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Continuous Range, RangeSet, and RangeDict data structures

Project description


This module provides data structures for representing

  • Continuous Ranges
  • Non-continuous Ranges (i.e. sets of continous Ranges)
  • dict-like structures that use ranges as keys


One curious missing feature in Python (and several other programming languages) is the absence of a proper Range data structure - a continuous set of values from some starting point to some ending point. Python's built-in range() produces an object that can be used to iterate over numbers, but it's not continuous (e.g. 1.5 in range(1, 2) returns False) and doesn't work for non-numeric types like dates. Instead, we have to make do with verbose if/else comparisons:

if value >= start and value < end:
    # do something

And to have a graded sequence of ranges with different behavior for each, we have to chain these if/elif/else blocks together:

# 2019 U.S. income tax brackets, filing Single
income = int(input("What is your income? $"))
if income < 9701:
    tax = 0.1 * income
elif 9701 <= income < 39476:
    tax = 970 + 0.12 * (income - 9700)
elif 39476 <= income < 84201:
    tax = 4543 + 0.22 * (income - 39475)
elif 84201 <= income < 160726:
    tax = 14382.5 + 0.24 * (income - 84200)
elif 160726 <= income < 204101:
    tax = 32748.5 + 0.32 * (income - 160725)
elif 204101 <= income < 510301:
    tax = 46628.5 + 0.35 * (income - 204100)
    tax = 153798.5 + 0.37 * (income - 510300)
print(f"Your tax on that income is ${tax:.2f}")

And if we want to restrict a user input to within certain bounds, we need to do some complicated, verbose construct like this:

user_input = int(input())
value_we_want = min(max(user_input, start), end)

This module, ranges, fixes this problem by introducing a data structure Range to represent a continuous range, and a dict-like data structure RangeDict to map ranges to values. This makes simple range checks more intuitive:

if value in Range(start, end):
    # do something

user_input = int(input())
value_we_want = Range(start, end).clamp(user_input)

and does away with the tedious if/elif/else blocks:

# 2019 U.S. income tax brackets, filing Single
tax_info = RangeDict({
    Range(0, 9701):        (0,        0.10, 0),
    Range(9701,   39476):  (970,      0.12, 9700),
    Range(39476,  84201):  (4543,     0.22, 39475),
    Range(84201,  160726): (14382.2,  0.24, 84200),
    Range(160726, 204101): (32748.5,  0.32, 160725),
    Range(204101, 510301): (46628.5,  0.35, 204100),
    Range(start=510301):   (153798.5, 0.37, 510300),
income = int(input("What is your income? $"))
base, marginal_rate, bracket_floor = tax_info[income]
tax = base + marginal_rate * (income - bracket_floor)
print(f"Your tax on that income is ${tax:.2f}")

The Range data structure also accepts strings, dates, and any other data type, so long as the start value is less than the end value (and so long as checking that doesn't raise an error).

See the in-depth documentation for more details.


Install python-ranges via pip:

$ pip install python-ranges

Due to use of format strings in the code, this module will only work with python 3.6 or higher. Some post-3.9 features are also used in the module's type hinting, which may pose a problem for earlier versions of python.


Simply import ranges like any other python package, or import the Range, RangeSet, and RangeDict classes from it:

import ranges

my_range = ranges.Range("anaconda", "viper")
from ranges import Range

my_range = Range("anaconda", "viper")

Then, you can use these data types however you like.


To make a Range, simply call Range() with start and end values. Both of these work:

rng1 = Range(1.5, 7)
rng2 = Range(start=4, end=8.5)

You can also use the include_start and include_end keyword arguments to specify whether or not each end of the range should be inclusive. By default, the start is included and the end is excluded, just like python's built-in range() function.

If you use keyword arguments and don't specify either the start or the end of the range, then the Range's bounds will be negative or positive infinity, respectively. Range uses a special notion of infinity that's compatible with non-numeric data types - so Range(start="journey") will include any string that's lexicographically greater than "journey", and Range(, 10, 4)) will include any date before October 4, 1989, despite neither str nor datetime having any built-in notion of infinity.

You can import Inf in order to invoke this infinity explicitly:

from ranges import Range, Inf
rngA = Range(-Inf, Inf)
rngB = Range()
# rng1 and rng2 are identical

and you can check whether a range is infinite on either end by calling .isinfinite():

rngC = Range(end=0)
rngD = Range(start=0)
rngE = Range(-1, 1)
print(rng1.isinfinite(), rng2.isinfinite(), rng3.isinfinite())
# True True False

If you're making a range of numbers, then you can also use a single string as an argument, with circle-brackets () meaning "exclusive" and square-brackets [] meaning "inclusive":

rng3 = Range("[1.5, 7)")
rng4 = Range("[1.5 .. 7)")

Range's interface is similar to the built-in set, and the following methods all act exactly how you'd expect:

print(rng1.union(rng2))  # [1.5, 8.5)
print(rng1.intersection(rng2))  # [4, 7)
print(rng1.difference(rng2))  # [1.5, 4)
print(rng1.symmetric_difference(rng2))  # {[1.5, 4), [7, 8.5)}

Of course, the operators |, &, -, and ^ can be used in place of those methods, just like for python's built-in sets.

See the documentation for more details.


A RangeSet is just an ordered set of Ranges, all of the same kind. Like Range, its interface is similar to the built-in set. Unlike Range, which isn't mutable, RangeSet can be modified just like set can, with the methods .add(), .extend(), .discard(), etc.

To construct a RangeSet, just call RangeSet() with a bunch of ranges (or iterables containing ranges) as positional arguments:

rngset1 = RangeSet("[1, 4.5]", "(6.5, 10)")
rngset2 = RangeSet([Range(2, 3), Range(7, 8)])

Range and RangeSet objects are mutually compatible for things like union(), intersection(), difference(), and symmetric_difference(). If you give these methods a range-like object, it'll get automatically converted:

print(rngset1.union(Range(3, 8)))  # {[1, 10)}
print(rngset1.intersection("[3, 8)"))  # {[3, 4.5], (6.5, 8)}
print(rngset1.symmetric_difference("[3, 8)"))  # {[1, 3), (4.5, 6], [8, 10)}

Of course, RangeSets can operate with each other, too:

print(rngset1.difference(rngset2))  # {[1, 2), [3, 4.5], (6.5, 7), [8, 10)}

The operators |, &, ^, and - all work with RangeSet as they do with set, as do their associated assignment operators |=, &=, ^=, and -=.

Finally, you can iterate through a RangeSet to get all of its component ranges:

for rng in rngset1:
# [1, 4.5]
# (6.5, 10)

See the documentation for more details.


This data structure is analagous to python's built-in dict data structure, except it uses Ranges/RangeSets as keys. As shown above, you can use RangeDict to concisely express different behavior depending on which range a value falls into.

To make a RangeDict, call RangeDict() with an either a dict or an iterable of 2-tuples corresponding Ranges or RangeSets with values. You can also use a tuple of Ranges as a key.
A RangeDict can handle any type of Range, or even multiple different types of Ranges all at once:

advisors = RangeDict([
    (Range(end="I"), "Gilliam"),
    (Range("I", "Q"), "Jones"),
    (Range(start="Q"), "Chapman"),

mixmatch = RangeDict({
    (Range(0, 8),     Range("A", "I")): "Gilliam",
    (Range(8, 16),    Range("I", "Q")): "Jones",
    (Range(start=16), Range(start="Q")): "Chapman",

See the documentation for more details.

Support / Contributing

If you spot any bugs in this module, please submit an issue detailing what you did, what you were expecting, and what you saw, and I'll make a prompt effort to isolate the root cause and fix it. The error should be reproducible.

If, looking through the code, you spot any other improvements that could be made, then feel free to submit issues detailing those as well. Also feel free to submit a pull request with improvements to the code.

This module is extensively unit-tested. All code contributions should be accompanied by thorough unit tests for every conceivable use case of the new functionality. If you spot any use cases that aren't currently covered by the unit test suite, feel free to either submit a GitHub issue detailing them, or simply add them yourself and submit a pull request.

Possible To-Do List:

  • Add a notion of a PermissiveRangeSet (name pending) which allows multiple types of Ranges that are not necessarily mutually comparable. In the initial design I considered a number of ways to implement this, but ran into conceptual difficulties, mainly in terms of handling performance and algorithms. If you can build a PermissiveRangeSet or similar class that implements this functionality, along with a suitable set of unit tests, then feel free to do so and submit a pull request (if you do, please include the reasoning for your design decisions).
  • Rewrite RangeSet.intersection() to use a pair-stepping algorithm (akin to the "merge" part of MergeSort - iterate through the two _LinkedList data structures simultaneously and only advance one element of one list at a time) instead of the current "compare every element with every other element" solution. Adding short-circuiting to this (returning early from the method once it's clear that there is no longer work to be done, even if the entire list has not yet been iterated through) would also be useful, and the two approaches synergize nicely. This won't lower the complexity class below its current worst-case O(n^2), but it could drastically improve performance.
  • Rewrite RangeSet.isdisjoint() to use pair-stepping and short-circuiting. The reasoning here is the same as for RangeSet.intersection().
  • Rewrite RangeDict.getitem() and RangeDict.getoverlapitems() to use a binary search, for efficiency on potentially large dicts.
  • Add pretty-printing for RangeSet and especially RangeDict. The pprint module does not seem to work on them, unfortunately.
  • Replace the _LinkedList data structure (contained in with an interval list, an O(sqrt(n)) list, or some other data structure more tailored to the particular problem. Linked List was chosen because it supported quick insertion/deletion and was easy to implement; the latter concern is no longer relevant.

Any open issues or bugs are also fair game for contribution. See above for directions.


MIT License. Feel free to use ranges however you like.

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