Create minimum-non-zero-product-of-the-array-elements.py

Author: kamyu104

Python/minimum-non-zero-product-of-the-array-elements.py

@@ -0,0 +1,26 @@
+# Time:  O(min(p, logM))
+# Space: O(1)
+
+class Solution(object):
+    def minNonZeroProduct(self, p):
+        """
+        :type p: int
+        :rtype: int
+        """
+        MOD = 10**9+7
+
+        # max_num = 2^p-1
+        max_num_mod = (pow(2, p, MOD)-1)%MOD  # max_num % MOD
+
+        # pair_product = max_num-1
+        pair_product_mod = (max_num_mod-1)%MOD  # (max_num_mod-1) % MOD
+
+        # since pair_product^MOD % MOD = pair_product_mod^MOD % MOD  = pair_product_mod
+        # => pair_product_mod^(MOD-1) % MOD = 1
+        # => pair_product_mod^(pair_cnt) % MOD = pair_product_mod^(pair_cnt%(MOD-1)) %MOD
+        pair_cnt_mod_m_1 = (pow(2, p-1, MOD-1)-1) % (MOD-1)  # pair_cnt%(MOD-1)
+
+        # the ans is:
+        #   max_num * pair_product^pair_cnt % MOD
+        # = max_num_mod * pair_product_mod^(pair_cnt_mod_m_1) % MOD
+        return (max_num_mod*pow(pair_product_mod, pair_cnt_mod_m_1, MOD)) % MOD