-
Notifications
You must be signed in to change notification settings - Fork 0
/
2597. The Number of Beautiful Subsets.py
50 lines (45 loc) · 1.38 KB
/
2597. The Number of Beautiful Subsets.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
# e.g. nums = [2, 3, 4, 4], k = 2
#
# subset[0] = [2, 4, 4']
# subset[1] = [1]
# count = {2: 1, 4: 2, 1: 1}
#
# Initially, skip = len([]) = 0, pick = len([]) = 0
#
# * For values in subset[0]:
# After 2:
# skip = skip + pick = len([]) = 0
# pick = (2^count[2] - 1) * (1 + skip + pick)
# = len([[2]]) * len([[]])
# = len([[2]]) = 1
# After 4:
# skip = skip + pick = len([[2]]) = 1
# pick = (2^count[4] - 1) * (1 + skip)
# = len([[4], [4'], [4, 4']]) * len([[]])
# = len([[4], [4'], [4, 4']]) = 3
#
# * For values in subset[1]:
# After 1:
# skip = skip + pick
# = len([[2], [4], [4'], [4, 4']]) = 4
# pick = (2^count[1] - 1) * (1 + skip + pick)
# = len([[1]]) * len([[], [2], [4], [4'], [4, 4']])
# = len([[1], [1, 2], [1, 4], [1, 4'], [1, 4, 4']]) = 5
#
# So, ans = skip + pick = 9
class Solution:
def beautifulSubsets(self, nums: List[int], k: int) -> int:
count = collections.Counter(nums)
modToSubset = collections.defaultdict(set)
for num in nums:
modToSubset[num % k].add(num)
prevNum = -k
skip = 0
pick = 0
for subset in modToSubset.values():
for num in sorted(subset):
nonEmptyCount = 2**count[num] - 1
skip, pick = skip + pick, nonEmptyCount * \
(1 + skip + (0 if num - prevNum == k else pick))
prevNum = num
return skip + pick