# Source code for Goulib.interval

```#!/usr/bin/env python
# coding: utf8
"""
operations on [a..b[ intervals
"""
__author__ = "Philippe Guglielmetti"
__credits__ = []

from sortedcontainers import SortedListWithKey

def _order(interval):
""":return: (a,b) interval such that a<=b"""
if interval[0]==interval[1]: #allows to order None,None in Py3
return (interval[0], interval[1])
elif interval[0]<interval[1]:
return (interval[0], interval[1])
else:
return (interval[1], interval[0])

[docs]def in_interval(interval,x,closed=True):
""":return: bool True if x is in interval [a,b] or [b,a] (tuple)"""
a,b = _order(interval)
return (a <= x <= b) if closed else (a <= x < b)

[docs]def intersect(t1, t2):
""":return: bool True if intervals [t1[ [t2[ intersect"""
'''http://stackoverflow.com/questions/3721249/python-date-interval-intersection'''
t1start, t1end = _order(t1)
t2start, t2end = _order(t2)
return (t1start <= t2start < t1end) or (t2start <= t1start < t2end)

[docs]def intersection(t1, t2):
""":return: tuple intersection between 2 intervals (tuples),
or None if intervals don't intersect"""
t1start, t1end = _order(t1)
t2start, t2end = _order(t2)
start=max(t1start,t2start)
end=min(t1end,t2end)
if start>end: #no intersection
return None
return (start,end)

[docs]def intersectlen(t1, t2, none=0):
"""
:param t1: interval 1 (tuple)
:param t2: interval 2 (tuple)
:param none: value to return when t1 does not intersect t2
:return: len of intersection between 2 intervals (tuples),
or none if intervals don't intersect
"""
i=intersection(t1,t2)
if i is None:
return none #the parameter...
return i[1]-i[0]

[docs]class Interval(list):
"""
Represents an interval.
Defined as half-open interval [start,end),
which includes the start position but not the end.
Start and end do not have to be numeric types.
They might especially be time, date or timedate as used in datetime2

inspired from http://code.activestate.com/recipes/576816-interval/
alternatives could be https://pypi.python.org/pypi/interval/
(outdated, no more doc)
or https://pypi.python.org/pypi/pyinterval/
"""

[docs]    def __init__(self, start, end):
"""Construct, start must be <= end."""
self[0:1] = _order((start,end))

start = property(fget=lambda self: self[0], doc="The interval's start")
end = property(fget=lambda self: self[1], doc="The interval's end")

[docs]    def __str__(self):
return '[%s,%s)' % (self.start, self.end)

[docs]    def __repr__(self):
return '[%s,%s)' % (self.start, self.end)

[docs]    def __hash__(self):
return hash(self.start) ^ hash(self.end)

[docs]    def __lt__(self, other):
return self.end<other.start #it has to be < even if ==

[docs]    def __eq__(self,other):
return self.start==other.start and self.end==other.end

@property
def size(self):
return self.end-self.start

@property
def center(self):
return (self.end+self.start)/2

def _combine(self,other):
"""used in several methods below"""
start=max(self.start,other.start)
end=min(self.end,other.end)
return start,end

[docs]    def separation(self, other):
""":return: distance between self and other, negative if overlap"""
start,end=self._combine(other)
return start-end #yes, in this order ...

[docs]    def overlap(self, other, allow_contiguous=False):
""":return: True iff self intersects other."""
d=self.separation(other)
zero=type(d)()
if allow_contiguous and d==zero:
return True
else:
return d<zero

[docs]    def intersection(self, other):
""":return: Intersection with other, or None if no intersection."""
start,end=self._combine(other)
if start>end: #no intersection
return None
return Interval(start, end)

[docs]    def __iadd__(self, other):
"""expands self to contain other."""
if isinstance(other,Interval):
s,e=other.start,other.end
else:
s,e=other,other
self[0]=s if self.start is None else min(self.start,s)
self[1]=e if self.end is None else max(self.end,e)
return self

[docs]    def hull(self, other):
""":return: new Interval containing both self and other."""
res=Interval(self.start,self.end)
res+=other
return res

if self.overlap(other,True):
return self.hull(other)
else:
return Intervals([self,other])

[docs]    def __contains__(self, x):
""":return: True if x in self."""
if isinstance(x,Interval):
return self.start <= x.start and x.end < self.end
else:
return self.start <= x and x < self.end

[docs]    def subset(self, other):
":return: True iff self is subset of other."
return self.start >= other.start and self.end <= other.end

[docs]    def proper_subset(self, other):
":return: True iff self is proper subset of other."
return self.start > other.start and self.end < other.end

[docs]    def empty(self):
":return: True iff self is empty."
return self.start == self.end

[docs]    def __nonzero__(self):
return not self.empty()

[docs]    def singleton(self):
":return: True iff self.end - self.start == 1."
return self.size == 1

[docs]class Intervals(SortedListWithKey):
"""a list of intervals kept in ascending order"""

[docs]    def update(self, iterable):
"""Update the list by adding all elements from *iterable*."""
# overload needed because SortedListWithKey doesn't call add/insert
for item in iterable:

_update = update # defined and used in SortedListWithKey.__init__

[docs]    def add(self, item):
k = self._key(item)
i = self.bisect_left(k)  #item starts before self[i], but overlaps maybe with i, i+1, ... th intervals
if i<len(self) and self[i].overlap(item,True):
item=self.pop(i).hull(item)

return self

[docs]    def insert(self, item):

[docs]    def __call__(self,x):
""" returns intervals containing x"""
for interval in self:
if x in interval:
return interval
return None

[docs]    def __str__(self):
""" string representation : like a list of Intervals"""
return str([x for x in self])

[docs]class Box(list):
"""a N dimensional rectangular box defined by a list of N Intervals"""
[docs]    def __init__(self,*args):
if len(args)==1 and type(args[0]) is int:
super(Box,self).__init__([Interval(None,None) for _ in range(args[0])])
return
if isinstance(args[0],Interval): #works also as copy constructor
super(Box,self).__init__(args)
else: #consider data as points in the box (as in a bounding box)
super(Box,self).__init__([Interval(None,None) for _ in args[0]])
for pt in args:
self+=pt

[docs]    def corner(self,n):
"""return n-th corner of box
0-th corner is "start" made of all minimal values of intervals
-1.th corner is "end", made of all maximal values of intervals
"""
return tuple(inter.end if n&(1<<i) else inter.start for i,inter in enumerate(self))

@property
def start(self):
return tuple(i.start for i in self)

@property
def end(self):
return tuple(i.end for i in self)

min,max=start,end #alias

@property
def size(self):
return tuple(i.size for i in self)

@property
def center(self):
return tuple(i.center for i in self)

[docs]    def __call__(self):
""":return: tuple of all intervals as tuples"""
return tuple(i() for i in self)

[docs]    def __iadd__(self, other):
"""
enlarge box if required to contain specified point
:param other: :class:`Box` or (list of) N-tuple point(s)
"""
for interval,x in zip(self,other):
interval+=x
return self

[docs]    def __add__(self, other):
"""
enlarge box if required to contain specified point
:param other: :class:`Box` or (list of) N-tuple point(s)
:return: new Box containing both
"""
res=Box(self)
res+=other
return res

[docs]    def __contains__(self, other):
""":return: True if x in self."""
return all(x in i for i,x in zip(self,other))

[docs]    def __nonzero__(self):
return any(self)

[docs]    def empty(self):
":return: True iff Box is empty."
return not self

```