我有数千行 1 到 100 的数字,每一行都定义了一组数字以及它们之间的关系。 我需要获取相关数字集。
小例子: 如果我有这7行数据
T1 T2
T3
T4
T5
T6 T1
T5 T4
T3 T4 T7
我需要一个不太慢的算法来知道这里的集合是:
T1 T2 T6 (because T1 is related with T2 in the first line and T1 related with T6 in the line 5)
T3 T4 T5 T7 (because T5 is with T4 in line 6 and T3 is with T4 and T7 in line 7)
但是当你有非常大的集合时,在每个大集合中搜索 T(x) 并进行集合的并集...等等会非常慢。
您是否有提示以不那么蛮力的方式执行此操作?
我正尝试在 Python 中执行此操作。
最佳答案
一旦您构建了数据结构,您究竟想要针对它运行哪些查询?向我们展示您现有的代码。什么是 T(x)?您谈论“数字组”,但您的示例数据显示 T1、T2 等;请解释。
你读过这个吗:http://en.wikipedia.org/wiki/Disjoint-set_data_structure
尝试查看这个 Python 实现:http://code.activestate.com/recipes/215912-union-find-data-structure/
或者您可以自行编写一些相当简单易懂的内容,例如
[更新:全新的代码]
class DisjointSet(object):
def __init__(self):
self.leader = {} # maps a member to the group's leader
self.group = {} # maps a group leader to the group (which is a set)
def add(self, a, b):
leadera = self.leader.get(a)
leaderb = self.leader.get(b)
if leadera is not None:
if leaderb is not None:
if leadera == leaderb: return # nothing to do
groupa = self.group[leadera]
groupb = self.group[leaderb]
if len(groupa) < len(groupb):
a, leadera, groupa, b, leaderb, groupb = b, leaderb, groupb, a, leadera, groupa
groupa |= groupb
del self.group[leaderb]
for k in groupb:
self.leader[k] = leadera
else:
self.group[leadera].add(b)
self.leader[b] = leadera
else:
if leaderb is not None:
self.group[leaderb].add(a)
self.leader[a] = leaderb
else:
self.leader[a] = self.leader[b] = a
self.group[a] = set([a, b])
data = """T1 T2
T3 T4
T5 T1
T3 T6
T7 T8
T3 T7
T9 TA
T1 T9"""
# data is chosen to demonstrate each of 5 paths in the code
from pprint import pprint as pp
ds = DisjointSet()
for line in data.splitlines():
x, y = line.split()
ds.add(x, y)
print
print x, y
pp(ds.leader)
pp(ds.group)
这是最后一步的输出:
T1 T9
{'T1': 'T1',
'T2': 'T1',
'T3': 'T3',
'T4': 'T3',
'T5': 'T1',
'T6': 'T3',
'T7': 'T3',
'T8': 'T3',
'T9': 'T1',
'TA': 'T1'}
{'T1': set(['T1', 'T2', 'T5', 'T9', 'TA']),
'T3': set(['T3', 'T4', 'T6', 'T7', 'T8'])}
关于python - 集合联合查找算法,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/3067529/