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from typing import List
class UnionFind:
def __init__(self, data: List, union_condition: callable):
self.__data__ = data
self.__union_condition__ = union_condition
length = len(data)
self.__parents__ = [i for i in range(length)]
self.__ranks__ = [0] * length
self.__unions__ = {}
def __find_parent__(self, id: int):
return self.__parents__[id]
def __find_root__(self, id: int):
parent = self.__find_parent__(id)
while parent != id:
id = parent
parent = self.__find_parent__(id)
return id
def __union__(self, i: int, j: int):
root_i = self.__find_root__(i)
root_j = self.__find_root__(j)
# if roots are different, let one be the parent of the other
if root_i == root_j:
return
else:
if self.__ranks__[root_i] <= self.__ranks__[root_j]:
# root of i --> child
self.__parents__[root_i] = root_j
self.__ranks__[root_j] = max(self.__ranks__[root_j], self.__ranks__[root_i]+1)
else:
self.__parents__[root_j] = root_i
self.__ranks__[root_i] = max(self.__ranks__[root_i], self.__ranks__[root_j]+1)
def union_step(self):
length = len(self.__data__)
for i in range(length - 1):
for j in range(i + 1, length):
if self.__union_condition__(self.__data__[i], self.__data__[j]):
self.__union__(i, j)
for i in range(length):
root = self.__find_root__(i)
if root not in self.__unions__.keys():
self.__unions__[root] = [self.__data__[i]]
else:
self.__unions__[root].append(self.__data__[i])
def get_unions(self):
return self.__unions__
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