Create 238_product_of_array_except_self.md

Author: Joseph Luce

leetcode/medium/238_product_of_array_except_self.md

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+# 238. Product of Array Except Self
+
+## Dynamic Programming Approach
+- Runtime: O(N)
+- Space: O(N)
+- N = Number of elements in array
+
+The idea is to calculate the products going from left to right, then again going right to left.
+Storing these calculations as two arrays will allow one last calculation to find the products from the left and right for each number.
+
+```
+class Solution:
+    def productExceptSelf(self, nums: List[int]) -> List[int]:
+        if len(nums) == 0:
+            return []
+        left, right = self.calc_left_product(nums), self.calc_left_product(nums[::-1])[::-1]
+        result = [1]*len(nums)
+        for index, n in enumerate(zip(left, right)):
+            result[index] = n[0]*n[1]
+        return result
+        
+    def calc_left_product(self, nums):
+        result = [1]*len(nums)
+        curr_prod = nums[0]
+        for index, n in enumerate(nums[1:], 1):
+            result[index] = curr_prod
+            curr_prod *= n
+        return result
+```