 if a is equal to b
* 1 if a greater than b
*/
const
defaultComparator
=
function
(
x
,
y
)
{
if
(
x
===
undefined
&&
y
===
undefined
)
return
0
if
(
x
===
undefined
)
return
1
if
(
y
===
undefined
)
return
-
1
const
xString
=
toString
(
x
)
const
yString
=
toString
(
y
)
if
(
xString
<
yString
)
return
-
1
if
(
xString
>
yString
)
return
1
return
0
}
/**
*
@function
helper function for defaultComparator
* Converts a given object to String
*
@throws
TypeError()
*
@param
{
Object
} obj
*
@returns
{
String
} String representation of given object
*/
const
toString
=
function
(
obj
)
{
if
(
obj
===
null
)
return
'null'
if
(
typeof
obj
===
'boolean'
||
typeof
obj
===
'number'
)
{
return
obj
.
toString
(
)
}
if
(
typeof
obj
===
'string'
)
return
obj
if
(
typeof
obj
===
'symbol'
)
throw
new
TypeError
(
)
return
obj
.
toString
(
)
}
/**
* Checks if the value passed is an array
* or not
*/
if
(
Array
.
isArray
(
array
)
===
false
)
{
return
}
/**
* If the compare parameter is not a function
* or not passed at all use default comparator
* function
*/
if
(
typeof
compare
!==
'function'
)
{
compare
=
defaultComparator
// If compare is not a comparator function
}
/**
* Use a closure to define the whole sort
* implementation this is done through
* [IIFE](https://en.wikipedia.org/wiki/Immediately_invoked_function_expression)
*/
return
(
function
(
array
,
comparator
)
{
const
swap
=
function
(
index1
,
index2
)
{
const
temp
=
array
[
index1
]
array
[
index1
]
=
array
[
index2
]
array
[
index2
]
=
temp
}
/**
*
@constant
THRESHOLD
* If the length of array is less than
* this then we simply perform insertion sort
*/
const
THRESHOLD
=
16
/**
*
@constant
TUNEMAXDEPTH
* Constant used to increase or decrease value
* of maxDepth
*/
const
TUNEMAXDEPTH
=
1
const
len
=
array
.
length
/**
* Return if array is only of length 1
* Array of size 1 is always sorted
*/
if
(
len
===
1
)
{
return
}
/**
* Calculate maxDepth = log2(len)
* Taken from implementation in stdc++
*/
const
maxDepth
=
Math
.
floor
(
Math
.
log2
(
len
)
)
*
TUNEMAXDEPTH
/**
* The very first call to quicksort
* this initiates sort routine
*/
quickSort
(
0
,
len
,
maxDepth
)
/**
* A final check call to insertion sort
* on sorted array
*/
insertionSort
(
0
,
len
)
/** ********************* Implementation of various routines **************************/
/**
*
@function
* This is recursive quicksort implementation in array
* of segment [start,last-1]
* [QuickSort](https://en.wikipedia.org/wiki/Quicksort)
*
@param
{
Number
} start the start index of array segment to be sorted
*
@param
{
Number
} last one more than the last index of array segment
*
@param
{
Number
} depth this measures how many recursive calls are done
*/
function
quickSort
(
start
,
last
,
depth
)
{
if
(
last
-
start
<=
THRESHOLD
)
{
insertionSort
(
start
,
last
)
return
}
else
if
(
depth
<=
0
)
{
heapSort
(
start
,
last
)
return
}
let
pivot
=
(
last
+
start
)
>>
1
pivot
=
partition
(
start
,
last
,
pivot
)
quickSort
(
start
,
pivot
,
depth
-
1
)
quickSort
(
pivot
+
1
,
last
,
depth
-
1
)
}
/**
*
@function
Helper function to quicksort
*
@param
{
Number
} start the start of array segment to partition
*
@param
{
Number
} last one more than last index of the array segment
*
@param
{
Number
} pivot the index of pivot to be used
*
@returns
{
Number
} the index of pivot after partition
*/
function
partition
(
start
,
last
,
pivot
)
{
swap
(
start
,
pivot
)
pivot
=
start
let
lo
=
start
let
hi
=
last
while
(
true
)
{
lo
++
while
(
comparator
(
array
[
lo
]
,
array
[
pivot
]
)
<=
0
&&
lo
!==
last
)
{
lo
++
}
hi
--
while
(
comparator
(
array
[
hi
]
,
array
[
pivot
]
)
>
0
&&
hi
!==
start
)
{
hi
--
}
if
(
lo
>=
hi
)
{
break
}
swap
(
lo
,
hi
)
}
swap
(
start
,
hi
)
return
hi
}
/**
*
@function
* Performs insertion sort on array of range
* [start, last-1]
*
@param
{
Number
} start the first index of array segment to be sorted
*
@param
{
Number
} last one more than last index of array to be sorted
*/
function
insertionSort
(
start
,
last
)
{
let
i
,
j
for
(
i
=
start
+
1
;
i
<
last
;
i
++
)
{
j
=
i
-
1
while
(
j
>=
0
&&
comparator
(
array
[
j
]
,
array
[
j
+
1
]
)
>
0
)
{
swap
(
j
,
j
+
1
)
j
--
}
}
}
/**
*
@function
* Performs heapsort in array segment of range [start, last-1]
* [HeapSort](https://en.wikipedia.org/wiki/Heapsort)
*
@param
{
Number
} start the first index of array segment to be sorted
*
@param
{
Number
} last one more than last index of array to be sorted
*/
function
heapSort
(
start
,
last
)
{
let
x
=
(
last
+
start
)
>>
1
while
(
x
-
start
>=
0
)
{
heapify
(
x
,
start
,
last
)
x
--
}
x
=
last
-
1
while
(
x
-
start
>
0
)
{
swap
(
start
,
x
)
heapify
(
start
,
start
,
x
)
x
--
}
}
/**
*
@function
Helper function to heapsort routine
*
@param
{
Number
} cur the index we need to heapify
*
@param
{
Number
} start the start index of array segment that cur belongs to
*
@param
{
Number
} last one more than last index of segment that cur belongs to
*/
function
heapify
(
cur
,
start
,
last
)
{
const
size
=
last
-
start
let
max
,
lt
,
rt
cur
=
cur
-
start
while
(
true
)
{
max
=
cur
lt
=
2
*
max
+
1
rt
=
2
*
max
+
2
if
(
lt
<
size
&&
comparator
(
array
[
start
+
max
]
,
array
[
start
+
lt
]
)
<
0
)
{
max
=
lt
}
if
(
rt
<
size
&&
comparator
(
array
[
start
+
max
]
,
array
[
start
+
rt
]
)
<
0
)
{
max
=
rt
}
if
(
max
!==
cur
)
{
swap
(
start
+
cur
,
start
+
max
)
cur
=
max
}
else
{
break
}
}
}
}
)
(
array
,
compare
)
}
/**
*
@example
Demo run of the sort routine
* The data is randomly generated
* Returns 'RIGHT:)' if the sort routine worked as expected,
* 'WRONG!!' otherwise
*/
function
demo1
(
)
{
const
data
=
[
]
const
size
=
1000000
let
i
=
0
let
temp
const
c
=
function
(
a
,
b
)
{
return
a
-
b
}
for
(
i
=
0
;
i
<
size
;
i
++
)
{
temp
=
Math
.
random
(
)
*
Number
.
MAX_SAFE_INTEGER
data
.
push
(
temp
)
}
introsort
(
data
,
c
)
let
faulty
=
false
for
(
i
=
1
;
i
<
size
;
i
++
)
{
if
(
data
[
i
]
<
data
[
i
-
1
]
)
{
faulty
=
true
break
}
}
if
(
faulty
)
{
return
'WRONG!!'
}
else
{
return
'RIGHT:)'
}
}
/**
*
@example
Demo run of the sort routine
* using the default compare function and
* comparing the results with Array.sort
*/
function
demo2
(
)
{
const
data
=
[
]
const
data2
=
[
]
const
size
=
1000000
let
i
=
0
let
temp
for
(
i
=
0
;
i
<
size
;
i
++
)
{
temp
=
Math
.
random
(
)
*
Number
.
MAX_SAFE_INTEGER
data
.
push
(
temp
)
data2
.
push
(
temp
)
}
introsort
(
data
)
data2
.
sort
(
)
let
faulty
=
false
for
(
i
=
1
;
i
<
size
;
i
++
)
{
if
(
data
[
i
]
!==
data2
[
i
]
)
{
faulty
=
true
break
}
}
if
(
faulty
)
{
return
'WRONG Implemented Comparator!!'
}
else
{
return
'Comparator Works Fine:)'
}
}
export
{
introsort
,
demo1
,
demo2
}
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