Create maximize-number-of-nice-divisors.py

Author: kamyu104

Python/maximize-number-of-nice-divisors.py

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+# Time:  O(logn)
+# Space: O(1)
+
+# variant of "343. integer break"
+class Solution(object):
+    def maxNiceDivisors(self, primeFactors):
+        """
+        :type primeFactors: int
+        :rtype: int
+        """
+        # given a1 + a2 + ... + ak <= n, find max of a1 * a2 * ... * ak 
+        # => given a1 + a2 + ... + ak = n, find max of a1 * a2 * ... * ak 
+        # => ai is either 3 or 2, see proof in "343. integer break"
+        MOD = 10**9 + 7
+        if primeFactors <= 3:
+            return primeFactors
+        if primeFactors % 3 == 0:  # 6 => 3*3
+            return pow(3, primeFactors//3, MOD)
+        if primeFactors % 3 == 1:  # 4 => 2*2 
+            return (2*2*pow(3, (primeFactors-4)//3, MOD)) % MOD
+        return (2*pow(3, (primeFactors-2)//3, MOD)) % MOD  # 5 => 2*3