From c829dd4896423bf2aca3356546f19fff1dccf351 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sun, 28 Feb 2021 13:17:09 -0800
Subject: [PATCH] Add more explanation

---
 .../get_products_of_all_other_elements.rb     | 24 ++++++++++++++++++-
 1 file changed, 23 insertions(+), 1 deletion(-)

diff --git a/data_structures/arrays/get_products_of_all_other_elements.rb b/data_structures/arrays/get_products_of_all_other_elements.rb
index 467ac65..0a46f88 100644
--- a/data_structures/arrays/get_products_of_all_other_elements.rb
+++ b/data_structures/arrays/get_products_of_all_other_elements.rb
@@ -5,6 +5,11 @@
 # each element at index `i` of the new array is the product of
 # all the numbers in the original array except the one at `i`.
 
+# Generates prefix products
+# prefix_products[i] contains the product of all the elements to the left
+# Note: for the element at index '0', there are no elements to the left,
+# so the prefix_products[0] would be 1
+
 #
 # 1. Brute force solution
 #
@@ -23,11 +28,22 @@ end
 puts(calculate_products_of_all_other_elements([1, 2, 3]))
 
 #
-# 2. O(n) time and space
+# Approach 2: Left and Right product lists
 # Arrays - Get Products of all other elements in Ruby
 #
 
+# Complexity analysis
+#
+# Time complexity: O(N) where N represents the number of elements in the input
+# array. We use one iteration to construct the array prefix_products, one to construct
+# the array suffix_products and one last to construct the answeranswer array using L and R.
+# Space complexity: O(N) used up by the two intermediate arrays that
+# we constructed to keep track of product of elements to the left and right.
+
 # Generates prefix products
+# prefix_products[i] contains the product of all the elements to the left
+# Note: for the element at index '0', there are no elements to the left,
+# so the prefix_products[0] would be 1
 def build_prefix_products(nums)
   prefix_products = []
 
@@ -43,6 +59,9 @@ def build_prefix_products(nums)
 end
 
 # Generates suffix products
+# suffix_products[i] contains the product of all the elements to the right
+# Note: for the element at index 'length - 1', there are no elements to the right,
+# so the suffix_products[length - 1] would be 1
 def build_suffix_products(nums)
   suffix_products = []
 
@@ -58,6 +77,9 @@ def build_suffix_products(nums)
 end
 
 # Builds output
+# For the first element, suffix_products[i] would be product except self
+# For the last element of the array, product except self would be prefix_products[i]
+# Else, multiple product of all elements to the left and to the right
 def output(prefix_products, suffix_products, nums)
   result = []