"""intervals
Union, intersection, set difference and symmetric difference
of possibly overlapping or touching integer intervals.
Intervals are defined right-open. (1, 4) -> 1, 2, 3
e.g.
union([(1, 4), (7, 9)], (3, 5)) -> [(1, 5), (7, 9)]
intersection([(1, 4), (7, 9)], (3, 5)) -> [(3, 4)]
set_difference([(1, 4), (7, 9)], (3, 5)) -> [(1, 3), (7, 9)]
set_difference([(3, 5)], [(1, 4), (7, 9)]) -> [(4, 5)]
symmetric_difference([(1, 4), (7, 9)], (3, 5)) -> [(1, 3), (4, 5), (7, 9)]
see: http://e...content-available-to-author-only...a.org/wiki/Set_theory#Basic_concepts_and_notation
"""
import copy
from collections import namedtuple
from itertools import accumulate, chain, islice, repeat
from operator import itemgetter
import unittest
class Intervals( object ) :
"""Holds a non overlapping list of intervals.
One single interval is just a pair.
Overlapping or touching intervals are automatically merged.
"""
def __init__ ( self , interval_list= ( ) ) :
"""Raises a ValueError if the length of one of the
intervals in the list is negative.
"""
if any ( begin > end for begin, end in interval_list) :
raise ValueError ( 'Invalid interval' )
self ._interval_list = _merge_interval_lists(
interval_list, [ ] , OP_UNION)
def __repr__ ( self ) :
"""Just write out all included intervals.
"""
return 'Intervals ' + str ( self ._interval_list)
def get( self , copy_content= True ) :
"""Return the list of intervals.
"""
return copy .copy ( self ._interval_list) if copy_content\
else self ._interval_list
def union( a, b) :
"""Merge a and b (union).
"""
return Intervals( _merge_interval_lists(
a.get ( False ) , b.get ( False ) , OP_UNION) )
def intersections( a, b) :
"""Intersects a and b.
"""
return Intervals( _merge_interval_lists(
a.get ( False ) , b.get ( False ) , merge_type= OP_INTERSECTIONS) )
def set_difference( a, b) :
"""Removes b from a.
Set difference is not commutative.
"""
return Intervals( _merge_interval_lists(
a.get ( False ) , b.get ( False ) , merge_type= OP_SET_DIFFERENCE) )
def symmetric_difference( a, b) :
"""Symmetric difference of a and b.
"""
return Intervals( _merge_interval_lists(
a.get ( False ) , b.get ( False ) , merge_type= OP_SYMMETRIC_DIFFERENCE) )
def compose( func_1, func_2, unpack= False ) :
"""
compose(func_1, func_2, unpack=False) -> function
The function returned by compose is a composition of func_1 and func_2.
That is, compose(func_1, func_2)(5) == func_1(func_2(5)).
"""
if not callable ( func_1) :
raise TypeError ( "First argument to compose must be callable." )
if not callable ( func_2) :
raise TypeError ( "Second argument to compose must be callable." )
if unpack:
def composition( *args, **kwargs) :
return func_1( *func_2( *args, **kwargs) )
else :
def composition( *args, **kwargs) :
return func_1( func_2( *args, **kwargs) )
return composition
# Helper to avoid repetitive lambdas.
def check_for( cond) :
return lambda val: val == cond
# http://e...content-available-to-author-only...a.org/wiki/Identity_function
identity = lambda x: x
# Depending on the operation carried out,
# the criteria for interval begins and ends in the result differ.
# E.g:
# a = | - - - - | | - - - |
# b = | - - - - |
# counts = 1 2 1 0 1 0 (union, intersection, sym diff)
# counts = 1 0 -1 0 1 0 (set diff)
# union = | - - - - - - | | - - - |
# inter = | - - - - |
# sym d = | - |
# set d = | - | | - - - |
#
# One can see that union begins if the count changes from 0 to 1
# and ends if the count changes from 1 to 0
# An intersection begins at a change from 1 to 2 and ends with 2 to 1.
# A symmetric difference begins at every change to one
# and ends at every change away from one.
# The conditions for the set difference are the same as for the union.
set_op = namedtuple( 'set_op' , [ 'transform' , 'begin' , 'end' ] )
OP_UNION = set_op(
transform = identity,
begin = check_for( ( 0 , 1 ) ) ,
end = check_for( ( 1 , 0 ) ) )
OP_INTERSECTIONS = set_op(
transform = identity,
begin = check_for( ( 1 , 2 ) ) ,
end = check_for( ( 2 , 1 ) ) )
OP_SYMMETRIC_DIFFERENCE = set_op(
transform = identity,
begin = lambda change: change[ 1 ] == 1 ,
end = lambda change: change[ 1 ] != 1 )
OP_SET_DIFFERENCE = set_op(
# If we want to calculate the set difference
# we invert the second interval list,
# i.e. swap begin and end.
transform = compose( tuple , reversed ) ,
begin = check_for( ( 0 , 1 ) ) ,
end = check_for( ( 1 , 0 ) ) )
# class Intervals makes sure, by always building the union first,
# that no invalid a's or b's are fed here.
def _merge_interval_lists( a, b, merge_type) :
"""Merges two lists of intervals in O(n*log(n)).
Overlapping or touching intervals are simplified to one.
Arguments:
a and b -- The interval lists to merge.
merge_type -- Can be:
OP_UNION,
OP_INTERSECTIONS,
OP_SYMMETRIC_DIFFERENCE, or
OP_SET_DIFFERENCE.
Return the sorted result as a list.
"""
# Adjust the operand for the selected operator.
b = map ( merge_type.transform , b)
# Separately sort begins and ends
# and pair them with the implied change
# of the count of currently open intervals.
# e.g. (1, 4), (7, 9), (3, 5) ->
# begins = [(1, 1), (3, 1), (7, 1)]
# ends = [(4, -1), (5, -1), (9, -1)]
both = list ( chain( a, b) )
begins = zip ( sorted ( map ( itemgetter( 0 ) , both) ) ,
repeat( 1 ) )
ends = zip ( sorted ( map ( itemgetter( 1 ) , both) ) ,
repeat( -1 ) )
# Sort begins and ends together.
# If the value is the same, begins come before ends
# to ensure touching intervals being merged to one.
# In our example above this means:
# edges = [(1, 4), (3, 1), (4, -1), (5, -1), (7, 1), (9, -1)]
edges = sorted ( chain( begins, ends) , key= lambda x: ( x[ 0 ] , -x[ 1 ] ) )
# The number of opened intervals after each edge.
counts = list ( accumulate( map ( itemgetter( 1 ) , edges) ) )
# The changes of opened intervals at each edge.
changes = zip ( chain( [ 0 ] , counts) , counts)
# Just the x positions of the edges.
xs = map ( itemgetter( 0 ) , edges)
xs_and_changes = list ( zip ( xs, changes) )
# Now we filter out the begins and ends from the changes
# and get their x positions.
res_begins = map ( itemgetter( 0 ) ,
starfilter( lambda x, change: merge_type.begin ( change) ,
xs_and_changes) )
res_ends = map ( itemgetter( 0 ) ,
starfilter( lambda x, change: merge_type.end ( change) ,
xs_and_changes) )
# The result is then just pairing up the sorted begins and ends.
result = pairwise( sorted ( chain( res_begins, res_ends) ) , False )
# No empty intervals in the result.
def length_greater_than_zero( interval) :
return interval[ 0 ] < interval[ 1 ]
return list ( filter ( length_greater_than_zero, result) )
class TestIntervals( unittest .TestCase ) :
def test_ctor( self ) :
# Check ctors sanity check.
self .assertRaises ( ValueError , Intervals, [ ( 2 , 4 ) , ( 3 , 1 ) ] )
def test_add_behind( self ) :
# Check adding right of the last interval.
intervals = Intervals( [ ( 0 , 2 ) ] )
intervals = union( intervals, Intervals( [ ( 3 , 4 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 0 , 2 ) , ( 3 , 4 ) ] )
def test_add_in_front( self ) :
# Check adding left to the first interval.
intervals = Intervals( [ ( 3 , 4 ) ] )
intervals = union( intervals, Intervals( [ ( 1 , 2 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 1 , 2 ) , ( 3 , 4 ) ] )
def test_add_in_between( self ) :
# Check adding between two intervals.
intervals = Intervals( [ ( 1 , 2 ) ] )
intervals = union( intervals, Intervals( [ ( 6 , 9 ) ] ) )
intervals = union( intervals, Intervals( [ ( 3 , 5 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 1 , 2 ) , ( 3 , 5 ) , ( 6 , 9 ) ] )
def test_add_touching( self ) :
# Check adding a interval touching an existing one.
intervals = Intervals( [ ( 1 , 3 ) ] )
intervals = union( intervals, Intervals( [ ( 3 , 5 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 1 , 5 ) ] )
def test_add_overlapping( self ) :
# Check adding a interval overlapping an existing one.
intervals = Intervals( [ ( 1 , 4 ) ] )
intervals = union( intervals, Intervals( [ ( 3 , 5 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 1 , 5 ) ] )
def test_add_overlapping_multiple( self ) :
# Check adding a interval overlapping multiple existing ones.
intervals = Intervals( [ ( 1 , 4 ) ] )
intervals = union( intervals, Intervals( [ ( 5 , 7 ) ] ) )
intervals = union( intervals, Intervals( [ ( 8 , 10 ) ] ) )
intervals = union( intervals, Intervals( [ ( 3 , 9 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 1 , 10 ) ] )
def test_add_swallow( self ) :
# Check adding a interval completely covering an existing one.
intervals = Intervals( [ ( 2 , 3 ) ] )
intervals = union( intervals, Intervals( [ ( 1 , 4 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 1 , 4 ) ] )
def test_sub( self ) :
# Check removing an interval
intervals = Intervals( [ ( 0 , 3 ) ] )
intervals = union( intervals, Intervals( [ ( 5 , 7 ) ] ) )
intervals = set_difference( intervals, Intervals( [ ( 2 , 6 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 0 , 2 ) , ( 6 , 7 ) ] )
def test_intersections( self ) :
# Check adding right of the last interval.
intervals = Intervals( [ ( 0 , 3 ) ] )
intervals = union( intervals, Intervals( [ ( 5 , 7 ) ] ) )
intervals = intersections( intervals, Intervals( [ ( 2 , 6 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 2 , 3 ) , ( 5 , 6 ) ] )
def test_symmetric_difference( self ) :
# Check symmetric difference
intervals = Intervals( [ ( 0 , 3 ) ] )
intervals = union( intervals, Intervals( [ ( 5 , 7 ) ] ) )
intervals = symmetric_difference( intervals, Intervals( [ ( 2 , 6 ) ] ) )
self .assertEqual ( intervals.get ( ) , [ ( 0 , 2 ) , ( 3 , 5 ) , ( 6 , 7 ) ] )
def tuple_wise( iterable, size, step) :
"""Tuples up the elements of iterable.
Arguments:
iterable -- source data
size -- size of the destination tuples
step -- step to do in iterable per destination tuple
tuple_wise(s, 3, 1): "s -> (s0,s1,s2), (s1,s2,s3), (s3,s4,s5), ...
tuple_wise(s, 2, 4): "s -> (s0,s1), (s4,s5), (s8,s9), ...
"""
return zip (
*( islice( iterable, start, None , step)
for start in range ( size) ) )
def pairwise( iterable, overlapping) :
"""Pairs up the elements of iterable.
overlapping: "s -> (s0,s1), (s2,s3), (s4,s5), ...
not overlapping: "s -> (s0,s1), (s1,s2), (s2,s3), ...
"""
return tuple_wise( iterable, 2 , 1 if overlapping else 2 )
def starfilter( function, iterable) :
"""starfilter <--> filter == starmap <--> map"""
return ( item for item in iterable if function( *item) )
if __name__ == '__main__' :
unittest .main ( verbosity= 2 )
"""intervals

Union, intersection, set difference and symmetric difference
of possibly overlapping or touching integer intervals.
Intervals are defined right-open. (1, 4) -> 1, 2, 3

e.g.
union([(1, 4), (7, 9)], (3, 5)) -> [(1, 5), (7, 9)]
intersection([(1, 4), (7, 9)], (3, 5)) -> [(3, 4)]
set_difference([(1, 4), (7, 9)], (3, 5)) -> [(1, 3), (7, 9)]
set_difference([(3, 5)], [(1, 4), (7, 9)]) -> [(4, 5)]
symmetric_difference([(1, 4), (7, 9)], (3, 5)) -> [(1, 3), (4, 5), (7, 9)]

see: http://e...content-available-to-author-only...a.org/wiki/Set_theory#Basic_concepts_and_notation
"""

import copy
from collections import namedtuple
from itertools import accumulate, chain, islice, repeat
from operator import itemgetter
import unittest

class Intervals(object):
    """Holds a non overlapping list of intervals.
    One single interval is just a pair.
    Overlapping or touching intervals are automatically merged.
    """

    def __init__(self, interval_list=()):
        """Raises a ValueError if the length of one of the
        intervals in the list is negative.
        """
        if any(begin > end for begin, end in interval_list):
                raise ValueError('Invalid interval')
        self._interval_list = _merge_interval_lists(
                interval_list, [], OP_UNION)

    def __repr__(self):
        """Just write out all included intervals.
        """
        return 'Intervals ' + str(self._interval_list)

    def get(self, copy_content=True):
        """Return the list of intervals.
        """
        return copy.copy(self._interval_list) if copy_content\
                else self._interval_list


def union(a, b):
    """Merge a and b (union).
    """
    return Intervals(_merge_interval_lists(
        a.get(False), b.get(False), OP_UNION))

def intersections(a, b):
    """Intersects a and b.
    """
    return Intervals(_merge_interval_lists(
         a.get(False), b.get(False), merge_type=OP_INTERSECTIONS))

def set_difference(a, b):
    """Removes b from a.
    Set difference is not commutative.
    """
    return Intervals(_merge_interval_lists(
            a.get(False), b.get(False), merge_type=OP_SET_DIFFERENCE))

def symmetric_difference(a, b):
    """Symmetric difference of a and b.
    """
    return Intervals(_merge_interval_lists(
            a.get(False), b.get(False), merge_type=OP_SYMMETRIC_DIFFERENCE))


def compose(func_1, func_2, unpack=False):
    """
    compose(func_1, func_2, unpack=False) -> function

    The function returned by compose is a composition of func_1 and func_2.
    That is, compose(func_1, func_2)(5) == func_1(func_2(5)).
    """
    if not callable(func_1):
        raise TypeError("First argument to compose must be callable.")
    if not callable(func_2):
        raise TypeError("Second argument to compose must be callable.")

    if unpack:
        def composition(*args, **kwargs):
            return func_1(*func_2(*args, **kwargs))
    else:
        def composition(*args, **kwargs):
            return func_1(func_2(*args, **kwargs))
    return composition


# Helper to avoid repetitive lambdas.
def check_for(cond):
    return lambda val: val == cond

# http://e...content-available-to-author-only...a.org/wiki/Identity_function
identity = lambda x: x


# Depending on the operation carried out,
# the criteria for interval begins and ends in the result differ.
# E.g:
#      a = | - - - - |      | - - - |
#      b =     | - - - - |
# counts = 1   2     1   0  1       0   (union, intersection, sym diff)
# counts = 1   0    -1   0  1       0   (set diff)
# union  = | - - - - - - |  | - - - |
# inter  =     | - - - - |
# sym d  =           | - |
# set d  = | - |            | - - - |
#
# One can see that union begins if the count changes from 0 to 1
# and ends if the count changes from 1 to 0
# An intersection begins at a change from 1 to 2 and ends with 2 to 1.
# A symmetric difference begins at every change to one
# and ends at every change away from one.
# The conditions for the set difference are the same as for the union.
set_op = namedtuple('set_op', ['transform', 'begin', 'end'])

OP_UNION = set_op(
    transform = identity,
    begin = check_for((0, 1)),
    end = check_for((1, 0)))

OP_INTERSECTIONS = set_op(
    transform = identity,
    begin = check_for((1, 2)),
    end = check_for((2, 1)))

OP_SYMMETRIC_DIFFERENCE = set_op(
    transform = identity,
    begin = lambda change: change[1] == 1,
    end = lambda change: change[1] != 1)

OP_SET_DIFFERENCE = set_op(
    # If we want to calculate the set difference
    # we invert the second interval list,
    # i.e. swap begin and end.
    transform = compose(tuple, reversed),
    begin = check_for((0, 1)),
    end = check_for((1, 0)))


# class Intervals makes sure, by always building the union first,
# that no invalid a's or b's are fed here.
def _merge_interval_lists(a, b, merge_type):
    """Merges two lists of intervals in O(n*log(n)).
    Overlapping or touching intervals are simplified to one.

    Arguments:
    a and b -- The interval lists to merge.
    merge_type -- Can be:
                  OP_UNION,
                  OP_INTERSECTIONS,
                  OP_SYMMETRIC_DIFFERENCE, or
                  OP_SET_DIFFERENCE.

    Return the sorted result as a list.
    """

    # Adjust the operand for the selected operator.
    b = map(merge_type.transform, b)

    # Separately sort begins and ends
    # and pair them with the implied change
    # of the count of currently open intervals.
    # e.g. (1, 4), (7, 9), (3, 5) ->
    #     begins = [(1, 1), (3, 1), (7, 1)]
    #     ends = [(4, -1), (5, -1), (9, -1)]
    both = list(chain(a, b))
    begins = zip(sorted(map(itemgetter(0), both)),
            repeat(1))
    ends = zip(sorted(map(itemgetter(1), both)),
            repeat(-1))

    # Sort begins and ends together.
    # If the value is the same, begins come before ends
    # to ensure touching intervals being merged to one.
    # In our example above this means:
    # edges = [(1, 4), (3, 1), (4, -1), (5, -1), (7, 1), (9, -1)]
    edges = sorted(chain(begins, ends), key=lambda x: (x[0], -x[1]))

    # The number of opened intervals after each edge.
    counts = list(accumulate(map(itemgetter(1), edges)))
    # The changes of opened intervals at each edge.
    changes = zip(chain([0], counts), counts)
    # Just the x positions of the edges.
    xs = map(itemgetter(0), edges)
    xs_and_changes = list(zip(xs, changes))

    # Now we filter out the begins and ends from the changes
    # and get their x positions.
    res_begins = map(itemgetter(0),
            starfilter(lambda x, change: merge_type.begin(change),
                xs_and_changes))
    res_ends = map(itemgetter(0),
            starfilter(lambda x, change: merge_type.end(change),
                xs_and_changes))

    # The result is then just pairing up the sorted begins and ends.
    result = pairwise(sorted(chain(res_begins, res_ends)), False)

    # No empty intervals in the result.
    def length_greater_than_zero(interval):
        return interval[0] < interval[1]

    return list(filter(length_greater_than_zero, result))


class TestIntervals(unittest.TestCase):

    def test_ctor(self):
        # Check ctors sanity check.
        self.assertRaises(ValueError, Intervals, [(2, 4), (3, 1)])

    def test_add_behind(self):
        # Check adding right of the last interval.
        intervals = Intervals([(0, 2)])
        intervals = union(intervals, Intervals([(3, 4)]))
        self.assertEqual(intervals.get(), [(0, 2), (3, 4)])

    def test_add_in_front(self):
        # Check adding left to the first interval.
        intervals = Intervals([(3, 4)])
        intervals = union(intervals, Intervals([(1, 2)]))
        self.assertEqual(intervals.get(), [(1, 2), (3, 4)])

    def test_add_in_between(self):
        # Check adding between two intervals.
        intervals = Intervals([(1, 2)])
        intervals = union(intervals, Intervals([(6, 9)]))
        intervals = union(intervals, Intervals([(3, 5)]))
        self.assertEqual(intervals.get(), [(1, 2), (3, 5), (6, 9)])

    def test_add_touching(self):
        # Check adding a interval touching an existing one.
        intervals = Intervals([(1, 3)])
        intervals = union(intervals, Intervals([(3, 5)]))
        self.assertEqual(intervals.get(), [(1, 5)])

    def test_add_overlapping(self):
        # Check adding a interval overlapping an existing one.
        intervals = Intervals([(1, 4)])
        intervals = union(intervals, Intervals([(3, 5)]))
        self.assertEqual(intervals.get(), [(1, 5)])

    def test_add_overlapping_multiple(self):
        # Check adding a interval overlapping multiple existing ones.
        intervals = Intervals([(1, 4)])
        intervals = union(intervals, Intervals([(5, 7)]))
        intervals = union(intervals, Intervals([(8, 10)]))
        intervals = union(intervals, Intervals([(3, 9)]))
        self.assertEqual(intervals.get(), [(1, 10)])

    def test_add_swallow(self):
        # Check adding a interval completely covering an existing one.
        intervals = Intervals([(2, 3)])
        intervals = union(intervals, Intervals([(1, 4)]))
        self.assertEqual(intervals.get(), [(1, 4)])

    def test_sub(self):
        # Check removing an interval
        intervals = Intervals([(0, 3)])
        intervals = union(intervals, Intervals([(5, 7)]))
        intervals = set_difference(intervals, Intervals([(2, 6)]))
        self.assertEqual(intervals.get(), [(0, 2), (6, 7)])

    def test_intersections(self):
        # Check adding right of the last interval.
        intervals = Intervals([(0, 3)])
        intervals = union(intervals, Intervals([(5, 7)]))
        intervals = intersections(intervals, Intervals([(2, 6)]))
        self.assertEqual(intervals.get(), [(2, 3), (5, 6)])

    def test_symmetric_difference(self):
        # Check symmetric difference
        intervals = Intervals([(0, 3)])
        intervals = union(intervals, Intervals([(5, 7)]))
        intervals = symmetric_difference(intervals, Intervals([(2, 6)]))
        self.assertEqual(intervals.get(), [(0, 2), (3, 5), (6, 7)])



def tuple_wise(iterable, size, step):
    """Tuples up the elements of iterable.

    Arguments:
    iterable -- source data
    size -- size of the destination tuples
    step -- step to do in iterable per destination tuple

    tuple_wise(s, 3, 1): "s -> (s0,s1,s2), (s1,s2,s3), (s3,s4,s5), ...
    tuple_wise(s, 2, 4): "s -> (s0,s1), (s4,s5), (s8,s9), ...
    """
    return zip(
            *(islice(iterable, start, None, step)
            for start in range(size)))

def pairwise(iterable, overlapping):
    """Pairs up the elements of iterable.
    overlapping: "s -> (s0,s1), (s2,s3), (s4,s5), ...
    not overlapping: "s -> (s0,s1), (s1,s2), (s2,s3), ...
    """
    return tuple_wise(iterable, 2, 1 if overlapping else 2)

def starfilter(function, iterable):
    """starfilter <--> filter  ==  starmap <--> map"""
    return (item for item in iterable if function(*item))


if __name__ == '__main__':
    unittest.main(verbosity=2)