Add "key" argument to "bisect" module functions

[tebeka]

BPO	4356
Nosy	@rhettinger, @terryjreedy, @gpshead, @tebeka, @mdickinson, @alex, @vadmium, @dimaqq, @1st1, @NeilGirdhar, @MojoVampire, @wumpus, @pablogsal, @miss-islington, @remilapeyre, @GPery
PRs	bpo-4356: Add key parameter to functions in bisect module #11781 bpo-4356: Add key parameter to functions in bisect module #11781 bpo-4356: Add key function support to the bisect module #20556 bpo-4356: Mention the new key arguments for the bisect module APIs in the 3.10 What's new #28339 [3.10] bpo-4356: Mention the new key arguments for the bisect module APIs in the 3.10 What's new (GH-28339) #28340
Files	bisect-trunk.patch: bisect for trunk bisect-py3k.patch: patch for py3k bench_bisect_key.py: benchmark SortedCollection.py: Draft for a Sorted Collection class

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = 'https://github.com/rhettinger'
closed_at = <Date 2020-10-20.05:04:39.386>
created_at = <Date 2008-11-19.17:17:27.762>
labels = ['type-feature', 'library', '3.10']
title = 'Add "key" argument to "bisect" module functions'
updated_at = <Date 2021-10-04.19:18:43.811>
user = 'https://github.com/tebeka'

bugs.python.org fields:

activity = <Date 2021-10-04.19:18:43.811>
actor = 'pablogsal'
assignee = 'rhettinger'
closed = True
closed_date = <Date 2020-10-20.05:04:39.386>
closer = 'rhettinger'
components = ['Library (Lib)']
creation = <Date 2008-11-19.17:17:27.762>
creator = 'tebeka'
dependencies = []
files = ['15248', '15249', '15250', '16944']
hgrepos = []
issue_num = 4356
keywords = ['patch']
message_count = 43.0
messages = ['76060', '76073', '76084', '76092', '76098', '76099', '76203', '76230', '94836', '103143', '103145', '103155', '103158', '103180', '103294', '113222', '115176', '115189', '115288', '152967', '152969', '152983', '208020', '237408', '242267', '246371', '246384', '261007', '305518', '335841', '337737', '337741', '343529', '343544', '343548', '343549', '345220', '345227', '345228', '379086', '401796', '401798', '403173']
nosy_count = 22.0
nosy_names = ['rhettinger', 'terry.reedy', 'gregory.p.smith', 'jafo', 'tebeka', 'mark.dickinson', 'alex', 'milko.krachounov', 'dmtr', 'bls', 'martin.panter', 'Dima.Tisnek', 'yselivanov', 'NeilGirdhar', 'josh.r', 'ericreynolds', 'wumpus', 'pablogsal', 'miss-islington', 'remi.lapeyre', 'gpery', 'flyingosprey']
pr_nums = ['11781', '11781', '20556', '28339', '28340']
priority = 'normal'
resolution = 'fixed'
stage = 'resolved'
status = 'closed'
superseder = None
type = 'enhancement'
url = 'https://bugs.python.org/issue4356'
versions = ['Python 3.10']

[tebeka]

It'd be helpful of the functions in the "bisect" modules will have a
"key" argument just like "sort".

[mdickinson]

This request has come up repeatedly (and been rejected) in the past. See issues 2954, 3374, 1185383, 1462228, 1451588, 1619060.

Could you perhaps explain your particular use case for this? A few truly
convincing use-cases might increase the chances of this getting accepted.

[rhettinger]

Miki, the issue is that bisect calls tend to be made repeatedly, so the
key function can be called over and over again for the same argument.
It is almost always a better design to simply decorate the list so the
key function never gets called more than once per element in the list.
If we added key= to bisect, it would encourage bad design and steer
people after from better solutions.

[mdickinson]

What about cases where performance is unimportant, or where the key
function is fast (e.g. an attribute access)? Then something like

bisect(a, x, key=attrgetter('size'))

is easy to write and read. Mightn't this be considered good design,
from some perspectives?

Another thought: if your list is a list of user-defined objects then a
natural way to do the 'decorate' step of DSU might be to add a 'key'
attribute to each object, rather than the usual method of constructing
pairs. (This has the advantage that you might not have to bother with the
'undecorate' step.) With a key argument, bisect could make use of this
technique too.

Disclaimer: I haven't personally had any need for a key argument on
bisect, so all this is hypothetical. That's why I'm asking for real use-
cases.

[rhettinger]

I had said "almost always". Sure, if you don't care about performance
or scalability, a key= argument would be a net win.

We're responsible for creating an API that steers most programmers in
the right direction (Tim sez "we read Knuth so you don't have to").
Algorithmically, the bisect functions are at the wrong level of
granularity for applying a key function.

For user-defined objects, there is no need for a key-attribute since can
just supply a custom comparison method:

class UserDefined:
  . . .
  def cmp(self, other):
      return cmp(self.key, other.key)

[mdickinson]

One case I've been thinking about is that of maintaining a list of Decimal
objects that are sorted by absolute value. For this, having to create a
list of (abs(x), x) pairs just seems clumsy compared to using a key
argument to bisect.

Perhaps this is a contrived use case, but it doesn't seem totally
implausible.

[tebeka]

I agree you can get around this with defining __cmp__, however same goes
to "sort" and it was added anyway.

My take on it is that sometimes I need to find something in a big list
of objects, and I don't like to do DSU and not add __cmp__ to the
objects (since some of the lists might be sorted by different attributes

• say one list for time and one line for price).

I'd prefer if we do implement "key" and add a warning in the docs it
might slow you down. Which what will happen in the case of __cmp__ anyway.

I don't see why the "key" function should be called all the time on
inserted item, it's very easy to cache this value

def bisect(a, x, lo=0, hi=None, key=lambda x: x):
    assert low >= 0, "low must be non-negative"
    hi = hi or len(a)

    x_key = key(x) 
    while lo < hi:
        mid = (lo+hi)//2
        if x_key < key(a[mid]): hi = mid
        else: lo = mid+1
    return lo

(I'd also wish for "identity" built in, however this is another subject :)

[terryjreedy]

Just a reminder that __cmp__ is gone in 3.0.
I presume bisect, like sort, only requires __lt__ and perhaps __eq__,
though I can find no doc of either.

[milkokrachounov]

I've been bugged by the lack of key= argument for bisect for some time
now, and today I got to read this and the previous issues about the
matter. I still fail to understand the reasons for the rejections. It
might encourage bad design in which expensive key functions will get
called more than once for the same element. However:

1. Not all key= functions are computationally expensive, in fact a quick
   search shows that most key= uses come are with itemgetter, attrgetter or
   some cousin.
2. Even for a computationally expensive function precached key isn't
   necessarily the right answer. And if the keys are huge, a key= function
   can actually be useful in implementing intelligent caching.
3. The reason for rejection is merely a performance issue which *can* be
   fixed without any significant changes to the design of the app should it
   prove to be a real issue.

I was writing a module that keeps a sorted list of items in which items
can be added, removed, or changed (they might get reordered). I used
bisect to avoid useless slow linear searches, which would be one
obstacle for the app to scale well. However, the sort key can be changed
at any time, so implementing __lt__ wasn't an option. Keeping a second
list with the keys is both memory and computationally expensive as
inserting into a list is slow. It's not a shiny example of a bisect
use-case as the only thing I've used my module so far is to display the
files in a directory, which means the lists are small and the changes
are seldom, so any implementation is good enough. But bisect with key=
would have been best if it was available. What's worse, I have a buggy
unreadable ad hoc implementation of bisect in my code right now. ;)

I see the following as reasons why key= would provide benefit:

1. If you have a sorted list, bisect is a net win. Having a key= would
   enable you to utilize it without refactoring anything. The lack of key
   may as well encourage you to continue using linear searches, or other
   sub-optimal solutions.
2. Using key= is more readable and less error-prone than keeping two
   lists in simple cases where defining a class with __le__ is an overkill.
   Two examples I had where this was the case:
   a) A class I implemented to pick numbers from a certain discrete random
   distribution with bisect. Oh, but yeah, the implementation without key=
   is twice faster.
   b) I gave a hand to someone who was implementing a dictionary looked up
   the words as you typed them with bisect.
3. Insort. Insort is already slow enough as it is, a key= wouldn't slow
   it down much if at all. In fact, if you are keeping two lists, key=
   would speed it up. Insort with key= is a net win.

I've implemented key= and quickly hacked a benchmark to show what
performance hit it might have, and to put things into perspective. The
results:

1. Cheap key function, integers and abs(), 1000000 items, 5000 bisects
   or insorts:
   a) Bisect with a key: 0.02205014s
   b) Bisect with a second list: 0.01328707s
   c) Insort with a key: 5.83688211s
   d) Bisect with a second list, and two inserts: 16.17302299s

2. Cheap key function, ~4000 char bytestrings and len(), 100000 items,
   5000 bisects or insorts:
   a) Bisect with a key: 0.01829195s
   b) Bisect with a second list: 0.00945401s
   c) Insort with a key: 0.25511408s
   d) Bisect with a second list, and two inserts: 0.49303603s

3. Expensive key function, ~4000 char bytestrings and str.lower(),
   100000 (500 MB) items, 5000 bisects or insorts:
   a) Bisect with a key: 1.26837015s
   b) Bisect with a second list: 0.08390594s
   c) Insort with a key: 1.50406289s
   d) Bisect with a second list, and two inserts: 0.57737398s

4. Expensive key function, ~4000 char bytestrings and str.lower(),
   500000 (2.5 GB) items, 5000 bisects or insorts:
   a) Bisect with a key: 1.46136308s
   b) Bisect with a second list: 0.08768606s
   c) Insort with a key: 3.05218720s
   d) Bisect with a second list, and two inserts: 6.43227386s

5. Expensive key function, ~4000 char bytestrings and str.strip(),
   100000 (500 MB) items, 5000 bisects or insorts:
   a) Bisect with a key: 0.03311396s
   b) Bisect with a second list: 0.01374602s
   c) Insort with a key: 0.27423000s
   d) Bisect with a second list, and two inserts: 0.49585080s

6. Expensive key function, ~4000 char bytestrings and str.strip(),
   500000 (2.5 GB) items, 5000 bisects or insorts:
   a) Bisect with a key: 0.04530501
   b) Bisect with a second list: 0.01912594
   c) Insort with a key: 1.62209797
   d) Bisect with a second list, and two inserts: 5.91734695

Also, I tried to bench linear searches, but as they had to run in Python
code they aren't representative of anything. In the integer test they
went for about 250 seconds without recalculating the key, and for about
500 with. Also, replacing them with .index() gave about 60 seconds if I
ensured there's high probability that the number is in the list, and for
500 if I didn't.

In short, key= for bisect would be convenient and neat, really useful in
rare cases, leading to more readable code in the most common cases, and
I'm unconvinced of the perceived harm that it would cause.

I attach a patch implementing it for trunk, py3k, and the benchmark
script I used to test it (on trunk).

[bls]

This was closed over a year ago, but since mark.dickinson was asking for convincing use-cases: I'm breaking up a file into line-delimited chunks. These chunks are non-overlapping, contiguous, and tend to be fairly large, so I'm just recording the start line of each chunk in a 2-ple:

mapping = [
  (10, 'first chunk'),
  (50, 'second chunk'),
  (60, 'third chunk')
]

Lines 10-49 are in the first chunk, lines 50-59 are in the second, lines 60+ are in the third. So:

def CategorizeLine(line, mapping):
   loc = bisect.bisect([m[0] for m in mapping], line)
   if loc == 0:
      return None # before first chunk
   return mapping[loc-1][1]

It Would Be Nice if I could write the second line as:

   loc = bisect.bisect(mapping, line, key=lambda m:m[0])

The bisect documentation suggests pre-computing the key list, but it seems messy and error-prone to keep a redundant data structure in sync with its source. I could also rewrite my "mapping" data structure to be two parallel lists instead of one list of 2-ples, but this data structure is more readable and extensible and handles empty lists more naturally.

[rhettinger]

I'll take another look at this one.