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authorjack <[email protected]>2024-06-14 13:13:15 -0600
committerjack <[email protected]>2024-06-14 13:13:15 -0600
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tree96df922dae2a5073d9a50ea70c7aae6aa37e3ebe /num_beautiful_subset.py
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+# 2597. The Number of Beautiful Subsets
+import collections
+
+"""
+given an array 'nums' of positive integers and a positive integer 'k'. a
+subset of 'nums' is beautiful if it does not contain integers with an
+absolute difference equal to 'k'. return the number of non empty beautiful
+subsets of the array 'nums'. a subset of 'nums' is an array that can be
+obtained by deleting some elements from 'nums'. two subsets are different iff
+the chosen indices to delete are different.
+"""
+
+
+class Solution(object):
+ def beautifulSubsets(self, nums, k):
+ """
+ :type nums: List[int]
+ :type k: int
+ :rtype: int
+ """
+ ans = 1
+ freq = collections.defaultdict(collections.Counter)
+ for i in nums:
+ freq[i % k][i] += 1
+ for i in freq.values():
+ prev_num, curr, prev1, prev2 = -k, 1, 1, 0
+ for n in sorted(i):
+ skip = prev1
+ take = (2 ** i[n] - 1) * (prev2 if n - prev_num == k else prev1)
+ curr = skip + take
+ prev2, prev1 = prev1, curr
+ prev_num = n
+ ans *= curr
+ return ans - 1
+
+
+if __name__ == "__main__":
+ obj = Solution()
+ print(obj.beautifulSubsets(nums=[2, 4, 6], k=2))
+ print(obj.beautifulSubsets(nums=[1], k=1))