IntIntervals

IntIntervals is a Python module for representing disjoint integer intervals in a memory-efficient manner while supporting set operations.

Overview

Instead of storing every integer explicitly, IntIntervals represents intervals as the starting and ending value [a, b]. This provides a large memory reduction in the case of long runs of consecutive integers. IntIntervals is intended for cases where storing every integer is an unacceptable memory overhead and involves tradeoffs: some operations are slower than if they were performed on a standard Python set or dictionary. In particular, lookup (x in s) now takes logarithmic instead of constant time.

The only class provided is IntIntervals, which supports the standard operations a Python frozenset supports, plus a few additional operations that have proved useful.

This code is based upon the Interval class I originally developed for PGDB. It seems that the concept is the same as in a discrete interval encoding tree (diet) augmented with set-theoretic operations, but I wasn't aware of diets when I originally wrote this.

Installation

To install, just run the setup.py script:

python setup.py install

Example

import random
from intintervals import IntIntervals

# Generate some random integers.
ints1 = [random.randint(0, 99) for i in range(50)]
ints2 = [random.randint(0, 99) for i in range(50)]

# Create our integer intervals.
intv1 = IntIntervals(ints1)
intv2 = IntIntervals(ints2)

# Look at our intervals.
print intv1
print intv2

# Check membership.
42 in intv1
13 not in intv2

# Set operations.
intv1.union(intv2)
intv1.intersection(intv2)
intv1.difference(intv2)
intv1.symmetric_difference(intv2)
intv1.isdisjoint(intv2)
intv1.issubset(intv2)
intv1.issuperset(intv2)

# Identify the smallest and largest values.
intv1.smallest()
intv1.largest()

# Iterate over every integer in the intervals.
for i in intv1: print i

Testing

Currently testing is minimal. The tests/fuzz.py script will exercise the union, intersection, difference, and symmetric_difference operations with large amounts of random input and verify it using Python's built-in set.