我试图做一些不同的事情:这个算法为每个集合循环一次,为每个元素循环一次:
# Our test sets
setA = set([0,1,2])
setB = set([6,7,8,9])
setC = set([4,5,6])
setD = set([3,4,5,0])
setE = set([10,11,12])
setF = set([11,13,14,15])
setG = set([16,17,18,19])
list_of_sets = [setA,setB,setC,setD,setE,setF,setG]
# We will use a map to store our new merged sets.
# This map will work as an reference abstraction, so it will
# map set ids to the set or to other set id.
# This map may have an indirection level greater than 1
merged_sets = {}
# We will also use a map between indexes and set ids.
index_to_id = {}
# Given a set id, returns an equivalent set id that refers directly
# to a set in the merged_sets map
def resolve_id(id):
if not isinstance(id, (int, long)):
return None
while isinstance(merged_sets[id], (int, long)):
id = merged_sets[id]
return id
# Points the informed set to the destination id
def link_id(id_source, id_destination):
point_to = merged_sets[id_source]
merged_sets[id_source] = id_destination
if isinstance(point_to, (int, long)):
link_id(point_to, id_destination)
empty_set_found = False
# For each set
for current_set_id, current_set in enumerate(list_of_sets):
if len(current_set) == 0 and empty_set_found:
continue
if len(current_set) == 0:
empty_set_found = True
# Create a set id for the set and place it on the merged sets map
merged_sets[current_set_id] = current_set
# For each index in the current set
possibly_merged_current_set = current_set
for index in current_set:
# See if the index is free, i.e., has not been assigned to any set id
if index not in index_to_id:
# If it is free, then assign the set id to the index
index_to_id[index] = current_set_id
# ... and then go to the next index
else:
# If it is not free, then we may need to merge the sets
# Find out to which set we need to merge the current one,
# ... dereferencing if necessary
id_to_merge = resolve_id(index_to_id[index])
# First we check to see if the assignment is to the current set or not
if id_to_merge == resolve_id(merged_sets[current_set_id]):
continue
# Merge the current set to the one found
print 'Merging %d with %d' % (current_set_id, id_to_merge)
merged_sets[id_to_merge] |= possibly_merged_current_set
possibly_merged_current_set = merged_sets[id_to_merge]
# Map the current set id to the set id of the merged set
link_id(current_set_id, id_to_merge)
# Return all the sets in the merged sets map (ignore the references)
print [x for x in merged_sets.itervalues() if not isinstance(x, (int, long))]
它打印:
Merging 2 with 1
Merging 3 with 0
Merging 3 with 1
Merging 5 with 4
[set([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), set([10, 11, 12, 13, 14, 15]), set([16, 17, 18, 19])]