Create number-of-single-divisor-triplets.py

Author: kamyu104

Python/number-of-single-divisor-triplets.py

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+# Time:  O(d^3), d is the number of distinct nums
+# Space: O(d)
+
+import collections
+import itertools
+
+# combinatorics
+class Solution(object):
+    def singleDivisorTriplet(self, nums):
+        """
+        :type nums: List[int]
+        :rtype: int
+        """
+        def check(a, b, c):
+            return sum((a+b+c)%x == 0 for x in (a, b, c)) == 1
+
+        cnt = collections.Counter(nums)
+        return 6*(sum(cnt[a]*cnt[b]*cnt[c] for a, b, c in itertools.combinations(cnt.keys(), 3) if check(a, b, c)) +
+                  sum(cnt[a]*(cnt[a]-1)//2*cnt[b] for a, b in itertools.permutations(cnt.keys(), 2) if check(a, a, b)))