计算集合列表中所有组合的交叉点

Question

我有一组集合。 我想找到每个组合组合中仅在交叉点中找到的项目数。 我基本上想做与在维恩图中创建数字相同的事情。

一个基本的例子可能会让它更清晰。

a = set(1,2,5,10,12)
b = set(1,2,6,9,12,15)
c = set(1,2,7,8,15)

我最终应该只找到以下项目：

• 一个
• b
• C
• a和b的交点
• a和c的交集
• b和c的交点
• a，b和c的交集

这是一种不可扩展的方法

num_a = len(a - b - c)  # len(set([5,10])) -> 2
num_b = len(b - a - c)  # len(set([6,9])) -> 2
num_c = len(c - a - b)  # len(set([7,8])) -> 2

num_ab = len((a & b) - c)  # 1
num_ac = len((a & c) - b)  # 0
num_bc = len((b & c) - a)  # 1

num_abc = len(a & b & c)  # 2

虽然这适用于3集，但我的集合集并不是静态的。

Answer 1

IIUC，这样的事情应该有效：

from itertools import combinations

def venn_count(named_sets):
    names = set(named_sets)
    for i in range(1, len(named_sets)+1):
        for to_intersect in combinations(sorted(named_sets), i):
            others = names.difference(to_intersect)
            intersected = set.intersection(*(named_sets[k] for k in to_intersect))
            unioned = set.union(*(named_sets[k] for k in others)) if others else set()
            yield to_intersect, others, len(intersected - unioned)


ns = {"a": {1,2,5,10,12}, "b": {1,2,6,9,12,15}, "c": {1,2,7,8,15}}
for intersected, unioned, count in venn_count(ns):
    print 'len({}{}) = {}'.format(' & '.join(sorted(intersected)),
                                  ' - ' + ' - '.join(sorted(unioned)) if unioned else '',
                                  count)

这使

len(a - b - c) = 2
len(b - a - c) = 2
len(c - a - b) = 2
len(a & b - c) = 1
len(a & c - b) = 0
len(b & c - a) = 1
len(a & b & c) = 2

Answer 2

您可以使用itertools.combinations获取所有可能的组合。 http://docs.python.org/2/library/itertools.html

Answer 3

我尝试使用位掩码：

sets = [
    set([1,2,5,10,12]),
    set([1,2,6,9,12,15]),
    set([1,2,7,8,15]),
]

d = {}

for n, s in enumerate(sets):
    for i in s:
        d[i] = d.get(i, 0) | (1 << n)

for mask in range(1, 2**len(sets)):
    cnt = sum(1 for x in d.values() if x & mask == mask)
    num = ','.join(str(j) for j in range(len(sets)) if mask & (1 << j))
    print 'number of items in set(s) %s = %d' % (num, cnt)

您输入的结果：

number of items in set(s) 0 = 5
number of items in set(s) 1 = 6
number of items in set(s) 0,1 = 3
number of items in set(s) 2 = 5
number of items in set(s) 0,2 = 2
number of items in set(s) 1,2 = 3
number of items in set(s) 0,1,2 = 2