# efficient idiomatic queue?

6 views

### David Eppstein

Jan 14, 2002, 7:17:55 PM1/14/02
to
What is the idiomatic way in Python of implementing the following
operations on a list of elements:
- return the element at the front of the list, without changing the list
- remove the element from the front of the list
- add a new element to the rear of the list

My first choice would be L[0], del L[0], and L.append(), however it
seems from some brief experiments that the del operation takes time linear
in the length of the list, so this would be very inefficient for long
lists. I also tried replacing the del with L=L[1:] but that wasn't any
better. A third possibility would be to have to variables L and i, and
implement the three operations with L[i], i=i+1, and L.append(), which is
fast but not good in space usage when the total number of operations is
much larger than the length of the list.

Is there a simple Pythonic way of implementing these three operations in
constant (amortized) time per operation and space linear in the length of
the list?

The application this came up for me is a merge sort example for an
algorithms class. So, I don't want to confuse the students with additional
code that has nothing to do with the actual algorithm, otherwise it would
be easy to do linked lists, or to do the third possibility above plus
slicing L down to size when i grows too large, or something like that.
--
David Eppstein UC Irvine Dept. of Information & Computer Science
epps...@ics.uci.edu http://www.ics.uci.edu/~eppstein/

### Jason Orendorff

Jan 14, 2002, 10:00:10 PM1/14/02
to
> What is the idiomatic way in Python of implementing the following
> operations on a list of elements:
> - return the element at the front of the list, without changing the list
> - remove the element from the front of the list
> - add a new element to the rear of the list
>
> [...]

> The application this came up for me is a merge sort example for an
> algorithms class. So, I don't want to confuse the students with
> additional code that has nothing to do with the actual algorithm,
> [...]

Your analysis of the situation is correct, and there's no idiomatic
Python way around it, unfortunately.

The given operations are usually "quick enough", for small lists
(less than, say, 5000 items) since the constant coefficient is
small, compared to the ordinary semi-inefficiency of running
Python code in the first place.

For merge sort, you could probably

L = []
... populate L using L.append() ...
L.reverse()
... drain L using L.pop() ...

This way you're O(N) instead of O(N^2). But it might baffle the
students.

## Jason Orendorff http://www.jorendorff.com/

### Tim Peters

Jan 14, 2002, 9:49:17 PM1/14/02
to
[David Eppstein]

> What is the idiomatic way in Python of implementing the following
> operations on a list of elements:
> - return the element at the front of the list, without changing the list
> - remove the element from the front of the list
> - add a new element to the rear of the list
>
> My first choice would be L[0], del L[0], and L.append(),

Yes, that's "the usual". L[-1], L.pop() and L.insert(0, item) (looking at
it "from the other end") is a less usual combo.

> however it seems from some brief experiments that the del operation
> takes time linear in the length of the list,

Yes, all the elements in L[1:] are physically moved left a slot.

> so this would be very inefficient for long lists.

Sure.

> I also tried replacing the del with L=L[1:] but that wasn't any
> better.

That makes a physical copy of the slice.

> A third possibility would be to have to variables L and i, and
> implement the three operations with L[i], i=i+1, and L.append(), which is
> fast but not good in space usage when the total number of operations is
> much larger than the length of the list.
>
> Is there a simple Pythonic way of implementing these three operations in
> constant (amortized) time per operation and space linear in the length of
> the list?

You can wrap your approch with index vrbls into a smarter class.

> The application this came up for me is a merge sort example for an
> algorithms class.

IME mergesort runs fastest if implemented in a more straightforward way,
using a continguous vector of the same length as the input vector for temp
storage, and swapping the roles of "real vector" and "temp vector" on
succeeding iterations. Then there's no dynamic allocation beyond getting a
temp vector once at the start, and a fixed handful of auxiliary index
variables suffices to keep track of where you are.

> The application this came up for me is a merge sort example for an
> algorithms class. So, I don't want to confuse the students with

> additional ode that has nothing to do with the actual algorithm,

> otherwise it would be easy to do linked lists, or to do the third
> possibility above plus slicing L down to size when i grows too large, or
> something like that.

It seems that your only objection to your original idea was that it's "very
inefficient for long lists". Why? That is, if you're only trying to get
across the idea of the algorithm, speed doesn't seem relevant ("assume these
primitives take constant time; then here's the interesting result: ...").
If you're actually worried about efficiency implications of details, I'd
expect you'd be keen to teach about those too.

BTW, is it necessary to destory the input lists? Rather than remove the
element at the front of a list, most people <wink> would just increment an
index vrbl. Then all mutation occurs only via .append() on the output list,
and your efficiency worry goes away.

saving-an-index-vrbl-isn't-worth-much-thought-ly y'rs - tim

### David Eppstein

Jan 14, 2002, 11:19:05 PM1/14/02
to
In article <mailman.1011063021...@python.org>,
"Tim Peters" <tim...@home.com> wrote:

> It seems that your only objection to your original idea was that it's "very
> inefficient for long lists". Why? That is, if you're only trying to get
> across the idea of the algorithm, speed doesn't seem relevant ("assume these
> primitives take constant time; then here's the interesting result: ...").
> If you're actually worried about efficiency implications of details, I'd
> expect you'd be keen to teach about those too.

It's an algorithms design and analysis class. If I'm going to tell the
students that some algorithm takes O(n log n) time, it would be helpful if
the code I show them actually takes O(n log n) instead of something slower
that one could make efficient only with more detailed knowledge of Python's
implementation details.

I realize implementation speed is not the primary concern of Python
language designers, but for Python programmers I think Python's relatively
slow speeds make it especially important to be careful about asymptotics:
there's less slack for using a bad algorithm and letting today's gigahertz

> BTW, is it necessary to destory the input lists? Rather than remove the
> element at the front of a list, most people <wink> would just increment an
> index vrbl. Then all mutation occurs only via .append() on the output list,
> and your efficiency worry goes away.
>
> saving-an-index-vrbl-isn't-worth-much-thought-ly y'rs - tim

List destruction is not necessary. The index variable approach is
probably best in this example, since merge sort doesn't need the full
power of a queue (each list has all its appends before it is scanned). I
was just hoping that Python's powerful list processing primitives would
let me simplify the code by avoiding those extra index variables. And a
queue is such a basic data structure that I thought surely Python already
allowed it to be implemented efficiently with its built-in list
operations.

Actually, the merge step in merge sort is a great example for simple
generators, or would be if not for the difficulty of keeping track of the
first item of each input iterator:

def merge(A,B):
try:
Afirst=A.next()
Aempty=0
except StopIteration:
Aempty=1
try:
Bfirst=B.next()
Bempty=0
except StopIteration:
Bempty=1
while not Aempty and not Bempty:
if Afirst < Bfirst:
yield Afirst
try:
Afirst=A.next()
except StopIteration:
Aempty=1
else:
yield Bfirst
try:
Bfirst=B.next()
except StopIteration:
Bempty=1
if not Aempty:
yield Afirst
while 1:
yield A.next()
if not Bempty:
yield Bfirst
while 1:
yield B.next()

def mergesort(L):
if len(L) < 2:
return iter(L)
else:
return merge(mergesort(L[:len(L)//2]),
mergesort(L[len(L)//2:]))

This (like the closely related heap sort) has the advantage that if you
start sorting n items, but only end up looking at the first k items of
sorted output, it takes time O(n + k log n), so the time is nonlinear only
when k is large. But this is way too much code for a blackboard, and the
students are confused enough by slices...

### David Eppstein

Jan 14, 2002, 11:31:27 PM1/14/02
to
In article <mailman.1011063861...@python.org>,
"Jason Orendorff" <ja...@jorendorff.com> wrote:

> The given operations are usually "quick enough", for small lists
> (less than, say, 5000 items) since the constant coefficient is
> small, compared to the ordinary semi-inefficiency of running
> Python code in the first place.

I'm not sure what you mean by quick enough, but when I tried draining a
list by repeated del L[0], on lists of 10000 elements it took roughly a
second -- more time than I'd like to spend in most interactive situations.

My philosophy to writing general purpose code like a sorting routine is to
use as efficient algorithms as reasonably possible, because even if you
think you are only going to see 5000-element lists and that 1-second delays
are acceptable, someone later may well try it on a million-element list and
get disgusted when the program takes hours to run. I don't mind using
Python compared to faster languages like C, for programs where fast runtime
is not as critical, if the slowdown is limited to constant factor like 10
or 100. But I wouldn't make me happy if the same "it's quick enough"
attitude led to programs with gratuitously inefficient algorithms that
don't scale.

### Delaney, Timothy

Jan 15, 2002, 12:07:20 AM1/15/02
to
> From: David Eppstein [mailto:epps...@ics.uci.edu]

>
> In article <mailman.1011063861...@python.org>,
> "Jason Orendorff" <ja...@jorendorff.com> wrote:
>
> > The given operations are usually "quick enough", for small lists
> > (less than, say, 5000 items) since the constant coefficient is
> > small, compared to the ordinary semi-inefficiency of running
> > Python code in the first place.
>
> My philosophy to writing general purpose code like a sorting
> routine is to
> use as efficient algorithms as reasonably possible, because
> even if you
> think you are only going to see 5000-element lists and that
> 1-second delays
> are acceptable, someone later may well try it on a
> million-element list and
> get disgusted when the program takes hours to run. I don't
> mind using

This very much falls under "knowing the data structures you will be using"
or "knowing which data structures your language uses.", as well as knowing

Students are notorious for taking an example and trying to apply it in all
cases.

The approach that should therefore be taken (for teaching an algorithms
class) would be along the lines of ...

"I will use the simplest algorithm possible in Python to demonstrate the
principles of the algorithm. The algorithm itself is O(n^2). For the data
sets you will be using in the examples and assignments, you can consider
this to be the case.

However, it is important to also consider the data structure that the
algorithm is being used on - in particular in this case, whether the data
structure is optimised for random access, access at the head of the
structure, the tail of the structure, or some other type of access. These
factors may well increase the running time of a particular algorithm
many-fold.

For example, you would expect that increasing the size of the dataset from
10 to 20 would increase the time required approximately 4-fold for this
algorithm. However, because of the data structure that is used, the increase
is actually approximately 16-fold. So don't use this exact implementation of
the algorithm on millions of elements (laugh)."

... thus making some of the students aware that you cannot simply say "this
is the best algorithm in all cases".

Tim Delaney

### Paul Rubin

Jan 15, 2002, 1:41:44 AM1/15/02
to
How's this (untested; uses nested scopes). It uses extra temp space
the size of the input, but runs in the correct order time.

def merge(a,b):
ia, ib = 0, 0 # indices
def next():
# peel next element off a or b.
m = 0 # selector between a and b
if ia < len(a) and ib < len(b):
m = a[ia] < b[ib]
else:
m = ia >= len(a)

if m == 0:
x, ia = a[ia], ia+1
else:
# if both a and b are exhausted, this throws IndexError.
x, ib = b[ib], ib+1
return x

result = []
try:
while 1:
result.append(next())
except IndexError:
return result

### David Eppstein

Jan 15, 2002, 2:04:59 AM1/15/02
to
In article <7xpu4cg...@ruckus.brouhaha.com>,
Paul Rubin <phr-n...@nightsong.com> wrote:

> How's this (untested; uses nested scopes). It uses extra temp space
> the size of the input, but runs in the correct order time.

Sure, that looks like the straightforward way of doing it using index
variables.

### Tim Peters

Jan 15, 2002, 2:36:06 AM1/15/02
to
[Tim]

>> It seems that your only objection to your original idea was
>> that it's "very inefficient for long lists". Why? That is, if
>> you're only trying to get across the idea of the algorithm, speed
>> doesn't seem relevant ("assume these primitives take constant time;
>> then here's the interesting result: ...").
>> If you're actually worried about efficiency implications of details, I'd
>> expect you'd be keen to teach about those too.

[David Eppstein]

> It's an algorithms design and analysis class. If I'm going to tell the
> students that some algorithm takes O(n log n) time, it would be
> helpful if the code I show them actually takes O(n log n) instead of
> something slower that one could make efficient only with more detailed
> knowledge of Python's implementation details.

Well, I suggested two ways to do that, in Python today. If Python *did*
have a list type "efficient at both ends", I don't think you'd be doing your
students a favor by having to add "and, by the way, this implementation is
only efficient in Python -- in any other language it would crawl, due to
implementation details we won't cover here".

BTW, Icon has an "efficient at both ends" list, but indexing isn't
constant-time there (it uses a doubly-linked list of buckets under the
covers -- or did last time I was familiar with its implementation).

> I realize implementation speed is not the primary concern of Python
> language designers,

Nothing is <wink>. But you misread this case: efficiency of *typical* list
operations is so important that we'd be loathe to slow those down in an
effort to cater to unusual operations. That's why Guido tossed ABC's list
implementation (using AVL trees under the covers) in favor of contiguous
vectors to begin with. "Almost all" programs ran much faster under Python
than they did under ABC as a result.

> but for Python programmers I think Python's relatively slow speeds make
> it especially important to be careful about asymptotics: there's less
> slack for using a bad algorithm and letting today's gigahertz

We've moved heaven and earth just to make appending an item at a time
efficient in extreme cases across 50 uncooperative platform malloc()
implementations; I expect you underestimate the difficulty of coding fast
portable data structures (not asymptotics, but the infinitely detailed pain
of avoiding pitfalls in real platform libraries and compilers). Note that I
wouldn't be *opposed* to making Python's list an efficent deque in all
cases, but I don't know how to do it without slowing typical uses.

> ...

> List destruction is not necessary. The index variable approach is
> probably best in this example, since merge sort doesn't need the full
> power of a queue (each list has all its appends before it is scanned).

Even better (according to me), your students would learn an algorithm that's
efficient even if written in something other than Python.

> I was just hoping that Python's powerful list processing primitives would
> let me simplify the code by avoiding those extra index variables. And a
> queue is such a basic data structure that I thought surely Python already
> allowed it to be implemented efficiently with its built-in list
> operations.

A plain list works fine for most uses of queues; they have to get pretty big
before memcpy() is a burden. For big queues, one person (Courageous?) did
code up a more-efficient extension type, but there is no "popular" extension
for this; that suggests demand is low.

> Actually, the merge step in merge sort is a great example for simple
> generators, or would be if not for the difficulty of keeping track of the
> first item of each input iterator:

This is a case where unbounded streams are much easier to live with (see the
"merge" function in test_generators.py -- not having to worry about
end-of-stream allows to eliminate most of the code, and all uses of
StopIteration).

I appreciate the abstract loveliness of this, but it's hard to see under all
the syntactic hair. A lazy functional language (like Haskell) is much more
pleasant for writing algorithms in this style.

### Alex Martelli

Jan 15, 2002, 3:22:46 AM1/15/02
to
"David Eppstein" <epps...@ics.uci.edu> wrote in message
news:eppstein-C4AE42...@news.service.uci.edu...
...

> Actually, the merge step in merge sort is a great example for simple
> generators, or would be if not for the difficulty of keeping track of the
> first item of each input iterator:

So, why not encapsulate that "difficulty"? E.g.:

class Peeker:
def __init__(self, iterator_or_sequence):
self.iterator = iter(iterator_or_sequence)
except StopIteration: self.more = 0
else: self.more = 1

With an ADT such as this one, operations such as merging get simpler:

def merge(A, B):
A=Peeker(A)
B=Peeker(B)
while A.more and B.more:

Note that the sum total of wrapper class Peeker and this merge version
is less than or equal to the merge version that tries to do everything,
in terms of both lines of code and "conceptual load". Basically, this
is because Peeker "captures" the right "primitive concepts" (attributes
eliminates duplication present in the "stand-alone version of merge".

work towards this one, as a way to motivate ADT's, I guess. But I'm
not sure such a bottom-up-and-refactor approach is didactically more
valid than top-down-and-refine, although it's closer to how one might
work to develop Peeker in real life.

Alex

### Alex Martelli

Jan 15, 2002, 3:46:51 AM1/15/02
to
"David Eppstein" <epps...@ics.uci.edu> wrote in message
news:eppstein-27FE15...@news.service.uci.edu...

> What is the idiomatic way in Python of implementing the following
> operations on a list of elements:
> - return the element at the front of the list, without changing the list
> - remove the element from the front of the list
> - add a new element to the rear of the list
>
> My first choice would be L[0], del L[0], and L.append(), however it
> seems from some brief experiments that the del operation takes time linear
> in the length of the list, so this would be very inefficient for long
> lists. I also tried replacing the del with L=L[1:] but that wasn't any
> better. A third possibility would be to have to variables L and i, and
> implement the three operations with L[i], i=i+1, and L.append(), which is
> fast but not good in space usage when the total number of operations is
> much larger than the length of the list.
>
> Is there a simple Pythonic way of implementing these three operations in
> constant (amortized) time per operation and space linear in the length of
> the list?

What about (warning, untested and particularly un-profiled code):

class fifo:
def __init__(self):
self.data = []
self.first = 0
return self.data[self.first]
def pop(self):
self.first += 1
if self.first > len(self.data)/2:
self.data = self.data[self.first:]
self.first = 0
def append(self, value):
self.data.append(value)

I think this should be constant-amortized-time, and never take more
space than K+2*N where N is the number of items in the list at a
given time. It may be possible to find sequences of pop and append
operations that degrade per-operation time beyond amortized constant.

Such anomalies, in similar cases, are generally ameliorated by some
further guard against too much churning in the data structure, e.g.
if self.first>self.Konstant and self.first>len(self.data)/2:
as the guard-clause for the self.data rebinding -- any constant
value self.Konstant will not matter asymptotically in terms of
space taken, of course (it goes into the K of "K+2*N").

Alex

### Paul Rubin

Jan 15, 2002, 5:04:22 AM1/15/02
to
"Alex Martelli" <al...@aleax.it> writes:
> I think this should be constant-amortized-time,

I think logarithmetic amortized time, i.e. calling pop N times takes
O(N log N) time (because it has to do a linear-time operation every so often).

### Raymond Hettinger

Jan 15, 2002, 7:38:49 AM1/15/02
to
"Paul Rubin" <phr-n...@nightsong.com> wrote in message
news:7xpu4cg...@ruckus.brouhaha.com...

FWIW, here's my crack at the same thing:

def merge(left, right):
ans = []
try:
while 1:
ans.append( (left[-1] > right[-1] and left or right ).pop() )
except IndexError:
ans.reverse()
return left + right + ans

def msort(ds):
if len(ds) <= 1: return ds
mid = len(ds) // 2
return merge( ms(ds[:mid]), ms(ds[mid:]) )

Raymond Hettinger

### Raymond Hettinger

Jan 15, 2002, 8:08:47 AM1/15/02
to

"Alex Martelli" <al...@aleax.it> wrote in message
news:a20q9p\$ej5\$1...@serv1.iunet.it...

> class fifo:
> def __init__(self):
> self.data = []
> self.first = 0
> return self.data[self.first]
> def pop(self):
> self.first += 1
> if self.first > len(self.data)/2:
> self.data = self.data[self.first:]
> self.first = 0
> def append(self, value):
> self.data.append(value)
>
>

> Alex
>

The Python Cookbook has an algorithm for O(n) FIFO queues submitted by
Sébastien Keim.
His approach is interesting and brilliant,

After tightening the code a bit, it looks a like this:

class Fifo:
stored = [None]
stored[0] = stored
def append(self,data): # to inside
if len(self.stored) == 1:
return self.stored.append(data)
self.stored[0] = self.stored = [self.stored[0], data]
def pop(self): # from outside
whole = self.stored[0]
self.stored[0] = whole[0]
return whole[1]

Raymond Hettinger

### Raymond Hettinger

Jan 15, 2002, 9:04:51 AM1/15/02
to
"Tim Peters" <tim...@home.com> wrote in message
news:mailman.1011063021...@python.org...
[snipped]

> BTW, is it necessary to destory the input lists? Rather than remove the
> element at the front of a list, most people <wink> would just increment an
> index vrbl. Then all mutation occurs only via .append() on the output
list,
> and your efficiency worry goes away.

I hate to beat this one to death, but it affords a great opportunity to
show-off Python2.2's iterators and sub-classing of built-in types.

class Queue(list):
def __init__(self, *args):
list.__init__(self, *args)
self.g = iter(self) # the index is implicit in the iterator
def pop(self):
return self.g.next()

q = Queue()
q.append(3); q.append(4)
print q.pop()
q.append(5)
print q.pop(),
print q.pop()

r = Queue([6,7,8])
print r.pop()
print r.pop()

Raymond Hettinger

### Magnus Lie Hetland

Jan 15, 2002, 9:23:53 AM1/15/02
to
In article [...], David Eppstein wrote:
>What is the idiomatic way in Python of implementing the following
>operations on a list of elements:
> - return the element at the front of the list, without changing the list
> - remove the element from the front of the list
> - add a new element to the rear of the list
>
>My first choice would be L[0], del L[0], and L.append(), however it
>seems from some brief experiments that the del operation takes time linear
>in the length of the list, so this would be very inefficient for long
>lists.
[snip]

>Is there a simple Pythonic way of implementing these three operations in
>constant (amortized) time per operation and space linear in the length of
>the list?

The simplest one I can think of is the trusty old linked list...

>The application this came up for me is a merge sort example for an
>algorithms class. So, I don't want to confuse the students with additional
>code that has nothing to do with the actual algorithm, otherwise it would
>be easy to do linked lists,

Hm. Well, it doesn't take *that* much code...

class Node:
def __init__(self, obj):
self.value = obj

dummy = Node(None)
dummy.next = dummy

class Queue:
def __init__(self):
def put(self, obj):
self.tail.next = Node(obj)
self.tail = self.tail.next
def get(self):
return result.value

I'm sure you can simplify it even further without much trouble, using
lists instead of node objects etc... Oh, well. If you don't want it
you don't want it.

BTW: The speedup is quite dramatic:

Problem size: 10
List version: 0.000274896621704
Queue version: 0.000545978546143
Problem size: 100
List version: 0.00122201442719
Queue version: 0.00465798377991
Problem size: 1000
List version: 0.0175099372864
Queue version: 0.0498030185699
Problem size: 10000
List version: 0.939693927765
Queue version: 0.538775920868
Problem size: 100000
List version: 91.8680340052
Queue version: 5.83884394169

(Repeated "problem size" times: Add integer, peek integer, remove
integer. The time is from time.time())

Sadly, the standard library object Queue also uses a list in its
implementation, so there is no help there ;)

--
Magnus Lie Hetland The Anygui Project
http://hetland.org http://anygui.org

### Alex Martelli

Jan 15, 2002, 9:21:52 AM1/15/02
to
"Paul Rubin" <phr-n...@nightsong.com> wrote in message
news:7xr8oso...@ruckus.brouhaha.com...

The "linear-time operation" in question is copying 1/2 of the current
list's contents, though. Assume a sequence of N appends followed by
N pops: then we copy N/2 + N/4 + N/8 + ... = about N items in all, no?
Thus, O(N) times for N pops -> constant *amortized* time per pop.

I'm not totally confident about what happens for other ways to interleave

Alex

### David Eppstein

Jan 15, 2002, 11:05:05 AM1/15/02
to
In article <7xr8oso...@ruckus.brouhaha.com>,
Paul Rubin <phr-n...@nightsong.com> wrote:

No, Alex was right, it is constant amortized time.
Each linear time operation (reducing the list length)
can be charged against the insertion operations that added the items being
removed from the list.

### Alex Martelli

Jan 15, 2002, 11:23:41 AM1/15/02
to
"David Eppstein" <epps...@ics.uci.edu> wrote in message
news:eppstein-B55AA6...@news.service.uci.edu...

> In article <7xr8oso...@ruckus.brouhaha.com>,
> Paul Rubin <phr-n...@nightsong.com> wrote:
>
> > "Alex Martelli" <al...@aleax.it> writes:
> > > I think this should be constant-amortized-time,
> >
> > I think logarithmetic amortized time, i.e. calling pop N times takes
> > O(N log N) time (because it has to do a linear-time operation every so
often).
>
> No, Alex was right, it is constant amortized time.
> Each linear time operation (reducing the list length)
> can be charged against the insertion operations that added the items being
> removed from the list.

Hmmm, nice way to frame things, and it does come close to convincing
me that it's indeed constant amortized time for any interleaving of
append and pop operations.

Alex

### Jason Orendorff

Jan 15, 2002, 11:16:16 AM1/15/02
to
David Eppstein wrote:
> In article <mailman.1011063861...@python.org>,
> "Jason Orendorff" <ja...@jorendorff.com> wrote:
>
> > The given operations are usually "quick enough", for small lists
> > (less than, say, 5000 items) since the constant coefficient is
> > small, compared to the ordinary semi-inefficiency of running
> > Python code in the first place.
>
> I'm not sure what you mean by quick enough, but when I tried draining a
> list by repeated del L[0], on lists of 10000 elements it took roughly a
> second -- more time than I'd like to spend in most interactive situations.
>
> My philosophy to writing general purpose code like a sorting
> routine is to use as efficient algorithms as reasonably possible,
> [...deletia...]

All you had to say was, "5000 items won't do it for me. I want
genuine O(N log N) behavior."

In which case you could have read on to the part of my email where
I suggested L.reverse().

Cheers.

### David Eppstein

Jan 15, 2002, 12:24:12 PM1/15/02
to
In article <mailman.1011111645...@python.org>,
"Jason Orendorff" <ja...@jorendorff.com> wrote:

> > I'm not sure what you mean by quick enough, but when I tried draining a
> > list by repeated del L[0], on lists of 10000 elements it took roughly a
> > second -- more time than I'd like to spend in most interactive situations.
>

> All you had to say was, "5000 items won't do it for me. I want
> genuine O(N log N) behavior."

I didn't say it that way because I think it's important to understand why
good asymptotics are important, and under what circumstances it would be ok
to use slower algorithms, rather than just blindly using the math.

Anyway, thanks for all the solutions posted so far.
The reverse trick is looking cleanest for merge sort, although Alex M.'s
queue implementation looks good (better I think than the more obvious

### James_...@i2.com

Jan 15, 2002, 3:37:16 PM1/15/02
to

David Eppstein wrote:
>Actually, the merge step in merge sort is a great example for simple
>generators, or would be if not for the difficulty of keeping track of the
>first item of each input iterator:

Tim Peters wrote:
>I appreciate the abstract loveliness of this, but it's hard to see under
all
>the syntactic hair. A lazy functional language (like Haskell) is much
more
>pleasant for writing algorithms in this style.

Here's an approach using generators that gets rid of some of the
"try:except StopIteration" clutter.

Jim

=======================================

from __future__ import generators

def gen(alist):
result = {'isempty':1,'value':None} # or you could use a list instead
for value in alist:
result['isempty'] = 0
result['value'] = value
yield result
result['isempty'] = 1
while 1:
yield result

def merge(list1,list2):
gen1, gen2 = gen(list1), gen(list2)
next1, next2 = gen1.next(), gen2.next()
resultList = []
while 1:
if next1['isempty'] and next2['isempty']:
break
if (next2['isempty'] or
(not next1['isempty'] and next1['value'] <= next2['value'])):
resultList.append(next1['value'])
next1 = gen1.next()
else:
resultList.append(next2['value'])
next2 = gen2.next()
return resultList

def mergesort(alist):
if len(alist) <= 1:
return alist[:]
return merge(mergesort(alist[:len(alist)//2]),
mergesort(alist[len(alist)//2:]))

### David Eppstein

Jan 15, 2002, 4:19:50 PM1/15/02
to
In article <mailman.101112710...@python.org>,
James_...@i2.com wrote:

> Here's an approach using generators that gets rid of some of the
> "try:except StopIteration" clutter.

Ok, but your merge routine gets rid of a key advantage of using generators:
it returns a list, rather than yielding the items one at a time, so the
total time is always Theta(n log n), while for the version I posted (and
the cleaner ADT-ized version someone else posted later) the merges all
happen in parallel as items are requested, and the time to pull off the
first k items from a sorted list of n items is O(n + k log n).

### Huaiyu Zhu

Jan 15, 2002, 4:46:09 PM1/15/02
to
On Tue, 15 Jan 2002 09:46:51 +0100, Alex Martelli <al...@aleax.it> wrote:
>
>What about (warning, untested and particularly un-profiled code):
>
>class fifo:
> def __init__(self):
> self.data = []
> self.first = 0
> return self.data[self.first]
> def pop(self):
> self.first += 1
> if self.first > len(self.data)/2:
> self.data = self.data[self.first:]
> self.first = 0
> def append(self, value):
> self.data.append(value)
>
>I think this should be constant-amortized-time, and never take more
>space than K+2*N where N is the number of items in the list at a
>given time. It may be possible to find sequences of pop and append
>operations that degrade per-operation time beyond amortized constant.

This can be extended to a fancier scheme, where you can save quite some
append and del if you also keep an attribute self.last and let the fifo wrap
around on the list. It is simple to implement in Python due to the way
negative indices are treated. In the following diagram * represents element
in the queue and . represents dummy element:

...... first ******** last ......
**** last .......first *********

When self.last catches up on self.first, the list size is enlarged, say, by
a factor of 0.2. It is reduced by a factor when the queue falls under a
certain proportion of the list. These factors represent the trade-off
between space and speed. This scheme is more useful when there are lots of
appned and pop but the queue length remains fairly stable, in which case the
cost of list changing operations approach zero-amortized time.

Huaiyu

### James_...@i2.com

Jan 15, 2002, 4:58:52 PM1/15/02
to

David Eppstein wrote:
>Ok, but your merge routine gets rid of a key advantage of using
generators:
>it returns a list, rather than yielding the items one at a time, so the
>total time is always Theta(n log n), while for the version I posted (and
>the cleaner ADT-ized version someone else posted later) the merges all
>happen in parallel as items are requested, and the time to pull off the
>first k items from a sorted list of n items is O(n + k log n).

Ok. Here is essentially the same thing but we return an interator instead
of a list (same idea as your version).

BTW, I also like Alex's ADT approach. Mine was just a suggestion if class
defs were to be avoided.

Jim

==========================

from __future__ import generators

def gen(alist):
result = {'isempty':1,'value':None}

for value in alist:
result['isempty'] = 0
result['value'] = value
yield result
result['isempty'] = 1
while 1:
yield result

def merge(list1,list2):
gen1, gen2 = gen(list1), gen(list2)
next1, next2 = gen1.next(), gen2.next()

while 1:
if next1['isempty'] and next2['isempty']:
break
if (next2['isempty'] or
(not next1['isempty'] and next1['value'] <= next2['value'])):

yield next1['value']
next1 = gen1.next()
else:
yield next2['value']
next2 = gen2.next()

def mergesort(alist):
if len(alist) <= 1:

return iter(alist)

### Tim Peters

Jan 15, 2002, 5:55:33 PM1/15/02
to
[James_...@i2.com]
> Speaking of generator abuse ...
>
> Anything like this:

>
> def mergesort(alist):
> if len(alist) <= 1:
> return iter(alist)
> return merge(mergesort(alist[:len(alist)//2]),
> mergesort(alist[len(alist)//2:]))
>
> is probably going to create way too many generator/iterator instances to
> scale well.

Well, it was clear from the start that there's no interest in a practical
algorithm here, else we'd just use a temp array and a handful of index
variables. "Theoretical efficiency" (O() where a multiplier of 10000000 is
as good as 1) is an interesting area of study, full of papers with schemes
so convoluted the authors cheerfully confess to not even trying to implement
them.

y'rs - tim

### James_...@i2.com

Jan 15, 2002, 5:34:48 PM1/15/02
to

Speaking of generator abuse ...

Anything like this:

def mergesort(alist):
if len(alist) <= 1:
return iter(alist)
return merge(mergesort(alist[:len(alist)//2]),
mergesort(alist[len(alist)//2:]))

is probably going to create way too many generator/iterator instances to
scale well.

Jim

### David Eppstein

Jan 15, 2002, 7:48:47 PM1/15/02
to
In article <mailman.101113540...@python.org>,
"Tim Peters" <tim...@home.com> wrote:

> > is probably going to create way too many generator/iterator instances to
> > scale well.
>
> Well, it was clear from the start that there's no interest in a practical
> algorithm here, else we'd just use a temp array and a handful of index
> variables.

I think heap sort would be a good choice for practicality, since it sorts
in-place with only a handful of index variables. But except for unusual
circumstances, I would likely just call Python's built-in sort().

### Aahz Maruch

Jan 15, 2002, 10:20:27 PM1/15/02
to
In article <eppstein-27FE15...@news.service.uci.edu>,

David Eppstein <epps...@ics.uci.edu> wrote:
>
>What is the idiomatic way in Python of implementing the following
>operations on a list of elements:
> - return the element at the front of the list, without changing the list
> - remove the element from the front of the list
> - add a new element to the rear of the list

Just to be a jerk, why not use a dict with a couple of index variables?
--
--- Aahz <*> (Copyright 2002 by aa...@pobox.com)

Hugs and backrubs -- I break Rule 6 http://www.rahul.net/aahz/
Androgynous poly kinky vanilla queer het Pythonista

"There are times when effort is important and necessary, but this should
not be taken as any kind of moral imperative." --jdecker

### Aahz Maruch

Jan 15, 2002, 10:21:09 PM1/15/02
to
In article <a20osj\$78u\$1...@serv1.iunet.it>, Alex Martelli <al...@aleax.it> wrote:
>
> [...]

### Andrew Dalke

Jan 15, 2002, 11:36:11 PM1/15/02
to
Aahz Maruch wrote:

"abstract data type"

It's a data structure with associated methods (wasn't called
class nor object 20+ years ago) which can be used unchanged
in many different codes.

ADTS include lists, dicts, binary trees, priority queues, stack,
quad and oct trees. Upon reflection, I seem to associate an

Here's the FOLDOC defintition from
> (ADT) A type whose internal form is hidden behind a set of access
> functions. Objects of the type are created and inspected only by
> calls to the access functions. This allows the implementation of
> the type to be changed without requiring any changes outside the
> module in which it is defined.

> Abstract data types are central to object-oriented programming
> where every class is an ADT.

But I wouldn't regard, say, the classes in rfy833.py as ADTs.

> A classic example of an ADT is a stack data type for which functions
> might be provided to create an empty stack, to push values onto a
> stack and to pop values from a stack.

### Aahz Maruch

Jan 15, 2002, 11:43:49 PM1/15/02
to
In article <a22vts\$5jg\$1...@slb4.atl.mindspring.net>,

Andrew Dalke <da...@dalkescientific.com> wrote:
>Aahz Maruch wrote:
>>
>
>"abstract data type"
>
>It's a data structure with associated methods (wasn't called
>class nor object 20+ years ago) which can be used unchanged
>in many different codes.
>
>ADTS include lists, dicts, binary trees, priority queues, stack,
>quad and oct trees. Upon reflection, I seem to associate an

Oh, right. I knew that, I just didn't know that I knew that. ;-)
(More precisely, I didn't remember that particular acronym.)

### David Eppstein

Jan 16, 2002, 12:32:06 AM1/16/02
to
In article <a22rhr\$bn1\$1...@panix3.panix.com>, aa...@panix.com (Aahz Maruch)
wrote:

> Just to be a jerk, why not use a dict with a couple of index variables?

Maybe you could unpack that a little? dicts are useful but AFAIK they
aren't the same thing as queues, index variables or no.

### Alex Martelli

Jan 16, 2002, 3:26:33 AM1/16/02
to
"Aahz Maruch" <aa...@panix.com> wrote in message
news:a22rj5\$bs6\$1...@panix3.panix.com...

> In article <a20osj\$78u\$1...@serv1.iunet.it>, Alex Martelli <al...@aleax.it>
wrote:
> >
> > [...]
>

Sorry -- I should not have used a three-letter-acronym (TLA) without
expanding it at least once, no matter how well-known I could assume
it to be to the specific poster I was responding to.

ADT = "Abstract Data Type". When teaching algorithms and data
structures, one approach is to "implement" an algorithm in terms
of abstract operations on some underlying data type, each operation
defined in terms of its just-as-abstract semantics and performance
characteristics. The issue of *implementing* an ADT in concrete
terms is then neatly separated from that of *using* it. As far as
I know the original idea came from abstract algebra, where one
does much the same with abstract structures -- one separates the
issue of "what can I prove about a monoid" (the latter being
abstractly defined in terms of its axioms) from the issue of
proving whether a given algebraic structure is indeed a monoid.

Of course, ADT's also mesh well with the concept of separation
between interface and implementation as used in actual software
design. Performance characteristics are rarely specified in
the latter case, but there are important exceptions (for example,
C++'s Standard Library does have O(N) performance specs for
various operations as part of its overall specifications).

Alex

### Alex Martelli

Jan 16, 2002, 3:11:34 AM1/16/02
to
"David Eppstein" <epps...@ics.uci.edu> wrote in message
news:eppstein-3B0408...@news.service.uci.edu...

> In article <a22rhr\$bn1\$1...@panix3.panix.com>, aa...@panix.com (Aahz Maruch)
> wrote:
>
> > Just to be a jerk, why not use a dict with a couple of index variables?
>
> Maybe you could unpack that a little? dicts are useful but AFAIK they
> aren't the same thing as queues, index variables or no.

Well, they obviously CAN be used to IMPLEMENT queues -- performance
characteristics apart:

class DictFifo:
def __init__(self):
self.data = {}
self.nextin = 0
self.nextout = 0
def append(self, value):
self.data[self.nextin] = value
self.nextin += 1
def pop(self):
value = self.data[self.nextout]
del self.data[self.nextout]
self.nextout += 1

No "being the same" asserted or implied, of course -- the dict and
the two indices are just tools to _implement_ a fifo queue, here.

Alex

### Aahz Maruch

Jan 16, 2002, 7:07:29 AM1/16/02
to

Yup. Note that for Python < 2.2, you should use:

def __init__(self):
self.data = {}
self.nextin = 0L
self.nextout = 0L

to make sure that you can use it for more than two billion entries. ;-)

I haven't tested this, but I think that if you expect queues to be
large, this might actually be a fast, clear implementation.

### Mitch Chapman

Jan 16, 2002, 11:41:56 AM1/16/02
to
Andrew Dalke wrote:
>
> Aahz Maruch wrote:
>
> "abstract data type"
>
> It's a data structure with associated methods (wasn't called
> class nor object 20+ years ago) which can be used unchanged
> in many different codes.

As Andrew hinted, a big distinction between OO classes
and ADTs is that the latter can't be subclassed.

ADT-based programming is useful in languages which don't
directly support OOP (e.g ANSI C). They don't provide subclassing
or protocol/interface-based programming, but ADTs do
simplify encapsulation and memory management.

My first exposure to ADTs came when I started using
Modula-2. Hence the claim that if you remove memory-management
(i.e. instantiation) from ADT-based programming you get
module-based programming :)

--
...and lots of singletons

Mitch Chapman
Mitch....@bioreason.com

### Terry Reedy

Jan 16, 2002, 2:11:41 PM1/16/02
to

"Alex Martelli" <al...@aleax.it> wrote in message
news:a23cjl\$dps\$1...@serv1.iunet.it...

> class DictFifo:
> def __init__(self):
> self.data = {}
> self.nextin = 0
> self.nextout = 0
> def append(self, value):
> self.data[self.nextin] = value
> self.nextin += 1
> def pop(self):
> value = self.data[self.nextout]
> del self.data[self.nextout]
> self.nextout += 1

This clearly indicates the point of abstract data types separating
inplementation from interface. In the real world, there are at least
two ways of implementing FIFO (first-in,first-out) service discipline.
One is to keep people in a physical line (sequence). Another is to
'label' people in their order of entry -- for instance by giving them
or having them take a sequenced ticket -- and call them in order
while letting them physically mill around before getting called.
DictInfo above, while counter-intuitive to me at first, nicely mirrors
the second method, with sequential counts being the numbered
'tickets'.

Terry J. Reedy

### Quinn Dunkan

Jan 16, 2002, 6:04:21 PM1/16/02
to

Aha! I always thought ADT stood for "Algebraic Data Type" and assumed people
idea of what they were supposed to exactly be (value semantics?). And fp
advocates would say things like "behold the power of adts, blah blah". And
then Limbo goes and has an adt keyword in an imperative context...

Thanks for the description!

### Delaney, Timothy

Jan 16, 2002, 6:19:47 PM1/16/02
to
> >class DictFifo:
> > def __init__(self):
> > self.data = {}
> > self.nextin = 0
> > self.nextout = 0
> > def append(self, value):
> > self.data[self.nextin] = value
> > self.nextin += 1
> > def pop(self):
> > value = self.data[self.nextout]
> > del self.data[self.nextout]
> > self.nextout += 1
return value

:)

> def __init__(self):
> self.data = {}

> self.nextin = 0L
> self.nextout = 0L
>
> to make sure that you can use it for more than two billion
> entries. ;-)
>
> I haven't tested this, but I think that if you expect queues to be
> large, this might actually be a fast, clear implementation.

I just tested it with the following code. Everything is wrapped in classes
to maintain similar overhead. Note that for DictIntFifo, OverflowError is
caught to allow conversion to long in any version of Python. I've also
included a normal list and array for comparison.

import time
import string
import array

class DictIntFifo:

def __init__(self):
self.data = {}
self.nextin = 0
self.nextout = 0

def append(self, value):

self.data[self.nextin] = value

try:
self.nextin += 1
except OverflowError:
self.nextin += long(1)

def pop(self):
value = self.data[self.nextout]
del self.data[self.nextout]

try:
self.nextout += 1
except OverflowError:
self.nextout += long(1)

return value

class DictLongFifo:

def __init__(self):
self.data = {}
self.nextin = long(0)
self.nextout = long(0)

def append(self, value):

self.data[self.nextin] = value
self.nextin += 1

def pop(self):
value = self.data[self.nextout]
del self.data[self.nextout]
self.nextout += 1

return value

class ListPrependFifo:
""""""

def __init__(self):
""""""
self.data = []

def append(self, value):
self.data.insert(0, value)

def pop(self):
return self.data.pop()

class ListAppendFifo:
""""""

def __init__(self):
""""""
self.data = []

def append(self, value):
self.data.append(value)

def pop(self):
return self.data.pop(0)

def test (fifo, iterations):
""""""

start = time.clock()

for i in xrange(iterations):
fifo.append(i)
j = fifo.pop()

end = time.clock()

try:
name = fifo.__class__.__name__
except:
name = type(fifo)

print "%-8s %-20s %-06f" % (iterations, name, end - start,)

for i in xrange(4):

print
test([], 10**(i + 3))
test(array.array('i'), 10**(i + 3))
test(DictIntFifo(), 10**(i + 3))
test(DictLongFifo(), 10**(i + 3))
test(ListPrependFifo(), 10**(i + 3))
test(ListAppendFifo(), 10**(i + 3))

1000 <type 'list'> 0.003968
1000 <type 'array'> 0.004607
1000 DictIntFifo 0.012154
1000 DictLongFifo 0.015508
1000 ListPrependFifo 0.010499
1000 ListAppendFifo 0.010357

10000 <type 'list'> 0.039399
10000 <type 'array'> 0.046923
10000 DictIntFifo 0.120931
10000 DictLongFifo 0.156747
10000 ListPrependFifo 0.105777
10000 ListAppendFifo 0.105253

100000 <type 'list'> 0.394604
100000 <type 'array'> 0.459258
100000 DictIntFifo 1.214058
100000 DictLongFifo 1.568331
100000 ListPrependFifo 1.060692
100000 ListAppendFifo 1.046310

1000000 <type 'list'> 4.071518
1000000 <type 'array'> 4.640713
1000000 DictIntFifo 12.192316
1000000 DictLongFifo 15.778213
1000000 ListPrependFifo 10.700729
1000000 ListAppendFifo 10.636400

So, it looks like there is a definite speed penalty with the dict versions,
although the majority of that is probably namespace lookup time (more
operations). A C version would probably do quite well.

Nonetheless, it is a good example of separating interface from
implementation.

Tim Delaney

### David Eppstein

Jan 16, 2002, 8:29:17 PM1/16/02
to
In article <mailman.101122322...@python.org>,
"Delaney, Timothy" <tdel...@avaya.com> wrote:

> So, it looks like there is a definite speed penalty with the dict versions,
> although the majority of that is probably namespace lookup time (more
> operations). A C version would probably do quite well.

It's good to see actual data, but I don't think this is a fair comparison:
your queues always have at most one item in them, so you never see how well
these versions scale to different lengths. Try replacing

for i in xrange(iterations):
fifo.append(i)
j = fifo.pop()

with

for i in xrange(iterations):
fifo.append(i)

for i in xrange(iterations):
j = fifo.pop()

When I did that, I got the following results, showing that among the
Fifo's, the dictionary versions are very competitive with the method of
indexing a list and replacing the list when the index gets too big
(ListIndexFifo, code below the data), while the other list-based Fifos are
not good for long queues. (List itself is just a stack, not a queue, of
course.)

1000 list 0.007062
1000 <type 'array.array'> 0.008669
1000 DictIntFifo 0.021960
1000 DictLongFifo 0.026667
1000 ListPrependFifo 0.024463
1000 ListAppendFifo 0.026615
1000 ListIndexFifo 0.021000

10000 list 0.072249
10000 <type 'array.array'> 0.086427
10000 DictIntFifo 0.222813
10000 DictLongFifo 0.262345
10000 ListPrependFifo 0.839607
10000 ListAppendFifo 1.063594
10000 ListIndexFifo 0.202094

100000 list 0.770646
100000 <type 'array.array'> 27.156242
100000 DictIntFifo 2.345710
100000 DictLongFifo 2.797171
100000 ListPrependFifo 76.949710
100000 ListAppendFifo 91.907281
100000 ListIndexFifo 2.047624

class ListIndexFifo:
""""""

def __init__(self):
""""""
self.data = []
self.index = -1

def append(self, value):
self.data.append(value)

def pop(self):
self.index = self.index + 1
if self.index > len(self.data) / 2:
self.data = self.data[self.index:]
self.index = 0
return self.data[self.index]

### Delaney, Timothy

Jan 16, 2002, 8:57:58 PM1/16/02
to
> From: David Eppstein [mailto:epps...@ics.uci.edu]

>
> In article <mailman.101122322...@python.org>,
> "Delaney, Timothy" <tdel...@avaya.com> wrote:
>
> > So, it looks like there is a definite speed penalty with
> the dict versions,
> > although the majority of that is probably namespace lookup
> time (more
> > operations). A C version would probably do quite well.
>
> It's good to see actual data, but I don't think this is a
> fair comparison:
> your queues always have at most one item in them, so you
> never see how well
> these versions scale to different lengths. Try replacing

Remind me to hit myself with a rubber chicken ...

Of course I completely invalidated the point of the entire exercise ... I
should have added all, then removed all (which in my mind I was doing). And
my comparison with list/array is incorrect as well ... I needed to change
every pop() to accept a position (and ignore it :) so I could pop(0) on the
list and array.

import time
import string
import array

class DictIntFifo:

def __init__(self):
self.data = {}
self.nextin = 0
self.nextout = 0

def append(self, value):

self.data[self.nextin] = value

try:
self.nextin += 1
except OverflowError:
self.nextin += long(1)

def pop(self, pos=-1):

value = self.data[self.nextout]
del self.data[self.nextout]

try:
self.nextout += 1
except OverflowError:
self.nextout += long(1)

return value

class DictLongFifo:

def __init__(self):
self.data = {}
self.nextin = long(0)
self.nextout = long(0)

def append(self, value):

self.data[self.nextin] = value
self.nextin += 1

def pop(self, pos=-1):

value = self.data[self.nextout]
del self.data[self.nextout]
self.nextout += 1
return value

class ListPrependFifo:
""""""

def __init__(self):
""""""
self.data = []

def append(self, value):
self.data.insert(0, value)

def pop(self, pos=-1):
return self.data.pop()

class ListAppendFifo:
""""""

def __init__(self):
""""""
self.data = []

def append(self, value):
self.data.append(value)

def pop(self, pos=-1):
return self.data.pop(0)

def test (fifo, iterations):
""""""

start = time.clock()

for i in xrange(iterations):
fifo.append(i)

for i in xrange(iterations):
j = fifo.pop(0)

end = time.clock()

try:
name = fifo.__class__.__name__
except:
name = type(fifo)

print "%-8s %-20s %-06f" % (iterations, name, end - start,)

for i in xrange(3):

print
test([], 10**(i + 3))
test(array.array('i'), 10**(i + 3))
test(DictIntFifo(), 10**(i + 3))
test(DictLongFifo(), 10**(i + 3))
test(ListPrependFifo(), 10**(i + 3))
test(ListAppendFifo(), 10**(i + 3))

---------- Run ----------

1000 <type 'list'> 0.007721
1000 <type 'array'> 0.007273
1000 DictIntFifo 0.012430
1000 DictLongFifo 0.017795
1000 ListPrependFifo 0.013849
1000 ListAppendFifo 0.014851

10000 <type 'list'> 0.329070
10000 <type 'array'> 0.234557
10000 DictIntFifo 0.123809
10000 DictLongFifo 0.185284
10000 ListPrependFifo 0.329698
10000 ListAppendFifo 0.398269

100000 <type 'list'> 76.195043
100000 <type 'array'> 56.828019
100000 DictIntFifo 1.269020
100000 DictLongFifo 1.961017
100000 ListPrependFifo 60.693928
100000 ListAppendFifo 77.094517

So once you get to decently large quantities in the queue, the dict versions
make real sense over a basic list (Win2000).

Tim Delaney

### Tim Peters

Jan 16, 2002, 9:03:38 PM1/16/02
to
[James Althoff, on an "elegant" mergesort]

> is probably going to create way too many generator/iterator
> instances to scale well.

[Tim]

> Well, it was clear from the start that there's no interest in a
> practical algorithm here, else we'd just use a temp array and a
> handful of index variables.

[David Eppstein]

> I think heap sort would be a good choice for practicality, since it sorts
> in-place with only a handful of index variables.

Following is the spelling of mergesort I've had in mind ("a temp array and a
handful of index variables"). It's eminently practical. Note that if the
list doesn't have an exact power-of-2 size, no attempt is made to "balance"
the excess across passes. That keeps the code simple, but doesn't harm
correctness or O() behavior. Better speedups can be obtained via simpler
means than balancing (like picking on the innermost loop, and splitting off
the first (s=1) pass to swap out-of-order pairs in-place directly).

def mergesort(A):
"Sort list, via stable mergesort."
n = len(A)
B = [None] * n
swapped = 0
s = 1
while s < n:
s2 = s+s
# Invariant: viewing A as a sequence of slices of length s (plus
# perhaps an oddball at the end), each slice is sorted. (This is
# trivially so when s=1; proceed by induction.) Now merge adjacent
# pairs of slices into sorted slices twice as large.
for i in range(0, n, s2):
ihi = j = i+s # start of adjacent slice
jhi = min(j+s, n) # final slice may have an oddball size
k = i # start of output slice
while i < ihi and j < jhi:
if A[i] <= A[j]:
B[k] = A[i]
i += 1
else:
B[k] = A[j]
j += 1
k += 1
# Copy tail. At most one of these isn't vaccuous.
B[k : k+ihi-i] = A[i : ihi]
B[k : k+jhi-j] = A[j : jhi]
# Swap input and output lists.
A, B = B, A
swapped = not swapped
s = s2

if swapped: # copy back into original input list
B[:] = A

This is easier to get right for most people than a heapsort, and, if you can
afford the memory hit for a temp vector, generally runs faster (esp. for
large arrays on VM machines -- this mergesort's sequential memory access
works much better with typical disks and OS paging policies than heapsort's
leaping around). Coding is straightforward even in assembler. It doesn't
lend itself to finding "just the first K" quicker, though.

> But except for unusual circumstances, I would likely just call Python's
> built-in sort().

That's at least sane <wink>. I wrote Python's current list.sort(), and it
runs faster than the quickest mergesort I was able to code in C at the time
(which was a variant of the above, plus playing every low-level speed trick
under the sun). The quickest mergesort was a little quicker than the
quickest quicksort I tried; heapsort wasn't competitive. The sort() Python
ended up with is a nightmarish hybrid of single-thread samplesort and binary
insertion sort. That was the clear winner out of about 20 sort
implementations, and I expect it remains very hard to beat (for Python's
specific ratio of slow comparison to cheap object movement (just pointer
copies)).

life-is-ugly-where-the-theory-collides-with-the-hw<wink>-ly y'rs - tim

### sebastien

Jan 17, 2002, 4:28:36 AM1/17/02
to
> The Python Cookbook has an algorithm for O(n) FIFO queues submitted by
> Sébastien Keim.
> His approach is interesting and brilliant,
>
> See: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/68436

Thank's

I've completed the page with some kind of benchmarking.
The results are quite amazing but I would be more confident if someone
could confirm them. (in fact I found them very rude for built-in
lists)

### Raymond Hettinger

Jan 17, 2002, 8:04:02 AM1/17/02
to
Delaney, Timothy" <tdel...@avaya.com> wrote in message
news:mailman.1011232764...@python.org...

> class DictLongFifo:
>
> def __init__(self):
> self.data = {}
> self.nextin = long(0)
> self.nextout = long(0)
>
> def append(self, value):
>
> self.data[self.nextin] = value
> self.nextin += 1
>
> def pop(self, pos=-1):
> value = self.data[self.nextout]
> del self.data[self.nextout]
> self.nextout += 1
> return value

I'm not sure why, but subclassing the built-in types gives amazing
performance
benefits. Please re-try the timings with this version of DictLongFifo:

class DictLongFifo(dict):
def __init__(self):

self.nextin = 0L
self.nextout = 0L

def append(self, value):
self[self.nextin] = value
self.nextin += 1
def pop(self):
value = self[self.nextout]
del self[self.nextout]

self.nextout += 1
return value

Raymond Hettinger

### Raymond Hettinger

Jan 17, 2002, 8:46:36 AM1/17/02
to

"Delaney, Timothy" <tdel...@avaya.com> wrote in message
news:mailman.1011232764...@python.org...
>
> 10000 <type 'list'> 0.329070
> 10000 <type 'array'> 0.234557
> 10000 DictIntFifo 0.123809
> 10000 DictLongFifo 0.185284
> 10000 ListPrependFifo 0.329698
> 10000 ListAppendFifo 0.398269
>
> 100000 <type 'list'> 76.195043
> 100000 <type 'array'> 56.828019
> 100000 DictIntFifo 1.269020
> 100000 DictLongFifo 1.961017
> 100000 ListPrependFifo 60.693928
> 100000 ListAppendFifo 77.094517
>
> So once you get to decently large quantities in the queue, the dict
versions
> make real sense over a basic list (Win2000).
>
> Tim Delaney

approach
to the mix:

class NestedListFifo:
def __init__(self):
self.first=[]
def append(self,data):
node = [data,[]]
if self.first == []:
self.first= node
else:
self.last[1] = node
self.last = node
def pop(self, n=-1):
node = self.first
self.first=node[1]
return node[0]

Raymond Hettinger

### Justin Sheehy

Jan 17, 2002, 9:11:09 AM1/17/02
to
qu...@hork.ugcs.caltech.edu (Quinn Dunkan) writes:

> Aha! I always thought ADT stood for "Algebraic Data Type" and assumed people
> idea of what they were supposed to exactly be (value semantics?). And fp
> advocates would say things like "behold the power of adts, blah blah".

Your confusion might have come from the fact that some of the more
rigorous software designers out there, especially some of those that
are also fp people, describe their ADTs via algebraic specification.

Then again, it might not have.

-Justin

### James_...@i2.com

Jan 17, 2002, 3:28:40 PM1/17/02
to

<Tim Peters>

Following is the spelling of mergesort I've had in mind ("a temp array and
a
handful of index variables"). It's eminently practical.
</Tim Peters>

Thanks for sharing this. I tried it on a list of 100,000 ints in reverse
order. It ran about 4.5x faster than the generator version (the
generator-with-list.append version was a little faster than the
all-generator version).

<Tim Peters>

I wrote Python's current list.sort(), and it
runs faster than the quickest mergesort I was able to code in C at the time

<snip>

I expect it remains very hard to beat (for Python's
specific ratio of slow comparison to cheap object movement (just pointer
copies)).

</Tim Peters>

On the list of 100,000 the builtin tim.list.sort was a mere 800x or so
faster than the generator version.

The bad news -- for us Jython users -- is that on the list of 100,000
Jython.list.sort was about 45x slower than cpython.list.sort. :-(

Jim

<Tim Peters>

</Tim Peters>

### Delaney, Timothy

Jan 17, 2002, 6:10:43 PM1/17/02
to
> From: Raymond Hettinger [mailto:oth...@javanet.com]

> "Delaney, Timothy" <tdel...@avaya.com> wrote in message
> news:mailman.1011232764...@python.org...
> >
> > 10000 <type 'list'> 0.329070
> > 10000 <type 'array'> 0.234557
> > 10000 DictIntFifo 0.123809
> > 10000 DictLongFifo 0.185284
> > 10000 ListPrependFifo 0.329698
> > 10000 ListAppendFifo 0.398269
> >
> > 100000 <type 'list'> 76.195043
> > 100000 <type 'array'> 56.828019
> > 100000 DictIntFifo 1.269020
> > 100000 DictLongFifo 1.961017
> > 100000 ListPrependFifo 60.693928
> > 100000 ListAppendFifo 77.094517
> >
> > So once you get to decently large quantities in the queue, the dict
> versions
> > make real sense over a basic list (Win2000).
> >
> > Tim Delaney
>
>
> Before drawing a conclusion on this one, please add Sébastien Keim's
> approach
> to the mix:

No question - there's lots of ways to do a FIFO list. I was merely
interested in how well Alex's version would perform compared to the naive
method of just using a list. And then of course I buggered up the test (in
two different ways!) and felt it important to acknowledge this and correct
any misconceptions that the dict method was inefficient which were formed
based on my erroneous test.

Tim Delaney

### Tim Peters

Jan 19, 2002, 1:49:11 AM1/19/02
to
[Tim]

>> Following is the spelling of mergesort I've had in mind ("a temp array
>> and a handful of index variables"). It's eminently practical.

[James Althoff]
> Thanks for sharing this.

Wait until you get the bill <wink>.

> I tried it on a list of 100,000 ints in reverse order. It ran about
> 4.5x faster than the generator version (the generator-with-list.append
> version was a little faster than the all-generator version).

Note that it was written for clarity rather than speed; commentary in the
original post suggested two effective ways to speed it up; anyone obsessed
with speed will think of others.

[on the builtin list.sort()]

> On the list of 100,000 the builtin tim.list.sort was a mere 800x or so
> faster than the generator version.

I'm afraid that wasn't "a fair" comparison: assuming you were still using a
list of 100,000 ints "in reverse order", list.sort() manages to sort
reverse-sorted inputs in linear time, while mergesort is always (best case
and worst case) N log N. A fairer test would apply random.shuffle() to the
input first. Note that if the "split off the s=1 iteration" suggestion for
speeding the mergesort is taken, it's easy to add a bit of code to the
split-off first iteration to detect already-sorted and
already-reverse-sorted in mergesort too (count how many swaps are done in
the split-off first iteration; a result of either 0 or total-number-of-pairs
is astronomically unlikely for random input, so if either obtains and
worth doing (at most) another n/2 compares to finish the job in linear time
when you can).

> The bad news -- for us Jython users -- is that on the list of 100,000
> Jython.list.sort was about 45x slower than cpython.list.sort. :-(

Last I looked, Java used a quicksort. In the common median-of-3 variant of
quicksort, reverse-sorted input is one of the best cases, but it's still an
N log N case. Again it would be fairer to shuffle the input first. The
thing that hurts quicksort for use in Python is that it does significantly
more comparisons (on average) than the theoretical minimum (on average), and
comparison of Python objects is a long-winded OO adventure <wink>.

### Kragen Sitaker

Jan 23, 2002, 5:41:57 PM1/23/02
to
David Eppstein <epps...@ics.uci.edu> writes:
> I think heap sort would be a good choice for practicality, since it sorts
> in-place with only a handful of index variables. But except for unusual
> circumstances, I would likely just call Python's built-in sort().

That's good --- I was beginning to think you were delusional.

Even with hacks to make it less likely to hit its worst-case, though,
quicksort's constant factor makes it about twice as fast as mergesort.
How does heapsort's constant factor compare with mergesort's?

Python's built-in sort() uses quicksort (using a linear congruential
generator to pick pivot elements) to partition the array into small
chunks, and then uses an algorithm that looks a lot like a bubble sort
to sort the small chunks. It has special cases for already-sorted
data, all-the-same data, reverse-sorted data, and each of the above
followed by some unsorted data. This is the kind of thing you get
when you aim for practicality.

### David Eppstein

Jan 23, 2002, 7:22:56 PM1/23/02
to
In article <83it9s4...@panacea.canonical.org>,
Kragen Sitaker <kra...@pobox.com> wrote:

> Even with hacks to make it less likely to hit its worst-case, though,
> quicksort's constant factor makes it about twice as fast as mergesort.

This is either using clever tricks to pick a good pivot, or assuming that
comparisons are fast (probably not a good assumption in Python), right?
Merge sort uses very close to the optimal number of comparisons, single
randomly-chosen pivot quicksort is off by some constant factor.

It also depends on how your data was represented; several years ago when I
needed code (in C++) to sort linked-list data I chose merge sort, since
it's simple, for that representation it does not use any extra memory, and
the lists I was sorting were small enough that I didn't have to worry about
caching effects (as I think someone pointed out earlier, array-based
versions of quick sort and merge sort can be much better than heap sort in
their caching behavior).

> How does heapsort's constant factor compare with mergesort's?

Not as good, but it uses less memory. The problem is, quicksort doesn't
use much more memory than heapsort, and is I think usually much faster, so
heapsort is not so often the best choice.

> Python's built-in sort() uses quicksort (using a linear congruential
> generator to pick pivot elements) to partition the array into small
> chunks, and then uses an algorithm that looks a lot like a bubble sort
> to sort the small chunks. It has special cases for already-sorted
> data, all-the-same data, reverse-sorted data, and each of the above
> followed by some unsorted data. This is the kind of thing you get
> when you aim for practicality.

Yes, theory and practice are not the same thing.

Sometimes (as here) the theoretical algorithms are nice and clean, but
making them practical creates a mess. Other times theoreticians use lots
of complicated tricks to reduce the worst-case complexity while the better
practical solutions are simpler...

### John Schmitt

Jan 23, 2002, 9:03:43 PM1/23/02
to

I was hoping that someone else would comment on this post and I'm counting on people to correct me where I err.

"Abstract Data Type" is a computer science and a math term.  For that reason, I believe that the phrase 'ADT-based programming' has no meaning.  What would 'module-based programming' mean?

"Object Oriented Programming" is a programming term.  Myself being a wannabe computer science geek, I make a distinction between computer science and programming.

The other term that I see misused is "Data Structure".

Examples of data structures are pointers, arrays, records, and files.  Examples of abstract data types are stacks, queues, graphs, and FIFOs.  ADTs can be implemented in terms of data structures.

John

-----Original Message-----
From: Mitch Chapman [mailto:Mitch....@bioreason.com]
Sent: Wednesday, January 16, 2002 8:42 AM
To: pytho...@python.org
Subject: Re: algorithms and ADTs (was Re: efficient idiomatic queue?)

[quote deleted]

As Andrew hinted, a big distinction between OO classes
and ADTs is that the latter can't be subclassed.

ADT-based programming is useful in languages which don't
directly support OOP (e.g ANSI C).  They don't provide subclassing
or protocol/interface-based programming, but ADTs do
simplify encapsulation and memory management.

My first exposure to ADTs came when I started using
Modula-2.  Hence the claim that if you remove memory-management
(i.e. instantiation) from ADT-based programming you get
module-based programming :)

--
..and lots of singletons