From 989e20d15ee85cbbc372c79801d17a4a44733bef Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Mon, 22 Mar 2021 09:00:58 -0700
Subject: [PATCH 01/83] Add shuffle array challenge

---
 DIRECTORY.md                            |  1 +
 data_structures/arrays/shuffle_array.rb | 36 +++++++++++++++++++++++++
 2 files changed, 37 insertions(+)
 create mode 100644 data_structures/arrays/shuffle_array.rb

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 5983249..4eb3612 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -13,6 +13,7 @@
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
+    * [Shuffle Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/shuffle_array.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
     * [Two Sum Ii](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum_ii.rb)
diff --git a/data_structures/arrays/shuffle_array.rb b/data_structures/arrays/shuffle_array.rb
new file mode 100644
index 0000000..93efa84
--- /dev/null
+++ b/data_structures/arrays/shuffle_array.rb
@@ -0,0 +1,36 @@
+# Challenge name: Shuffle the array
+# Given the array nums consisting of 2n elements
+# in the form [x1,x2,...,xn,y1,y2,...,yn].
+# Return the array in the form [x1,y1,x2,y2,...,xn,yn].
+# Example 1:
+#
+# Input: nums = [2,5,1,3,4,7], n = 3
+# Output: [2,3,5,4,1,7]
+# Explanation: Since x1=2, x2=5, x3=1, y1=3, y2=4, y3=7 then the answer is [2,3,5,4,1,7].
+#
+# Example 2:
+#
+# Input: nums = [1,2,3,4,4,3,2,1], n = 4
+# Output: [1,4,2,3,3,2,4,1]
+#
+# Example 3:
+#
+# Input: nums = [1,1,2,2], n = 2
+# Output: [1,2,1,2]
+# @param {Integer[]} nums
+# @param {Integer} n
+# @return {Integer[]}
+def shuffle(nums, n)
+end
+nums = [2, 5, 1, 3, 4, 7]
+n = 3
+print(shuffle(nums, n))
+# Output: [2,3,5,4,1,7]
+nums = [1, 2, 3, 4, 4, 3, 2, 1]
+n = 4
+print(shuffle(nums, n))
+# Output: [1,4,2,3,3,2,4,1]
+nums = [1, 1, 2, 2]
+n = 2
+print(shuffle(nums, n))
+# Output: [1,2,1,2]
\ No newline at end of file

From 16fd8c756ff5508c611bf42173a9fc998c3f5e8e Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Tue, 23 Mar 2021 08:42:36 -0700
Subject: [PATCH 02/83] Add solution using a new array

---
 data_structures/arrays/shuffle_array.rb | 18 +++++++++++++++---
 1 file changed, 15 insertions(+), 3 deletions(-)

diff --git a/data_structures/arrays/shuffle_array.rb b/data_structures/arrays/shuffle_array.rb
index 93efa84..b4c6431 100644
--- a/data_structures/arrays/shuffle_array.rb
+++ b/data_structures/arrays/shuffle_array.rb
@@ -1,27 +1,39 @@
 # Challenge name: Shuffle the array
+#
 # Given the array nums consisting of 2n elements
 # in the form [x1,x2,...,xn,y1,y2,...,yn].
 # Return the array in the form [x1,y1,x2,y2,...,xn,yn].
-# Example 1:
 #
+# Example 1:
 # Input: nums = [2,5,1,3,4,7], n = 3
 # Output: [2,3,5,4,1,7]
 # Explanation: Since x1=2, x2=5, x3=1, y1=3, y2=4, y3=7 then the answer is [2,3,5,4,1,7].
 #
 # Example 2:
-#
 # Input: nums = [1,2,3,4,4,3,2,1], n = 4
 # Output: [1,4,2,3,3,2,4,1]
 #
 # Example 3:
-#
 # Input: nums = [1,1,2,2], n = 2
 # Output: [1,2,1,2]
+#
 # @param {Integer[]} nums
 # @param {Integer} n
 # @return {Integer[]}
+
+#
+# Approach 1: New Array
+#
+# Time Complexity: O(N)
+#
 def shuffle(nums, n)
+  result = []
+  (0..n-1).count do |i|
+    result.push(nums[i], nums[i+n])
+  end
+  result
 end
+
 nums = [2, 5, 1, 3, 4, 7]
 n = 3
 print(shuffle(nums, n))

From a8f816f984ad98f59942aae06eff775816bf83f8 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Wed, 24 Mar 2021 08:12:31 -0700
Subject: [PATCH 03/83] Add solution using Ruby methods

---
 data_structures/arrays/shuffle_array.rb | 28 +++++++++++++++++++++++++
 1 file changed, 28 insertions(+)

diff --git a/data_structures/arrays/shuffle_array.rb b/data_structures/arrays/shuffle_array.rb
index b4c6431..2f1b13f 100644
--- a/data_structures/arrays/shuffle_array.rb
+++ b/data_structures/arrays/shuffle_array.rb
@@ -34,6 +34,34 @@ def shuffle(nums, n)
   result
 end
 
+# nums = [2, 5, 1, 3, 4, 7]
+# n = 3
+# print(shuffle(nums, n))
+# # Output: [2,3,5,4,1,7]
+# nums = [1, 2, 3, 4, 4, 3, 2, 1]
+# n = 4
+# print(shuffle(nums, n))
+# # Output: [1,4,2,3,3,2,4,1]
+# nums = [1, 1, 2, 2]
+# n = 2
+# print(shuffle(nums, n))
+# # Output: [1,2,1,2]
+
+#
+# Approach 2: Use Ruby methods .insert() and .delete_at()
+#
+# Time Complexity: O(N)
+#
+
+def shuffle(nums, n)
+  current_index = 1
+  (0..n-1).each do |i|
+    nums.insert(current_index, nums.delete_at(i + n))
+    current_index += 2
+  end
+  nums
+end
+
 nums = [2, 5, 1, 3, 4, 7]
 n = 3
 print(shuffle(nums, n))

From 6a6d0b675a3df7eee3867782398ba186758e4abd Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Wed, 24 Mar 2021 08:19:11 -0700
Subject: [PATCH 04/83] Add challenge

---
 DIRECTORY.md                               |  1 +
 data_structures/arrays/richest_customer.rb | 31 ++++++++++++++++++++++
 2 files changed, 32 insertions(+)
 create mode 100644 data_structures/arrays/richest_customer.rb

diff --git a/DIRECTORY.md b/DIRECTORY.md
index e8d246d..910dd30 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -13,6 +13,7 @@
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
+    * [Richest Customer](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer.rb)
     * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
diff --git a/data_structures/arrays/richest_customer.rb b/data_structures/arrays/richest_customer.rb
new file mode 100644
index 0000000..8fc8173
--- /dev/null
+++ b/data_structures/arrays/richest_customer.rb
@@ -0,0 +1,31 @@
+# Challenge name: Richest Customer
+#
+# You are given an m x n integer grid accounts where accounts[i][j]
+# is the amount of money the i​​​​​​​​​​​th​​​​ customer has in the j​​​​​​​​​​​th​​​​ bank.
+#
+# Return the wealth that the richest customer has.
+# A customer's wealth is the amount of money they have in all
+# their bank accounts. The richest customer is the customer that
+# has the maximum wealth.
+#
+# Example 1:
+# Input: accounts = [[1,2,3],[3,2,1]]
+# Output: 6
+# Explanation:
+# 1st customer has wealth = 1 + 2 + 3 = 6
+# 2nd customer has wealth = 3 + 2 + 1 = 6
+# Both customers are considered the richest with a wealth of 6
+# each, so return 6.
+#
+# Example 2:
+# Input: accounts = [[1,5],[7,3],[3,5]]
+# Output: 10
+# Explanation:
+# 1st customer has wealth = 6
+# 2nd customer has wealth = 10
+# 3rd customer has wealth = 8
+# The 2nd customer is the richest with a wealth of 10.
+#
+# Example 3:
+# Input: accounts = [[2,8,7],[7,1,3],[1,9,5]]
+# Output: 17
\ No newline at end of file

From 187cdac8b137495c347c77ff0fa71b91ccb99a5b Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Thu, 25 Mar 2021 10:08:15 -0700
Subject: [PATCH 05/83] Add brute force solution

---
 DIRECTORY.md                                  |  2 +-
 ...customer.rb => richest_customer_wealth.rb} | 29 +++++++++++++++++--
 2 files changed, 28 insertions(+), 3 deletions(-)
 rename data_structures/arrays/{richest_customer.rb => richest_customer_wealth.rb} (63%)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 910dd30..ea0a672 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -13,7 +13,7 @@
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
-    * [Richest Customer](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer.rb)
+    * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer.rb)
     * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
diff --git a/data_structures/arrays/richest_customer.rb b/data_structures/arrays/richest_customer_wealth.rb
similarity index 63%
rename from data_structures/arrays/richest_customer.rb
rename to data_structures/arrays/richest_customer_wealth.rb
index 8fc8173..23cf3de 100644
--- a/data_structures/arrays/richest_customer.rb
+++ b/data_structures/arrays/richest_customer_wealth.rb
@@ -1,4 +1,4 @@
-# Challenge name: Richest Customer
+# Challenge name: Richest Customer Wealth
 #
 # You are given an m x n integer grid accounts where accounts[i][j]
 # is the amount of money the i​​​​​​​​​​​th​​​​ customer has in the j​​​​​​​​​​​th​​​​ bank.
@@ -28,4 +28,29 @@
 #
 # Example 3:
 # Input: accounts = [[2,8,7],[7,1,3],[1,9,5]]
-# Output: 17
\ No newline at end of file
+# Output: 17
+
+#
+# Approach 1: Brute Force
+#
+# Time Complexity: O(n)
+#
+def find_richest_customer_wealth(accounts)
+  summed_accounts = []
+  accounts.each do |customer|
+    summed = 0
+    customer.each do |account|
+      summed += account
+    end
+    summed_accounts.push(summed)
+  end
+
+  summed_accounts.sort.pop()
+end
+
+puts find_richest_customer_wealth([[1,2,3],[3,2,1]])
+# => 6
+puts find_richest_customer_wealth([[1,5],[7,3],[3,5]])
+# => 10
+puts find_richest_customer_wealth([[2,8,7],[7,1,3],[1,9,5]])
+# => 17
\ No newline at end of file

From 5e7efbb73d0e3f2c5973013d0f0a47b77c913cf2 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Thu, 25 Mar 2021 14:48:00 -0700
Subject: [PATCH 06/83] Add hash solution

---
 .../arrays/richest_customer_wealth.rb         | 30 ++++++++++++++++++-
 1 file changed, 29 insertions(+), 1 deletion(-)

diff --git a/data_structures/arrays/richest_customer_wealth.rb b/data_structures/arrays/richest_customer_wealth.rb
index 23cf3de..5842348 100644
--- a/data_structures/arrays/richest_customer_wealth.rb
+++ b/data_structures/arrays/richest_customer_wealth.rb
@@ -53,4 +53,32 @@ puts find_richest_customer_wealth([[1,2,3],[3,2,1]])
 puts find_richest_customer_wealth([[1,5],[7,3],[3,5]])
 # => 10
 puts find_richest_customer_wealth([[2,8,7],[7,1,3],[1,9,5]])
-# => 17
\ No newline at end of file
+# => 17
+
+#
+# Approach 2: Hash
+#
+# Time Complexity:
+#
+def find_richest_customer_wealth(accounts)
+  result_hash = {}
+  accounts.each_with_index do |customer, i| 
+    result_hash[i] = customer.sum
+  end
+
+  highest_value = 0
+  result_hash.each do |k, v|
+    if v > highest_value
+      highest_value = v
+    end
+  end
+
+  highest_value
+end
+
+puts find_richest_customer_wealth([[1,2,3],[3,2,1]])
+# => 6
+puts find_richest_customer_wealth([[1,5],[7,3],[3,5]])
+# => 10
+puts find_richest_customer_wealth([[2,8,7],[7,1,3],[1,9,5]])
+# => 17

From b4806f090372d4e2fadb66d3a5bb26eae031b02f Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Fri, 26 Mar 2021 09:48:52 -0700
Subject: [PATCH 07/83] Add remove vowels challenge

---
 DIRECTORY.md                            |  1 +
 data_structures/arrays/remove_vowels.rb | 29 +++++++++++++++++++++++++
 2 files changed, 30 insertions(+)
 create mode 100644 data_structures/arrays/remove_vowels.rb

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 8fea99b..4c10a66 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -14,6 +14,7 @@
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
     * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/jewels_and_stones.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
+    * [Remove Vowels](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_vowels.rb)
     * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
diff --git a/data_structures/arrays/remove_vowels.rb b/data_structures/arrays/remove_vowels.rb
new file mode 100644
index 0000000..d1dbabf
--- /dev/null
+++ b/data_structures/arrays/remove_vowels.rb
@@ -0,0 +1,29 @@
+# Challenge name: Remove vowels from a string
+#
+# Given a string s, remove the vowels 'a', 'e', 'i', 'o', and 'u'
+# from it, and return the new string.
+# Example 1:
+# Input: s = "leetcodeisacommunityforcoders"
+# Output: "ltcdscmmntyfrcdrs"
+#
+# Example 2:
+# Input: s = "aeiou"
+# Output: ""
+#
+# @param {String} s
+# @return {String}
+
+#
+# Approach 1:
+#
+# Time Complexity:
+#
+def remove_vowels(s)
+end
+
+s = 'leetcodeisacommunityforcoders'
+print(remove_vowels(s))
+# => "ltcdscmmntyfrcdrs"
+s = 'aeiou'
+print(remove_vowels(s))
+# => ""
\ No newline at end of file

From 8bafd5c74a329a86fd7f29954fb56fcb335d1a3c Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Fri, 26 Mar 2021 10:03:45 -0700
Subject: [PATCH 08/83] Add brute force solution

---
 data_structures/arrays/remove_vowels.rb | 15 +++++++++++++--
 1 file changed, 13 insertions(+), 2 deletions(-)

diff --git a/data_structures/arrays/remove_vowels.rb b/data_structures/arrays/remove_vowels.rb
index d1dbabf..c5c7af8 100644
--- a/data_structures/arrays/remove_vowels.rb
+++ b/data_structures/arrays/remove_vowels.rb
@@ -14,11 +14,22 @@
 # @return {String}
 
 #
-# Approach 1:
+# Approach 1: Brute Force
 #
-# Time Complexity:
+# Time Complexity: O(n)
 #
 def remove_vowels(s)
+  result_array = []
+  s.downcase
+  start_array = s.split('')
+
+  start_array.each do |letter|
+    if letter != 'a' && letter != 'e' && letter != 'i' && letter != 'o' && letter != 'u'
+      result_array.push(letter)
+    end
+  end
+
+  result_array.join('')
 end
 
 s = 'leetcodeisacommunityforcoders'

From 27abece8ad34ba84d0d353e65e8d137e229da498 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Fri, 26 Mar 2021 10:19:29 -0700
Subject: [PATCH 09/83] Add solution using regex

---
 data_structures/arrays/remove_vowels.rb | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/data_structures/arrays/remove_vowels.rb b/data_structures/arrays/remove_vowels.rb
index c5c7af8..d9b800f 100644
--- a/data_structures/arrays/remove_vowels.rb
+++ b/data_structures/arrays/remove_vowels.rb
@@ -32,6 +32,26 @@ def remove_vowels(s)
   result_array.join('')
 end
 
+# s = 'leetcodeisacommunityforcoders'
+# print(remove_vowels(s))
+# # => "ltcdscmmntyfrcdrs"
+# s = 'aeiou'
+# print(remove_vowels(s))
+# # => ""
+
+#
+# Approach 2: Regex
+#
+# Time Complexity: O(n)
+#
+def remove_vowels(s)
+  vowels = /[aeiou]+/
+  s.scan(vowels).each do |letter|
+    s.sub!(letter, '')
+  end
+  s
+end
+
 s = 'leetcodeisacommunityforcoders'
 print(remove_vowels(s))
 # => "ltcdscmmntyfrcdrs"

From 89a7af33e1a506f2f04e51808920a9b2f1ea27cb Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Fri, 26 Mar 2021 10:34:28 -0700
Subject: [PATCH 10/83] Add solution using Ruby .delete() method

---
 data_structures/arrays/remove_vowels.rb | 34 +++++++++++++++++--------
 1 file changed, 24 insertions(+), 10 deletions(-)

diff --git a/data_structures/arrays/remove_vowels.rb b/data_structures/arrays/remove_vowels.rb
index d9b800f..d8ddc31 100644
--- a/data_structures/arrays/remove_vowels.rb
+++ b/data_structures/arrays/remove_vowels.rb
@@ -32,12 +32,12 @@ def remove_vowels(s)
   result_array.join('')
 end
 
-# s = 'leetcodeisacommunityforcoders'
-# print(remove_vowels(s))
-# # => "ltcdscmmntyfrcdrs"
-# s = 'aeiou'
-# print(remove_vowels(s))
-# # => ""
+s = 'leetcodeisacommunityforcoders'
+print(remove_vowels(s))
+# => "ltcdscmmntyfrcdrs"
+s = 'aeiou'
+print(remove_vowels(s))
+# => ""
 
 #
 # Approach 2: Regex
@@ -45,13 +45,27 @@ end
 # Time Complexity: O(n)
 #
 def remove_vowels(s)
-  vowels = /[aeiou]+/
-  s.scan(vowels).each do |letter|
-    s.sub!(letter, '')
-  end
+  vowels = /[aeiou]/i
+  s.gsub!(vowels, '')
   s
 end
 
+s = 'leetcodeisacommunityforcoders'
+print(remove_vowels(s))
+# => "ltcdscmmntyfrcdrs"
+s = 'aeiou'
+print(remove_vowels(s))
+# => ""
+
+# 
+# Approach 3: Using Ruby .delete() method
+#
+# Time Complexity: O(n)
+#
+def remove_vowels(s)
+  s.downcase.delete('aeiou')
+end
+
 s = 'leetcodeisacommunityforcoders'
 print(remove_vowels(s))
 # => "ltcdscmmntyfrcdrs"

From 1e4d510748582d219d670a29917702de9efc4805 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Fri, 26 Mar 2021 10:43:21 -0700
Subject: [PATCH 11/83] Add anagram checker challenge

---
 DIRECTORY.md                              |  1 +
 data_structures/arrays/anagram_checker.rb | 31 +++++++++++++++++++++++
 2 files changed, 32 insertions(+)
 create mode 100644 data_structures/arrays/anagram_checker.rb

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 8fea99b..fe034ed 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -8,6 +8,7 @@
 ## Data Structures
   * Arrays
     * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/add_digits.rb)
+    * [Anagram Checker](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/anagram_checker.rb)
     * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_all_duplicates_in_an_array.rb)
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
diff --git a/data_structures/arrays/anagram_checker.rb b/data_structures/arrays/anagram_checker.rb
new file mode 100644
index 0000000..d082a36
--- /dev/null
+++ b/data_structures/arrays/anagram_checker.rb
@@ -0,0 +1,31 @@
+# Challenge name: Is anagram
+#
+# Given two strings s and t , write a function to determine
+# if t is an anagram of s.
+#
+# Note:
+# You may assume the string contains only lowercase alphabets.
+#
+# Follow up:
+# What if the inputs contain unicode characters?
+# How would you adapt your solution to such case?
+#
+# @param {String} s
+# @param {String} t
+# @return {Boolean}
+
+def is_anagram(s, t)
+end
+
+s = 'anagram'
+t = 'nagaram'
+puts(is_anagram(s, t))
+# => true
+s = 'rat'
+t = 'car'
+puts(is_anagram(s, t))
+# => false
+s = 'a'
+t = 'ab'
+puts(is_anagram(s, t))
+# => false
\ No newline at end of file

From 08e35de175bd75ca2d285c36e5b65ed409510a99 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <60627484+jsca-kwok@users.noreply.github.com>
Date: Fri, 26 Mar 2021 10:54:37 -0700
Subject: [PATCH 12/83] Update
 data_structures/arrays/richest_customer_wealth.rb

Co-authored-by: Vitor Oliveira <vbrazo@gmail.com>
---
 data_structures/arrays/richest_customer_wealth.rb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/arrays/richest_customer_wealth.rb b/data_structures/arrays/richest_customer_wealth.rb
index 5842348..7680ec9 100644
--- a/data_structures/arrays/richest_customer_wealth.rb
+++ b/data_structures/arrays/richest_customer_wealth.rb
@@ -58,7 +58,7 @@ puts find_richest_customer_wealth([[2,8,7],[7,1,3],[1,9,5]])
 #
 # Approach 2: Hash
 #
-# Time Complexity:
+# Time Complexity: O(n)
 #
 def find_richest_customer_wealth(accounts)
   result_hash = {}

From 6a80485c87a462f589fe55c91109544462d175e7 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sun, 28 Mar 2021 17:19:48 +0000
Subject: [PATCH 13/83] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 8fea99b..dbb7695 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -56,6 +56,7 @@
   * [Fibonacci](https://github.com/TheAlgorithms/Ruby/blob/master/maths/fibonacci.rb)
   * [Number Of Digits](https://github.com/TheAlgorithms/Ruby/blob/master/maths/number_of_digits.rb)
   * [Power Of Two](https://github.com/TheAlgorithms/Ruby/blob/master/maths/power_of_two.rb)
+  * [Prime Number](https://github.com/TheAlgorithms/Ruby/blob/master/maths/prime_number.rb)
   * [Square Root](https://github.com/TheAlgorithms/Ruby/blob/master/maths/square_root.rb)
   * [Square Root Test](https://github.com/TheAlgorithms/Ruby/blob/master/maths/square_root_test.rb)
   * [Sum Of Digits](https://github.com/TheAlgorithms/Ruby/blob/master/maths/sum_of_digits.rb)

From 5ed65199d74cb46fd2c187d4534f70ea313b6216 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <60627484+jsca-kwok@users.noreply.github.com>
Date: Mon, 29 Mar 2021 09:59:32 -0700
Subject: [PATCH 14/83] Update data_structures/arrays/remove_vowels.rb

Co-authored-by: vzvu3k6k <vzvu3k6k@gmail.com>
---
 data_structures/arrays/remove_vowels.rb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/data_structures/arrays/remove_vowels.rb b/data_structures/arrays/remove_vowels.rb
index d8ddc31..7a72f87 100644
--- a/data_structures/arrays/remove_vowels.rb
+++ b/data_structures/arrays/remove_vowels.rb
@@ -20,7 +20,7 @@
 #
 def remove_vowels(s)
   result_array = []
-  s.downcase
+  s.downcase!
   start_array = s.split('')
 
   start_array.each do |letter|
@@ -71,4 +71,4 @@ print(remove_vowels(s))
 # => "ltcdscmmntyfrcdrs"
 s = 'aeiou'
 print(remove_vowels(s))
-# => ""
\ No newline at end of file
+# => ""

From 5bf141f64f65e0286d4a0ac3b2760cc13dceccf1 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <60627484+jsca-kwok@users.noreply.github.com>
Date: Mon, 29 Mar 2021 10:00:33 -0700
Subject: [PATCH 15/83] Update data_structures/arrays/remove_vowels.rb

Co-authored-by: vzvu3k6k <vzvu3k6k@gmail.com>
---
 data_structures/arrays/remove_vowels.rb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/arrays/remove_vowels.rb b/data_structures/arrays/remove_vowels.rb
index 7a72f87..bd6da25 100644
--- a/data_structures/arrays/remove_vowels.rb
+++ b/data_structures/arrays/remove_vowels.rb
@@ -33,7 +33,7 @@ def remove_vowels(s)
 end
 
 s = 'leetcodeisacommunityforcoders'
-print(remove_vowels(s))
+puts(remove_vowels(s))
 # => "ltcdscmmntyfrcdrs"
 s = 'aeiou'
 print(remove_vowels(s))

From 31d9e8e0a22aefc791a912f14e145a2abd7257c0 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Mon, 29 Mar 2021 10:05:15 -0700
Subject: [PATCH 16/83] Change print to puts

---
 data_structures/arrays/remove_vowels.rb | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/data_structures/arrays/remove_vowels.rb b/data_structures/arrays/remove_vowels.rb
index bd6da25..5fa39fc 100644
--- a/data_structures/arrays/remove_vowels.rb
+++ b/data_structures/arrays/remove_vowels.rb
@@ -36,7 +36,7 @@ s = 'leetcodeisacommunityforcoders'
 puts(remove_vowels(s))
 # => "ltcdscmmntyfrcdrs"
 s = 'aeiou'
-print(remove_vowels(s))
+puts(remove_vowels(s))
 # => ""
 
 #
@@ -51,10 +51,10 @@ def remove_vowels(s)
 end
 
 s = 'leetcodeisacommunityforcoders'
-print(remove_vowels(s))
+puts(remove_vowels(s))
 # => "ltcdscmmntyfrcdrs"
 s = 'aeiou'
-print(remove_vowels(s))
+puts(remove_vowels(s))
 # => ""
 
 # 
@@ -67,8 +67,8 @@ def remove_vowels(s)
 end
 
 s = 'leetcodeisacommunityforcoders'
-print(remove_vowels(s))
+puts(remove_vowels(s))
 # => "ltcdscmmntyfrcdrs"
 s = 'aeiou'
-print(remove_vowels(s))
+puts(remove_vowels(s))
 # => ""

From ad685ac4ee922161ba193a13050e38f3f050825d Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Mon, 29 Mar 2021 10:22:09 -0700
Subject: [PATCH 17/83] Add two pointers approach

---
 data_structures/arrays/shuffle_array.rb | 57 +++++++++++++++++++------
 1 file changed, 45 insertions(+), 12 deletions(-)

diff --git a/data_structures/arrays/shuffle_array.rb b/data_structures/arrays/shuffle_array.rb
index 2f1b13f..22ec07a 100644
--- a/data_structures/arrays/shuffle_array.rb
+++ b/data_structures/arrays/shuffle_array.rb
@@ -34,18 +34,18 @@ def shuffle(nums, n)
   result
 end
 
-# nums = [2, 5, 1, 3, 4, 7]
-# n = 3
-# print(shuffle(nums, n))
-# # Output: [2,3,5,4,1,7]
-# nums = [1, 2, 3, 4, 4, 3, 2, 1]
-# n = 4
-# print(shuffle(nums, n))
-# # Output: [1,4,2,3,3,2,4,1]
-# nums = [1, 1, 2, 2]
-# n = 2
-# print(shuffle(nums, n))
-# # Output: [1,2,1,2]
+nums = [2, 5, 1, 3, 4, 7]
+n = 3
+print(shuffle(nums, n))
+# Output: [2,3,5,4,1,7]
+nums = [1, 2, 3, 4, 4, 3, 2, 1]
+n = 4
+print(shuffle(nums, n))
+# Output: [1,4,2,3,3,2,4,1]
+nums = [1, 1, 2, 2]
+n = 2
+print(shuffle(nums, n))
+# Output: [1,2,1,2]
 
 #
 # Approach 2: Use Ruby methods .insert() and .delete_at()
@@ -62,6 +62,39 @@ def shuffle(nums, n)
   nums
 end
 
+nums = [2, 5, 1, 3, 4, 7]
+n = 3
+print(shuffle(nums, n))
+# Output: [2,3,5,4,1,7]
+nums = [1, 2, 3, 4, 4, 3, 2, 1]
+n = 4
+print(shuffle(nums, n))
+# Output: [1,4,2,3,3,2,4,1]
+nums = [1, 1, 2, 2]
+n = 2
+print(shuffle(nums, n))
+# Output: [1,2,1,2]
+
+#
+# Approach 3: Two Pointers
+#
+# Time Complexity: O(N)
+#
+
+def shuffle(nums, n)
+  result = []
+  p1 = 0
+  p2 = n
+
+  while p1 < n
+    result.push(nums[p1], nums[p2])
+    p1 +=1
+    p2 +=1
+  end
+
+  result
+end
+
 nums = [2, 5, 1, 3, 4, 7]
 n = 3
 print(shuffle(nums, n))

From fded3fa4df2090ed3ae0d85207a209d59d0da2af Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Mon, 29 Mar 2021 14:33:12 -0700
Subject: [PATCH 18/83] Move approach to hash_table folder

---
 .../arrays/richest_customer_wealth.rb         | 30 +---------
 .../hash_table/richest_customer_wealth.rb     | 59 +++++++++++++++++++
 2 files changed, 60 insertions(+), 29 deletions(-)
 create mode 100644 data_structures/hash_table/richest_customer_wealth.rb

diff --git a/data_structures/arrays/richest_customer_wealth.rb b/data_structures/arrays/richest_customer_wealth.rb
index 7680ec9..4efabeb 100644
--- a/data_structures/arrays/richest_customer_wealth.rb
+++ b/data_structures/arrays/richest_customer_wealth.rb
@@ -31,7 +31,7 @@
 # Output: 17
 
 #
-# Approach 1: Brute Force
+# Approach: Brute Force
 #
 # Time Complexity: O(n)
 #
@@ -54,31 +54,3 @@ puts find_richest_customer_wealth([[1,5],[7,3],[3,5]])
 # => 10
 puts find_richest_customer_wealth([[2,8,7],[7,1,3],[1,9,5]])
 # => 17
-
-#
-# Approach 2: Hash
-#
-# Time Complexity: O(n)
-#
-def find_richest_customer_wealth(accounts)
-  result_hash = {}
-  accounts.each_with_index do |customer, i| 
-    result_hash[i] = customer.sum
-  end
-
-  highest_value = 0
-  result_hash.each do |k, v|
-    if v > highest_value
-      highest_value = v
-    end
-  end
-
-  highest_value
-end
-
-puts find_richest_customer_wealth([[1,2,3],[3,2,1]])
-# => 6
-puts find_richest_customer_wealth([[1,5],[7,3],[3,5]])
-# => 10
-puts find_richest_customer_wealth([[2,8,7],[7,1,3],[1,9,5]])
-# => 17
diff --git a/data_structures/hash_table/richest_customer_wealth.rb b/data_structures/hash_table/richest_customer_wealth.rb
new file mode 100644
index 0000000..11849e1
--- /dev/null
+++ b/data_structures/hash_table/richest_customer_wealth.rb
@@ -0,0 +1,59 @@
+# Challenge name: Richest Customer Wealth
+#
+# You are given an m x n integer grid accounts where accounts[i][j]
+# is the amount of money the i​​​​​​​​​​​th​​​​ customer has in the j​​​​​​​​​​​th​​​​ bank.
+#
+# Return the wealth that the richest customer has.
+# A customer's wealth is the amount of money they have in all
+# their bank accounts. The richest customer is the customer that
+# has the maximum wealth.
+#
+# Example 1:
+# Input: accounts = [[1,2,3],[3,2,1]]
+# Output: 6
+# Explanation:
+# 1st customer has wealth = 1 + 2 + 3 = 6
+# 2nd customer has wealth = 3 + 2 + 1 = 6
+# Both customers are considered the richest with a wealth of 6
+# each, so return 6.
+#
+# Example 2:
+# Input: accounts = [[1,5],[7,3],[3,5]]
+# Output: 10
+# Explanation:
+# 1st customer has wealth = 6
+# 2nd customer has wealth = 10
+# 3rd customer has wealth = 8
+# The 2nd customer is the richest with a wealth of 10.
+#
+# Example 3:
+# Input: accounts = [[2,8,7],[7,1,3],[1,9,5]]
+# Output: 17
+
+#
+# Approach: Hash
+#
+# Time Complexity: O(n)
+#
+def find_richest_customer_wealth(accounts)
+  result_hash = {}
+  accounts.each_with_index do |customer, i|
+    result_hash[i] = customer.sum
+  end
+
+  highest_value = 0
+  result_hash.each do |k, v|
+    if v > highest_value
+      highest_value = v
+    end
+  end
+
+  highest_value
+end
+
+puts find_richest_customer_wealth([[1,2,3],[3,2,1]])
+# => 6
+puts find_richest_customer_wealth([[1,5],[7,3],[3,5]])
+# => 10
+puts find_richest_customer_wealth([[2,8,7],[7,1,3],[1,9,5]])
+# => 17

From c0f28a73812b4a3f9b1576073486d4a58fb93a3f Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Mon, 29 Mar 2021 21:34:30 +0000
Subject: [PATCH 19/83] updating DIRECTORY.md

---
 DIRECTORY.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 361854e..059eebf 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -14,7 +14,7 @@
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
     * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/jewels_and_stones.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
-    * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer.rb)
+    * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer_wealth.rb)
     * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
@@ -24,6 +24,8 @@
     * [Invert](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/binary_trees/invert.rb)
     * [Postorder Traversal](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/binary_trees/postorder_traversal.rb)
     * [Preorder Traversal](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/binary_trees/preorder_traversal.rb)
+  * Hash Table
+    * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/richest_customer_wealth.rb)
   * Linked Lists
     * [Circular Linked List](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/linked_lists/circular_linked_list.rb)
     * [Doubly Linked List](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/linked_lists/doubly_linked_list.rb)

From c94b74543f893cac6a311ebf8fbf38302433f7cd Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Mon, 29 Mar 2021 21:37:05 +0000
Subject: [PATCH 20/83] updating DIRECTORY.md

---
 DIRECTORY.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 488e66b..698ebfc 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -15,8 +15,8 @@
     * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/jewels_and_stones.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
     * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer_wealth.rb)
-    * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Shuffle Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/shuffle_array.rb)
+    * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
     * [Two Sum Ii](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum_ii.rb)

From 3270667f8edc81b2d08d2058a4d35febb377f6e6 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Mon, 29 Mar 2021 14:52:06 -0700
Subject: [PATCH 21/83] Move algorithsm to appropriate folder

---
 data_structures/arrays/{ => strings}/remove_vowels.rb | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)
 rename data_structures/arrays/{ => strings}/remove_vowels.rb (99%)

diff --git a/data_structures/arrays/remove_vowels.rb b/data_structures/arrays/strings/remove_vowels.rb
similarity index 99%
rename from data_structures/arrays/remove_vowels.rb
rename to data_structures/arrays/strings/remove_vowels.rb
index 5fa39fc..30d3042 100644
--- a/data_structures/arrays/remove_vowels.rb
+++ b/data_structures/arrays/strings/remove_vowels.rb
@@ -2,6 +2,7 @@
 #
 # Given a string s, remove the vowels 'a', 'e', 'i', 'o', and 'u'
 # from it, and return the new string.
+#
 # Example 1:
 # Input: s = "leetcodeisacommunityforcoders"
 # Output: "ltcdscmmntyfrcdrs"
@@ -18,6 +19,7 @@
 #
 # Time Complexity: O(n)
 #
+
 def remove_vowels(s)
   result_array = []
   s.downcase!
@@ -57,7 +59,7 @@ s = 'aeiou'
 puts(remove_vowels(s))
 # => ""
 
-# 
+#
 # Approach 3: Using Ruby .delete() method
 #
 # Time Complexity: O(n)

From fb1ee12e8d66b3ee00617eec0689918f82f32c23 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Mon, 29 Mar 2021 21:54:54 +0000
Subject: [PATCH 22/83] updating DIRECTORY.md

---
 DIRECTORY.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 2d90daf..d1baadc 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -14,11 +14,12 @@
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
     * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/jewels_and_stones.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
-    * [Remove Vowels](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_vowels.rb)
     * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer_wealth.rb)
     * [Shuffle Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/shuffle_array.rb)
     * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
+    * Strings
+      * [Remove Vowels](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/remove_vowels.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
     * [Two Sum Ii](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum_ii.rb)
   * Binary Trees

From 66756bf5d43c1ecbc04e2aa3b4ddff1e61a918c3 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Mon, 29 Mar 2021 15:33:57 -0700
Subject: [PATCH 23/83] Move remove_vowels to strings folder

---
 data_structures/arrays/{ => strings}/jewels_and_stones.rb | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename data_structures/arrays/{ => strings}/jewels_and_stones.rb (100%)

diff --git a/data_structures/arrays/jewels_and_stones.rb b/data_structures/arrays/strings/jewels_and_stones.rb
similarity index 100%
rename from data_structures/arrays/jewels_and_stones.rb
rename to data_structures/arrays/strings/jewels_and_stones.rb

From 57a46a8271c8be49b199142fc0efa589a9bf6702 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Mon, 29 Mar 2021 15:35:18 -0700
Subject: [PATCH 24/83] Move two_sum to hash table folder

---
 data_structures/arrays/two_sum.rb     | 45 -----------------
 data_structures/hash_table/two_sum.rb | 70 +++++++++++++++++++++++++++
 2 files changed, 70 insertions(+), 45 deletions(-)
 create mode 100644 data_structures/hash_table/two_sum.rb

diff --git a/data_structures/arrays/two_sum.rb b/data_structures/arrays/two_sum.rb
index b872625..a08eefd 100644
--- a/data_structures/arrays/two_sum.rb
+++ b/data_structures/arrays/two_sum.rb
@@ -86,48 +86,3 @@ print(two_sum([3, 2, 4], 6))
 
 print(two_sum([3, 3], 6))
 # => [0,1]
-
-#
-# Approach 3: Using a Hash
-#
-
-# Complexity analysis
-
-# Time complexity: O(n). We traverse the list containing n elements exactly twice.
-# Since the hash table reduces the lookup time to O(1), the time complexity is O(n).
-
-# Space complexity: O(n). The extra space required depends on the number of items
-# stored in the hash table, which stores exactly n elements.
-
-def two_sum(nums, target)
-  hash = {}
-
-  # create a hash to store values and their indices
-  nums.each_with_index do |num, i|
-    hash[num] = i
-  end
-
-  # iterate over nums array to find the target (difference between sum target and num)
-  nums.each_with_index do |num, i|
-    difference_target = target - num
-
-    if hash[difference_target] && hash[difference_target] != i
-      return [i, hash[difference_target]]
-    end
-  end
-end
-
-nums = [2, 7, 11, 15]
-target = 9
-print(two_sum(nums, target))
-# => [0,1]
-
-nums = [3, 2, 4]
-target = 6
-print(two_sum(nums, target))
-# => [1,2]
-
-nums = [3, 3]
-target = 6
-print(two_sum(nums, target))
-# => [0,1]
diff --git a/data_structures/hash_table/two_sum.rb b/data_structures/hash_table/two_sum.rb
new file mode 100644
index 0000000..14dafcf
--- /dev/null
+++ b/data_structures/hash_table/two_sum.rb
@@ -0,0 +1,70 @@
+# Challenge name: Two Sum
+#
+# Given an array of integers nums and an integer target, return indices of the two numbers such that they add up to target.
+#
+# You may assume that each input would have exactly one solution, and you may not use the same element twice.
+#
+# You can return the answer in any order.
+#
+#
+# Examples
+#
+# Input: nums = [2, 7, 11, 15], target = 9
+# Output: [0,1]
+# Explanation: Because nums[0] + nums[1] == 9, we return [0, 1].
+#
+# Input: nums = [3, 2, 4], target = 6
+# Output: [1,2]
+#
+# Input: nums = [3, 3], target = 6
+# Output: [0,1]
+# Explanation: Because nums[0] + nums[1] == 9, we return [0, 1].
+#
+# @param {Integer[]} nums
+# @param {Integer} target
+# @return {Integer[]}
+
+#
+# Approach: Using Hash table
+#
+
+# Complexity analysis
+
+# Time complexity: O(n). We traverse the list containing n elements exactly twice.
+# Since the hash table reduces the lookup time to O(1), the time complexity is O(n).
+
+# Space complexity: O(n). The extra space required depends on the number of items
+# stored in the hash table, which stores exactly n elements.
+
+def two_sum(nums, target)
+  hash = {}
+
+  # create a hash to store values and their indices
+  nums.each_with_index do |num, i|
+    hash[num] = i
+  end
+
+  # iterate over nums array to find the target (difference between sum target and num)
+  nums.each_with_index do |num, i|
+    difference_target = target - num
+
+    if hash[difference_target] && hash[difference_target] != i
+      return [i, hash[difference_target]]
+    end
+  end
+end
+
+nums = [2, 7, 11, 15]
+target = 9
+print(two_sum(nums, target))
+# => [0,1]
+
+nums = [3, 2, 4]
+target = 6
+print(two_sum(nums, target))
+# => [1,2]
+
+nums = [3, 3]
+target = 6
+print(two_sum(nums, target))
+# => [0,1]

From f6a84ea326f626869b7876fff5f564b2f49a6de1 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Mon, 29 Mar 2021 15:37:02 -0700
Subject: [PATCH 25/83] Move more algos to hash table folders

---
 .../arrays/find_all_duplicates_in_an_array.rb | 41 -------------
 .../find_all_duplicates_in_an_array.rb        | 61 +++++++++++++++++++
 2 files changed, 61 insertions(+), 41 deletions(-)
 create mode 100644 data_structures/hash_table/find_all_duplicates_in_an_array.rb

diff --git a/data_structures/arrays/find_all_duplicates_in_an_array.rb b/data_structures/arrays/find_all_duplicates_in_an_array.rb
index 63e6517..7ee99ff 100644
--- a/data_structures/arrays/find_all_duplicates_in_an_array.rb
+++ b/data_structures/arrays/find_all_duplicates_in_an_array.rb
@@ -87,44 +87,3 @@ Benchmark.bmbm do |x|
     print(find_duplicates(long_array))
   end
 end
-
-#
-# Approach 3: Hash map
-#
-
-#
-# Complexity Analysis
-#
-# Time complexity: O(n) average case.
-#
-
-def find_duplicates(array)
-  result_hash = {}
-  result_array = []
-
-  # loop through array and build a hash with counters
-  # where the key is the array element and the counter is the value
-  # increase counter when duplicate is found
-  array.each do |num|
-    if result_hash[num].nil?
-      result_hash[num] = 1
-    else
-      result_hash[num] += 1
-    end
-  end
-
-  # loop through hash and look for values > 1
-  result_hash.each do |k, v|
-    result_array.push(k) if v > 1
-  end
-
-  # return keys
-  result_array
-end
-
-Benchmark.bmbm do |x|
-  x.report('execute algorithm 3') do
-    print(find_duplicates(array))
-    print(find_duplicates(long_array))
-  end
-end
diff --git a/data_structures/hash_table/find_all_duplicates_in_an_array.rb b/data_structures/hash_table/find_all_duplicates_in_an_array.rb
new file mode 100644
index 0000000..bc68423
--- /dev/null
+++ b/data_structures/hash_table/find_all_duplicates_in_an_array.rb
@@ -0,0 +1,61 @@
+# Find All Duplicates in an Array
+#
+# Given an array of integers, 1 ≤ a[i] ≤ n (n = size of array),
+# some elements appear twice and others appear once.
+#
+# Find all the elements that appear twice in this array.
+#
+# Could you do it without extra space and in O(n) runtime?
+#
+# Example:
+# Input:
+# [4,3,2,7,8,2,3,1]
+#
+# Output:
+# [2,3]
+
+require 'benchmark'
+
+array = [4, 3, 2, 7, 8, 2, 3, 1]
+long_array = [4, 3, 2, 7, 8, 2, 3, 1] * 100
+
+#
+# Approach: Hash table
+#
+
+#
+# Complexity Analysis
+#
+# Time complexity: O(n) average case.
+#
+
+def find_duplicates(array)
+  result_hash = {}
+  result_array = []
+
+  # loop through array and build a hash with counters
+  # where the key is the array element and the counter is the value
+  # increase counter when duplicate is found
+  array.each do |num|
+    if result_hash[num].nil?
+      result_hash[num] = 1
+    else
+      result_hash[num] += 1
+    end
+  end
+
+  # loop through hash and look for values > 1
+  result_hash.each do |k, v|
+    result_array.push(k) if v > 1
+  end
+
+  # return keys
+  result_array
+end
+
+Benchmark.bmbm do |x|
+  x.report('execute algorithm 3') do
+    print(find_duplicates(array))
+    print(find_duplicates(long_array))
+  end
+end

From e60cd1b5e66b6425820cf3577c4cf8bf2b6928b1 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Mon, 29 Mar 2021 22:37:23 +0000
Subject: [PATCH 26/83] updating DIRECTORY.md

---
 DIRECTORY.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index d1baadc..03f2942 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -12,13 +12,13 @@
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
-    * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/jewels_and_stones.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
     * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer_wealth.rb)
     * [Shuffle Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/shuffle_array.rb)
     * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
     * Strings
+      * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/jewels_and_stones.rb)
       * [Remove Vowels](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/remove_vowels.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
     * [Two Sum Ii](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum_ii.rb)
@@ -28,7 +28,9 @@
     * [Postorder Traversal](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/binary_trees/postorder_traversal.rb)
     * [Preorder Traversal](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/binary_trees/preorder_traversal.rb)
   * Hash Table
+    * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/find_all_duplicates_in_an_array.rb)
     * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/richest_customer_wealth.rb)
+    * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/two_sum.rb)
   * Linked Lists
     * [Circular Linked List](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/linked_lists/circular_linked_list.rb)
     * [Doubly Linked List](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/linked_lists/doubly_linked_list.rb)

From 6c785524fbad57ffb26d8858fdfb2f348a4fd296 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Tue, 30 Mar 2021 14:19:43 -0700
Subject: [PATCH 27/83] Add sort and compare solution

---
 DIRECTORY.md                                          |  2 +-
 .../arrays/{ => strings}/anagram_checker.rb           | 11 +++++++++++
 2 files changed, 12 insertions(+), 1 deletion(-)
 rename data_structures/arrays/{ => strings}/anagram_checker.rb (76%)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 3ae4c04..0014e38 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -8,7 +8,6 @@
 ## Data Structures
   * Arrays
     * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/add_digits.rb)
-    * [Anagram Checker](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/anagram_checker.rb)
     * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_all_duplicates_in_an_array.rb)
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
@@ -19,6 +18,7 @@
     * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
     * Strings
+      * [Anagram Checker](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/anagram_checker.rb)
       * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/jewels_and_stones.rb)
       * [Remove Vowels](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/remove_vowels.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
diff --git a/data_structures/arrays/anagram_checker.rb b/data_structures/arrays/strings/anagram_checker.rb
similarity index 76%
rename from data_structures/arrays/anagram_checker.rb
rename to data_structures/arrays/strings/anagram_checker.rb
index d082a36..b66eb3f 100644
--- a/data_structures/arrays/anagram_checker.rb
+++ b/data_structures/arrays/strings/anagram_checker.rb
@@ -14,7 +14,18 @@
 # @param {String} t
 # @return {Boolean}
 
+#
+# Approach 1: Sort and Compare
+#
+# Time Complexity: O(n log n)
+#
 def is_anagram(s, t)
+  return false if s.length != t.length
+
+  arr1 = s.split('').sort
+  arr2 = t.split('').sort
+
+  arr1 == arr2
 end
 
 s = 'anagram'

From 2fe1098805de6fb91f5b567484f01d3f90ae720a Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Wed, 31 Mar 2021 16:40:23 -0700
Subject: [PATCH 28/83] Add intersection challenge

---
 DIRECTORY.md                           |  1 +
 data_structures/arrays/intersection.rb | 23 +++++++++++++++++++++++
 2 files changed, 24 insertions(+)
 create mode 100644 data_structures/arrays/intersection.rb

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 03f2942..878bdcb 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -12,6 +12,7 @@
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
+    * [Intersection](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/intersection.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
     * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer_wealth.rb)
     * [Shuffle Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/shuffle_array.rb)
diff --git a/data_structures/arrays/intersection.rb b/data_structures/arrays/intersection.rb
new file mode 100644
index 0000000..bd826a0
--- /dev/null
+++ b/data_structures/arrays/intersection.rb
@@ -0,0 +1,23 @@
+# Challenge name: Intersection of two arrays ii
+#
+# Given two arrays, write a function to compute their intersection.
+#
+# @param {Integer[]} nums1
+# @param {Integer[]} nums2
+# @return {Integer[]}
+
+#
+# Approach 1:
+#
+# Time Complexity:
+#
+def intersect(arr1, arr2)
+end
+nums1 = [1, 2, 2, 1]
+nums2 = [2, 2]
+intersect(nums1, nums2)
+# => [2,2]
+nums1 = [4, 9, 5]
+nums2 = [9, 4, 9, 8, 4]
+intersect(nums1, nums2)
+# => [4,9]
\ No newline at end of file

From 3bc81b8195b91a2282b7eb4b3fdc916364ec373f Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Wed, 31 Mar 2021 18:37:57 -0700
Subject: [PATCH 29/83] Update
 data_structures/arrays/strings/anagram_checker.rb

---
 data_structures/arrays/strings/anagram_checker.rb | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/data_structures/arrays/strings/anagram_checker.rb b/data_structures/arrays/strings/anagram_checker.rb
index b66eb3f..71f59d6 100644
--- a/data_structures/arrays/strings/anagram_checker.rb
+++ b/data_structures/arrays/strings/anagram_checker.rb
@@ -17,7 +17,9 @@
 #
 # Approach 1: Sort and Compare
 #
-# Time Complexity: O(n log n)
+# Complexity analysis:
+#
+# Time Complexity: O(n log n). Assume that n is the length of s, sorting costs O(n log n), and comparing two strings costs O(n). Sorting time dominates and the overall time complexity is O(n log n).
 #
 def is_anagram(s, t)
   return false if s.length != t.length
@@ -39,4 +41,4 @@ puts(is_anagram(s, t))
 s = 'a'
 t = 'ab'
 puts(is_anagram(s, t))
-# => false
\ No newline at end of file
+# => false

From a93d5cc072d98981331661186ad8650405dc6bde Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Wed, 31 Mar 2021 18:38:01 -0700
Subject: [PATCH 30/83] Update
 data_structures/arrays/strings/anagram_checker.rb

---
 data_structures/arrays/strings/anagram_checker.rb | 1 +
 1 file changed, 1 insertion(+)

diff --git a/data_structures/arrays/strings/anagram_checker.rb b/data_structures/arrays/strings/anagram_checker.rb
index 71f59d6..bcd5e36 100644
--- a/data_structures/arrays/strings/anagram_checker.rb
+++ b/data_structures/arrays/strings/anagram_checker.rb
@@ -20,6 +20,7 @@
 # Complexity analysis:
 #
 # Time Complexity: O(n log n). Assume that n is the length of s, sorting costs O(n log n), and comparing two strings costs O(n). Sorting time dominates and the overall time complexity is O(n log n).
+# Space Complexity: O(1). Space depends on the sorting implementation which, usually, costs O(1) auxiliary space if heapsort is used.
 #
 def is_anagram(s, t)
   return false if s.length != t.length

From a472f9a6ffdd32cb41772b0dc14c969249b83a05 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Thu, 1 Apr 2021 01:57:23 +0000
Subject: [PATCH 31/83] updating DIRECTORY.md

---
 DIRECTORY.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 0014e38..d0c4469 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -5,6 +5,9 @@
 ## Ciphers
   * [Merkle Hellman Cryptosystem](https://github.com/TheAlgorithms/Ruby/blob/master/ciphers/merkle_hellman_cryptosystem.rb)
 
+## Conversions
+  * [Temperature Conversions](https://github.com/TheAlgorithms/Ruby/blob/master/conversions/temperature_conversions.rb)
+
 ## Data Structures
   * Arrays
     * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/add_digits.rb)

From 4674c2d97b205f14a2b471d00c24afca4e44048f Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Wed, 31 Mar 2021 19:02:57 -0700
Subject: [PATCH 32/83] Valid anagram: hash table approach

---
 .../arrays/strings/anagram_checker.rb         |  2 +-
 data_structures/hash_table/anagram_checker.rb | 55 +++++++++++++++++++
 2 files changed, 56 insertions(+), 1 deletion(-)
 create mode 100644 data_structures/hash_table/anagram_checker.rb

diff --git a/data_structures/arrays/strings/anagram_checker.rb b/data_structures/arrays/strings/anagram_checker.rb
index bcd5e36..1918b07 100644
--- a/data_structures/arrays/strings/anagram_checker.rb
+++ b/data_structures/arrays/strings/anagram_checker.rb
@@ -15,7 +15,7 @@
 # @return {Boolean}
 
 #
-# Approach 1: Sort and Compare
+# Approach: Sort and Compare
 #
 # Complexity analysis:
 #
diff --git a/data_structures/hash_table/anagram_checker.rb b/data_structures/hash_table/anagram_checker.rb
new file mode 100644
index 0000000..43163d4
--- /dev/null
+++ b/data_structures/hash_table/anagram_checker.rb
@@ -0,0 +1,55 @@
+# Challenge name: Is anagram
+#
+# Given two strings s and t , write a function to determine
+# if t is an anagram of s.
+#
+# Note:
+# You may assume the string contains only lowercase alphabets.
+#
+# Follow up:
+# What if the inputs contain unicode characters?
+# How would you adapt your solution to such case?
+#
+# @param {String} s
+# @param {String} t
+# @return {Boolean}
+
+#
+# Approach: Hash table
+#
+# Complexity analysis:
+#
+# Time complexity: O(n). Time complexity is O(n) since accessing the counter table is a constant time operation.
+# Space complexity: O(1). Although we do use extra space, the space complexity is O(1) because the table's size stays constant no matter how large n is.
+#
+def is_anagram(s, t)
+  s_length = s.length
+  t_length = t.length
+  counter = Hash.new(0)
+
+  return false unless s_length == t_length
+
+  (0...s_length).each do |i|
+    counter[s[i]] += 1
+    counter[t[i]] -= 1
+  end
+
+  counter.each do |k, v|
+    return false unless v == 0
+  end
+
+  true
+end
+
+s = 'anagram'
+t = 'nagaram'
+puts(is_anagram(s, t))
+# => true
+s = 'rat'
+t = 'car'
+puts(is_anagram(s, t))
+# => false
+s = 'a'
+t = 'ab'
+puts(is_anagram(s, t))
+# => false

From 2da2ec55f6e32b1c418e44c6b2a4576ecfbfb54f Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Thu, 1 Apr 2021 02:03:14 +0000
Subject: [PATCH 33/83] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index d0c4469..42b9add 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -32,6 +32,7 @@
     * [Postorder Traversal](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/binary_trees/postorder_traversal.rb)
     * [Preorder Traversal](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/binary_trees/preorder_traversal.rb)
   * Hash Table
+    * [Anagram Checker](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/anagram_checker.rb)
     * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/find_all_duplicates_in_an_array.rb)
     * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/richest_customer_wealth.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/two_sum.rb)

From ad959fcfb037a205a42bfed1b496624e2faa05ad Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Wed, 31 Mar 2021 19:04:39 -0700
Subject: [PATCH 34/83] Minor changes

---
 data_structures/hash_table/anagram_checker.rb | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/data_structures/hash_table/anagram_checker.rb b/data_structures/hash_table/anagram_checker.rb
index 43163d4..03f72fa 100644
--- a/data_structures/hash_table/anagram_checker.rb
+++ b/data_structures/hash_table/anagram_checker.rb
@@ -19,8 +19,11 @@
 #
 # Complexity analysis:
 #
-# Time complexity: O(n). Time complexity is O(n) since accessing the counter table is a constant time operation.
-# Space complexity: O(1). Although we do use extra space, the space complexity is O(1) because the table's size stays constant no matter how large n is.
+# Time complexity: O(n). Time complexity is O(n) since accessing the counter
+# table is a constant time operation.
+# Space complexity: O(1). Although we do use extra space,
+# the space complexity is O(1) because the table's size stays constant no
+# matter how large n is.
 #
 def is_anagram(s, t)
   s_length = s.length
@@ -45,10 +48,12 @@ s = 'anagram'
 t = 'nagaram'
 puts(is_anagram(s, t))
 # => true
+
 s = 'rat'
 t = 'car'
 puts(is_anagram(s, t))
 # => false
+
 s = 'a'
 t = 'ab'
 puts(is_anagram(s, t))

From 6b8529a1a698e7316cb809fd01c557f6b7726142 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Wed, 31 Mar 2021 19:05:51 -0700
Subject: [PATCH 35/83] Update anagram_checker.rb

---
 data_structures/hash_table/anagram_checker.rb | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/data_structures/hash_table/anagram_checker.rb b/data_structures/hash_table/anagram_checker.rb
index 03f72fa..1158134 100644
--- a/data_structures/hash_table/anagram_checker.rb
+++ b/data_structures/hash_table/anagram_checker.rb
@@ -17,6 +17,8 @@
 #
 # Approach: Hash table
 #
+
+# 
 # Complexity analysis:
 #
 # Time complexity: O(n). Time complexity is O(n) since accessing the counter

From dc533283a2a3c5743fae1548210f8968fb7a8d08 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 1 Apr 2021 09:36:46 -0700
Subject: [PATCH 36/83] Add hash table approach

---
 data_structures/hash_table/anagram_checker.rb | 73 ++++++++++++++++++-
 1 file changed, 71 insertions(+), 2 deletions(-)

diff --git a/data_structures/hash_table/anagram_checker.rb b/data_structures/hash_table/anagram_checker.rb
index 1158134..0d0f2f6 100644
--- a/data_structures/hash_table/anagram_checker.rb
+++ b/data_structures/hash_table/anagram_checker.rb
@@ -17,8 +17,6 @@
 #
 # Approach: Hash table
 #
-
-# 
 # Complexity analysis:
 #
 # Time complexity: O(n). Time complexity is O(n) since accessing the counter
@@ -60,3 +58,74 @@ s = 'a'
 t = 'ab'
 puts(is_anagram(s, t))
 # => false
+
+
+def is_anagram(s, t)
+  s_length = s.length
+  t_length = t.length
+  counter = Hash.new(0)
+
+  return false unless s_length == t_length
+
+  (0...s_length).each do |i|
+    counter[s[i]] += 1
+  end
+
+  (0...s_length).each do |i|
+    counter[t[i]] -= 1
+
+    return false if counter[t[i]] < 0
+  end
+
+  true
+end
+
+s = 'anagram'
+t = 'nagaram'
+puts(is_anagram(s, t))
+# => true
+
+s = 'rat'
+t = 'car'
+puts(is_anagram(s, t))
+# => false
+
+s = 'a'
+t = 'ab'
+puts(is_anagram(s, t))
+# => false
+
+#
+# Approach 2: Hash table
+#
+
+# Algorithm: we could also first increment the counter for s,
+# then decrement the counter for t. If at any point the counter
+# drops below zero, we know that t contains an extra letter,
+# not in s, and return false immediately.
+
+# Complexity analysis:
+#
+# Time complexity: O(n).
+# Space complexity: O(1).
+#
+
+def is_anagram(s, t)
+  s_length = s.length
+  t_length = t.length
+  counter = Hash.new(0)
+
+  return false unless s_length == t_length
+
+  (0...s_length).each do |i|
+    counter[s[i]] += 1
+  end
+
+  (0...s_length).each do |i|
+    counter[t[i]] -= 1
+
+    return false if counter[t[i]] < 0
+  end
+
+  true
+end

From 44c32084541b2679161577a1257d1454d4f4752d Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 1 Apr 2021 09:36:52 -0700
Subject: [PATCH 37/83] Add another hash table approach

---
 data_structures/hash_table/anagram_checker.rb | 35 +++++++++++++++++++
 1 file changed, 35 insertions(+)

diff --git a/data_structures/hash_table/anagram_checker.rb b/data_structures/hash_table/anagram_checker.rb
index 0d0f2f6..16fc429 100644
--- a/data_structures/hash_table/anagram_checker.rb
+++ b/data_structures/hash_table/anagram_checker.rb
@@ -129,3 +129,38 @@ def is_anagram(s, t)
 
   true
 end
+
+#
+# Approach 3: populate 2 hashes and compare them
+#
+
+def is_anagram(s, t)
+  s = s.chars
+  t = t.chars
+
+  return false if s.count != t.count
+
+  hash1 = {}
+  s.chars.each do |value|
+    hash1[value] = if hash1[value]
+                     hash1[value] + 1
+                   else
+                     1
+                   end
+  end
+
+  hash2 = {}
+  t.chars.each do |value|
+    hash2[value] = if hash2[value]
+                     hash2[value] + 1
+                   else
+                     1
+                   end
+  end
+
+  hash1.keys.each do |key|
+    return false if hash2[key] != hash1[key]
+  end
+
+  true
+end

From 434e72a4f7cc0cd977e98c941449e492929e1d2f Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 1 Apr 2021 09:38:27 -0700
Subject: [PATCH 38/83] Add very simple tests

---
 data_structures/hash_table/anagram_checker.rb | 34 +++++++++++++++++--
 1 file changed, 32 insertions(+), 2 deletions(-)

diff --git a/data_structures/hash_table/anagram_checker.rb b/data_structures/hash_table/anagram_checker.rb
index 16fc429..abbb209 100644
--- a/data_structures/hash_table/anagram_checker.rb
+++ b/data_structures/hash_table/anagram_checker.rb
@@ -130,6 +130,21 @@ def is_anagram(s, t)
   true
 end
 
+s = 'anagram'
+t = 'nagaram'
+puts(is_anagram(s, t))
+# => true
+
+s = 'rat'
+t = 'car'
+puts(is_anagram(s, t))
+# => false
+
+s = 'a'
+t = 'ab'
+puts(is_anagram(s, t))
+# => false
+
 #
 # Approach 3: populate 2 hashes and compare them
 #
@@ -141,7 +156,7 @@ def is_anagram(s, t)
   return false if s.count != t.count
 
   hash1 = {}
-  s.chars.each do |value|
+  s.each do |value|
     hash1[value] = if hash1[value]
                      hash1[value] + 1
                    else
@@ -150,7 +165,7 @@ def is_anagram(s, t)
   end
 
   hash2 = {}
-  t.chars.each do |value|
+  t.each do |value|
     hash2[value] = if hash2[value]
                      hash2[value] + 1
                    else
@@ -164,3 +179,18 @@ def is_anagram(s, t)
 
   true
 end
+
+s = 'anagram'
+t = 'nagaram'
+puts(is_anagram(s, t))
+# => true
+
+s = 'rat'
+t = 'car'
+puts(is_anagram(s, t))
+# => false
+
+s = 'a'
+t = 'ab'
+puts(is_anagram(s, t))
+# => false

From 515b076e61872aaeac08d09ad6c77007ce1d75d5 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 1 Apr 2021 09:42:45 -0700
Subject: [PATCH 39/83] remove duplication

---
 data_structures/hash_table/anagram_checker.rb | 37 +------------------
 1 file changed, 1 insertion(+), 36 deletions(-)

diff --git a/data_structures/hash_table/anagram_checker.rb b/data_structures/hash_table/anagram_checker.rb
index abbb209..e15eed4 100644
--- a/data_structures/hash_table/anagram_checker.rb
+++ b/data_structures/hash_table/anagram_checker.rb
@@ -17,6 +17,7 @@
 #
 # Approach: Hash table
 #
+
 # Complexity analysis:
 #
 # Time complexity: O(n). Time complexity is O(n) since accessing the counter
@@ -59,42 +60,6 @@ t = 'ab'
 puts(is_anagram(s, t))
 # => false
 
-
-def is_anagram(s, t)
-  s_length = s.length
-  t_length = t.length
-  counter = Hash.new(0)
-
-  return false unless s_length == t_length
-
-  (0...s_length).each do |i|
-    counter[s[i]] += 1
-  end
-
-  (0...s_length).each do |i|
-    counter[t[i]] -= 1
-
-    return false if counter[t[i]] < 0
-  end
-
-  true
-end
-
-s = 'anagram'
-t = 'nagaram'
-puts(is_anagram(s, t))
-# => true
-
-s = 'rat'
-t = 'car'
-puts(is_anagram(s, t))
-# => false
-
-s = 'a'
-t = 'ab'
-puts(is_anagram(s, t))
-# => false
-
 #
 # Approach 2: Hash table
 #

From c2bd60c2231b3ccbc385a4dd46d3e7ead10aab9b Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Thu, 1 Apr 2021 09:31:12 -0700
Subject: [PATCH 40/83] Add palindrome challenge

---
 DIRECTORY.md                                 |  1 +
 data_structures/arrays/strings/palindrome.rb | 44 ++++++++++++++++++++
 2 files changed, 45 insertions(+)
 create mode 100644 data_structures/arrays/strings/palindrome.rb

diff --git a/DIRECTORY.md b/DIRECTORY.md
index d0c4469..bca02fb 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -23,6 +23,7 @@
     * Strings
       * [Anagram Checker](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/anagram_checker.rb)
       * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/jewels_and_stones.rb)
+      * [Palindrome](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/palindrome.rb)
       * [Remove Vowels](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/remove_vowels.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum.rb)
     * [Two Sum Ii](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/two_sum_ii.rb)
diff --git a/data_structures/arrays/strings/palindrome.rb b/data_structures/arrays/strings/palindrome.rb
new file mode 100644
index 0000000..1ebcfbe
--- /dev/null
+++ b/data_structures/arrays/strings/palindrome.rb
@@ -0,0 +1,44 @@
+# Challenge name: Valid Palindrome
+#
+# Given a string s, determine if it is a palindrome,
+# considering only alphanumeric characters and ignoring cases.
+#
+# Example 1:
+# Input: s = "A man, a plan, a canal: Panama"
+# Output: true
+# Explanation: "amanaplanacanalpanama" is a palindrome.
+#
+# Example 2:
+# Input: s = "race a car"
+# Output: false
+# Explanation: "raceacar" is not a palindrome.
+#
+# Constraints:
+# 1 <= s.length <= 2 * 105
+# s consists only of printable ASCII characters.
+# @param {String} s
+# @return {Boolean}
+
+#
+# Approach 1: Brute Force
+#
+# Time Complexity:
+#
+def is_palindrome(s)
+  s.downcase
+end
+
+s = 'A man, a plan, a canal: Panama'
+puts is_palindrome(s)
+# Output: true
+# Explanation: "amanaplanacanalpanama" is a palindrome.
+
+s = 'race a car'
+puts is_palindrome(s)
+# Output: false
+# Explanation: "raceacar" is not a palindrome.
+
+s = 'ab_a'
+puts is_palindrome(s)
+# Output: true
+# Explanation: "aba" is a palindrome.
\ No newline at end of file

From 13aec345eaca265cc5ea218754faefc62fe557a6 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 1 Apr 2021 09:54:34 -0700
Subject: [PATCH 41/83] add generate_parenthesis backtracking approach

---
 backtracking/generate_paranthesis.rb | 47 ++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 backtracking/generate_paranthesis.rb

diff --git a/backtracking/generate_paranthesis.rb b/backtracking/generate_paranthesis.rb
new file mode 100644
index 0000000..5881aea
--- /dev/null
+++ b/backtracking/generate_paranthesis.rb
@@ -0,0 +1,47 @@
+# Given n pairs of parentheses, write a function to generate all combinations
+# of well-formed parentheses.
+#
+# Example 1:
+#
+# Input: n = 3
+# Output: ["((()))","(()())","(())()","()(())","()()()"]
+# Example 2:
+#
+# Input: n = 1
+# Output: ["()"]
+#
+#
+# Constraints:
+#
+# 1 <= n <= 8
+
+# @param {Integer} n
+# @return {String[]}
+def generate_parenthesis(n)
+  parenthesis = []
+  backtrack(parenthesis, "", 0, 0, n)
+  parenthesis
+end
+
+def backtrack(parenthesis, curr, open, close, max)
+  if curr.length == max * 2
+    parenthesis.push(curr)
+    return
+  end
+
+  if open < max
+    backtrack(parenthesis, curr + "(", open + 1, close, max)
+  end
+
+  if close < open
+    backtrack(parenthesis, curr + ")", open, close + 1, max)
+  end
+end
+
+n = 3
+print(generate_parenthesis(n))
+# Output: ["((()))","(()())","(())()","()(())","()()()"]
+
+n = 1
+print(generate_parenthesis(n))
+# Output: ["()"]

From 1350b46474aa437169639166e041ebdfdaa469af Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Thu, 1 Apr 2021 16:54:50 +0000
Subject: [PATCH 42/83] updating DIRECTORY.md

---
 DIRECTORY.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 42b9add..7c86a15 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -1,4 +1,7 @@
 
+## Backtracking
+  * [Generate Paranthesis](https://github.com/TheAlgorithms/Ruby/blob/master/backtracking/generate_paranthesis.rb)
+
 ## Bit Manipulation
   * [Power Of Two](https://github.com/TheAlgorithms/Ruby/blob/master/bit_manipulation/power_of_two.rb)
 

From 1d974b2ea18e646fe277ada716902d42ed95c659 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 1 Apr 2021 09:58:04 -0700
Subject: [PATCH 43/83] Add approach description

---
 backtracking/generate_paranthesis.rb | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/backtracking/generate_paranthesis.rb b/backtracking/generate_paranthesis.rb
index 5881aea..587a25c 100644
--- a/backtracking/generate_paranthesis.rb
+++ b/backtracking/generate_paranthesis.rb
@@ -15,6 +15,16 @@
 #
 # 1 <= n <= 8
 
+# Approach:
+#
+# Let's only add '(' or ')' when we know it will remain a valid sequence.
+# We can do this by keeping track of the number of opening and closing brackets
+# we have placed so far.
+#
+# We can start an opening bracket if we still have one (of n) left to place.
+# And we could start a closing bracket if it'd not exceed the number of opening
+# brackets.
+
 # @param {Integer} n
 # @return {String[]}
 def generate_parenthesis(n)

From 7eea20ed6e0369db5d5ff8d2f99aa431ac78a224 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 1 Apr 2021 10:06:40 -0700
Subject: [PATCH 44/83] Add complexity analysis and detailed example

---
 backtracking/generate_paranthesis.rb | 49 ++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)

diff --git a/backtracking/generate_paranthesis.rb b/backtracking/generate_paranthesis.rb
index 587a25c..0ea684e 100644
--- a/backtracking/generate_paranthesis.rb
+++ b/backtracking/generate_paranthesis.rb
@@ -25,6 +25,14 @@
 # And we could start a closing bracket if it'd not exceed the number of opening
 # brackets.
 
+# Complexity Analysis
+# 
+# Time Complexity: O(4^n/sqrt(n). Each valid sequence has at most n steps during the backtracking procedure.
+# Space Complexity: O(4^n/sqrt(n), as described above, and using O(n) space to store the sequence.
+
+# Refer to the attached diagram for recursion,
+# The numbers next to each node are the counts of left and right parantheses
+
 # @param {Integer} n
 # @return {String[]}
 def generate_parenthesis(n)
@@ -52,6 +60,47 @@ n = 3
 print(generate_parenthesis(n))
 # Output: ["((()))","(()())","(())()","()(())","()()()"]
 
+# *** Example: n = 3 *** Space after each DFS instance
+# backtrack called with  0 0 []
+#   backtrack called with ( 1 0 []
+#     backtrack called with (( 2 0 []
+#       backtrack called with ((( 3 0 []
+#         backtrack called with ((() 3 1 []
+#           backtrack called with ((()) 3 2 []
+#             backtrack called with ((())) 3 3 []
+#           backtrack return with ((()) 3 2 ["((()))"]
+#         backtrack return with ((() 3 1 ["((()))"]
+#       backtrack return with ((( 3 0 ["((()))"]
+#       backtrack called with (() 2 1 ["((()))"]
+#         backtrack called with (()( 3 1 ["((()))"]
+#           backtrack called with (()() 3 2 ["((()))"]
+#             backtrack called with (()()) 3 3 ["((()))"]
+#           backtrack return with (()() 3 2 ["((()))", "(()())"]
+#         backtrack return with (()( 3 1 ["((()))", "(()())"]
+#         backtrack called with (()) 2 2 ["((()))", "(()())"]
+#           backtrack called with (())( 3 2 ["((()))", "(()())"]
+#             backtrack called with (())() 3 3 ["((()))", "(()())"]
+#           backtrack return with (())( 3 2 ["((()))", "(()())", "(())()"]
+#         backtrack return with (()) 2 2 ["((()))", "(()())", "(())()"]
+#       backtrack return with (() 2 1 ["((()))", "(()())", "(())()"]
+#     backtrack return with (( 2 0 ["((()))", "(()())", "(())()"]
+#     backtrack called with () 1 1 ["((()))", "(()())", "(())()"]
+#       backtrack called with ()( 2 1 ["((()))", "(()())", "(())()"]
+#         backtrack called with ()(( 3 1 ["((()))", "(()())", "(())()"]
+#           backtrack called with ()(() 3 2 ["((()))", "(()())", "(())()"]
+#             backtrack called with ()(()) 3 3 ["((()))", "(()())", "(())()"]
+#           backtrack return with ()(() 3 2 ["((()))", "(()())", "(())()", "()(())"]
+#         backtrack return with ()(( 3 1 ["((()))", "(()())", "(())()", "()(())"]
+#         backtrack called with ()() 2 2 ["((()))", "(()())", "(())()", "()(())"]
+#           backtrack called with ()()( 3 2 ["((()))", "(()())", "(())()", "()(())"]
+#             backtrack called with ()()() 3 3 ["((()))", "(()())", "(())()", "()(())"]
+#           backtrack return with ()()( 3 2 ["((()))", "(()())", "(())()", "()(())", "()()()"]
+#         backtrack return with ()() 2 2 ["((()))", "(()())", "(())()", "()(())", "()()()"]
+#       backtrack return with ()( 2 1 ["((()))", "(()())", "(())()", "()(())", "()()()"]
+#     backtrack return with () 1 1 ["((()))", "(()())", "(())()", "()(())", "()()()"]
+#   backtrack return with ( 1 0 ["((()))", "(()())", "(())()", "()(())", "()()()"]
+# backtrack return with  0 0 ["((()))", "(()())", "(())()", "()(())", "()()()"]
+
 n = 1
 print(generate_parenthesis(n))
 # Output: ["()"]

From fc0c664f6bd123fd2e6f5dba7a06c05497240866 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 1 Apr 2021 10:45:41 -0700
Subject: [PATCH 45/83] close )

---
 backtracking/generate_paranthesis.rb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/backtracking/generate_paranthesis.rb b/backtracking/generate_paranthesis.rb
index 0ea684e..5c0e3fa 100644
--- a/backtracking/generate_paranthesis.rb
+++ b/backtracking/generate_paranthesis.rb
@@ -27,8 +27,8 @@
 
 # Complexity Analysis
 # 
-# Time Complexity: O(4^n/sqrt(n). Each valid sequence has at most n steps during the backtracking procedure.
-# Space Complexity: O(4^n/sqrt(n), as described above, and using O(n) space to store the sequence.
+# Time Complexity: O(4^n/sqrt(n)). Each valid sequence has at most n steps during the backtracking procedure.
+# Space Complexity: O(4^n/sqrt(n)), as described above, and using O(n) space to store the sequence.
 
 # Refer to the attached diagram for recursion,
 # The numbers next to each node are the counts of left and right parantheses

From e90238e1f712285bb87d421acdb34de0760d8ef5 Mon Sep 17 00:00:00 2001
From: Abhinav Anand <manasgmishra@gmail.com>
Date: Fri, 2 Apr 2021 23:01:29 +0530
Subject: [PATCH 46/83] Added factorial iterative  program

---
 maths/factorial_iterative.rb | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)
 create mode 100644 maths/factorial_iterative.rb

diff --git a/maths/factorial_iterative.rb b/maths/factorial_iterative.rb
new file mode 100644
index 0000000..cc070b3
--- /dev/null
+++ b/maths/factorial_iterative.rb
@@ -0,0 +1,28 @@
+=begin
+A ruby program calculate factorial of a given number.
+Mathematical Explanation: The factorial of a number is the product of all the integers from 1 to that number. 
+i.e: n! = n*(n-1)*(n-2)......*2*1
+=end
+
+def factorial(n)
+    if n < 0
+        return nil
+    end
+    
+    fac = 1
+    while n > 0
+        fac = fac * n
+        n -= 1
+    end
+    
+    return fac
+end
+
+puts '4! = ' + factorial(4).to_s
+# 4! = 24
+
+puts '0! = ' + factorial(0).to_s
+# 0! = 1
+
+puts '10! = ' + factorial(10).to_s
+# 10! = 3628800

From 30c9176098283561bee7598eaaebe3019bd345cd Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Fri, 2 Apr 2021 11:22:53 -0700
Subject: [PATCH 47/83] minor changes

---
 .../{factorial_iterative.rb => factorial.rb}  | 25 +++++++++++--------
 1 file changed, 14 insertions(+), 11 deletions(-)
 rename maths/{factorial_iterative.rb => factorial.rb} (72%)

diff --git a/maths/factorial_iterative.rb b/maths/factorial.rb
similarity index 72%
rename from maths/factorial_iterative.rb
rename to maths/factorial.rb
index cc070b3..e83b347 100644
--- a/maths/factorial_iterative.rb
+++ b/maths/factorial.rb
@@ -4,18 +4,21 @@ Mathematical Explanation: The factorial of a number is the product of all the in
 i.e: n! = n*(n-1)*(n-2)......*2*1
 =end
 
+#
+# Approach: Interative
+#
+
 def factorial(n)
-    if n < 0
-        return nil
-    end
-    
-    fac = 1
-    while n > 0
-        fac = fac * n
-        n -= 1
-    end
-    
-    return fac
+  return nil if n < 0
+  
+  fac = 1
+
+  while n > 0
+    fac *= n
+    n -= 1
+  end
+  
+  fac
 end
 
 puts '4! = ' + factorial(4).to_s

From 46ec0d4fecc019582272ee848f6be2659abd9d21 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Fri, 2 Apr 2021 18:23:23 +0000
Subject: [PATCH 48/83] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 42b9add..b732e81 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -66,6 +66,7 @@
   * [Ceil](https://github.com/TheAlgorithms/Ruby/blob/master/maths/ceil.rb)
   * [Ceil Test](https://github.com/TheAlgorithms/Ruby/blob/master/maths/ceil_test.rb)
   * [Decimal To Binary](https://github.com/TheAlgorithms/Ruby/blob/master/maths/decimal_to_binary.rb)
+  * [Factorial](https://github.com/TheAlgorithms/Ruby/blob/master/maths/factorial.rb)
   * [Fibonacci](https://github.com/TheAlgorithms/Ruby/blob/master/maths/fibonacci.rb)
   * [Number Of Digits](https://github.com/TheAlgorithms/Ruby/blob/master/maths/number_of_digits.rb)
   * [Power Of Two](https://github.com/TheAlgorithms/Ruby/blob/master/maths/power_of_two.rb)

From 04a4c9aaedfac2f3b9145be39f1201362a053a0d Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Mon, 5 Apr 2021 13:57:41 -0700
Subject: [PATCH 49/83] Add solution using .reverse

---
 data_structures/arrays/strings/palindrome.rb | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/data_structures/arrays/strings/palindrome.rb b/data_structures/arrays/strings/palindrome.rb
index 1ebcfbe..03490ac 100644
--- a/data_structures/arrays/strings/palindrome.rb
+++ b/data_structures/arrays/strings/palindrome.rb
@@ -20,12 +20,13 @@
 # @return {Boolean}
 
 #
-# Approach 1: Brute Force
+# Approach 1: Using Ruby method .reverse
 #
-# Time Complexity:
+# Time Complexity: O(n)
 #
 def is_palindrome(s)
-  s.downcase
+  letters_only = s.downcase.gsub(/[^0-9a-z]/i, '')
+  letters_only.reverse == letters_only
 end
 
 s = 'A man, a plan, a canal: Panama'

From 6c7b37ab76b1a52c93205d91fb65a9d0413cc1db Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Mon, 5 Apr 2021 14:08:23 -0700
Subject: [PATCH 50/83] Add solution using a reversed array

---
 data_structures/arrays/strings/palindrome.rb | 29 ++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/data_structures/arrays/strings/palindrome.rb b/data_structures/arrays/strings/palindrome.rb
index 03490ac..4d70171 100644
--- a/data_structures/arrays/strings/palindrome.rb
+++ b/data_structures/arrays/strings/palindrome.rb
@@ -39,6 +39,35 @@ puts is_palindrome(s)
 # Output: false
 # Explanation: "raceacar" is not a palindrome.
 
+s = 'ab_a'
+puts is_palindrome(s)
+# Output: true
+# Explanation: "aba" is a palindrome.
+
+#
+# Approach 2: Reversed array
+#
+# Time Complexity: O(n)
+#
+def is_palindrome(s)
+  letters_only_array = s.downcase.gsub(/[^0-9a-z]/i, '').split('')
+  reversed_array = []
+  letters_only_array.each do |letter|
+    reversed_array.unshift(letter)
+  end
+  letters_only_array == reversed_array
+end
+
+s = 'A man, a plan, a canal: Panama'
+puts is_palindrome(s)
+# Output: true
+# Explanation: "amanaplanacanalpanama" is a palindrome.
+
+s = 'race a car'
+puts is_palindrome(s)
+# Output: false
+# Explanation: "raceacar" is not a palindrome.
+
 s = 'ab_a'
 puts is_palindrome(s)
 # Output: true

From 7655003b6cc333ee1512a33f7c9fa0901974189d Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Mon, 5 Apr 2021 14:31:57 -0700
Subject: [PATCH 51/83] Add solution using two pointers

---
 data_structures/arrays/strings/palindrome.rb | 36 ++++++++++++++++++++
 1 file changed, 36 insertions(+)

diff --git a/data_structures/arrays/strings/palindrome.rb b/data_structures/arrays/strings/palindrome.rb
index 4d70171..28e7921 100644
--- a/data_structures/arrays/strings/palindrome.rb
+++ b/data_structures/arrays/strings/palindrome.rb
@@ -68,6 +68,42 @@ puts is_palindrome(s)
 # Output: false
 # Explanation: "raceacar" is not a palindrome.
 
+s = 'ab_a'
+puts is_palindrome(s)
+# Output: true
+# Explanation: "aba" is a palindrome.
+
+#
+# Approach 2: Two Pointers
+#
+# Time Complexity: O(n)
+#
+def is_palindrome(s)
+  letters_only = s.downcase.gsub(/[^0-9a-z]/i, '')
+  p1 = 0
+  p2 = letters_only.length - 1
+
+  while p1 < p2
+    if letters_only[p1] == letters_only[p2]
+      p1 += 1
+      p2 -= 1
+    else
+      return false
+    end
+  end
+  true
+end
+
+s = 'A man, a plan, a canal: Panama'
+puts is_palindrome(s)
+# Output: true
+# Explanation: "amanaplanacanalpanama" is a palindrome.
+
+s = 'race a car'
+puts is_palindrome(s)
+# Output: false
+# Explanation: "raceacar" is not a palindrome.
+
 s = 'ab_a'
 puts is_palindrome(s)
 # Output: true

From e6b674275ea56995dafe8e7e080e3789ea503f91 Mon Sep 17 00:00:00 2001
From: nyapsilon <maximbarsukov@bk.ru>
Date: Fri, 9 Apr 2021 21:24:04 +0300
Subject: [PATCH 52/83] Minor code style improvements

Tabs are corrected, semantic blocks are separated.
---
 Searches/binary_search.rb | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/Searches/binary_search.rb b/Searches/binary_search.rb
index bbc8efa..d0710a2 100644
--- a/Searches/binary_search.rb
+++ b/Searches/binary_search.rb
@@ -8,18 +8,21 @@ def binary_search(array, key)
     return middle if array[middle] == key
 
     if key < array[middle]
-  back = middle - 1
-else
-  front = middle + 1
-end
+      back = middle - 1
+    else
+      front = middle + 1
+    end
   end
+  
   nil
 end
 
 puts "Enter a sorted space-separated list:"
 arr = gets.chomp.split(' ').map(&:to_i)
+
 puts "Enter the value to be searched:"
 value = gets.chomp.to_i
+
 puts if binary_search(arr, value) != nil
   "Found at index #{binary_search(arr, value)}"
 else

From bd6b1067c0b56d206e7c4a9307c57312289bc197 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Fri, 9 Apr 2021 21:07:54 -0700
Subject: [PATCH 53/83] Update data_structures/arrays/strings/palindrome.rb

---
 data_structures/arrays/strings/palindrome.rb | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/data_structures/arrays/strings/palindrome.rb b/data_structures/arrays/strings/palindrome.rb
index 28e7921..176243e 100644
--- a/data_structures/arrays/strings/palindrome.rb
+++ b/data_structures/arrays/strings/palindrome.rb
@@ -76,7 +76,14 @@ puts is_palindrome(s)
 #
 # Approach 2: Two Pointers
 #
-# Time Complexity: O(n)
+
+#
+# Complexity Analysis:
+#
+# Time Complexity: O(n), in length n of the string. We traverse over each
+# character at most once until the two pointers meet in the middle, or when
+# we break and return early.
+# Space Complexity: O(1). No extra space required, at all.
 #
 def is_palindrome(s)
   letters_only = s.downcase.gsub(/[^0-9a-z]/i, '')
@@ -107,4 +114,4 @@ puts is_palindrome(s)
 s = 'ab_a'
 puts is_palindrome(s)
 # Output: true
-# Explanation: "aba" is a palindrome.
\ No newline at end of file
+# Explanation: "aba" is a palindrome.

From 49db26c56be44d2ca3ab00034e264a1ae877604e Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Fri, 9 Apr 2021 21:07:57 -0700
Subject: [PATCH 54/83] Update data_structures/arrays/strings/palindrome.rb

---
 data_structures/arrays/strings/palindrome.rb | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/data_structures/arrays/strings/palindrome.rb b/data_structures/arrays/strings/palindrome.rb
index 176243e..587e242 100644
--- a/data_structures/arrays/strings/palindrome.rb
+++ b/data_structures/arrays/strings/palindrome.rb
@@ -47,7 +47,17 @@ puts is_palindrome(s)
 #
 # Approach 2: Reversed array
 #
-# Time Complexity: O(n)
+# Complexity Analysis:
+#
+# Time Complexity: O(n), in length n of the string.
+#
+# We need to iterate through the string: When we filter out non-alphanumeric characters and convert the remaining
+# characters to lower-case. When we reverse the string. When we compare the original and the reversed strings. 
+# Each iteration runs linearly in time (since each character operation completes in constant time). 
+# Thus, the effective run-time complexity is linear.
+#
+# Space Complexity: O(n), in length n of the string. We need O(n) additional
+# space to store the filtered string and the reversed string.
 #
 def is_palindrome(s)
   letters_only_array = s.downcase.gsub(/[^0-9a-z]/i, '').split('')

From 443cf9db8850e78d45f1fde83907f1d021e597e0 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sat, 10 Apr 2021 04:07:57 +0000
Subject: [PATCH 55/83] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index d118dca..c94db91 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -65,6 +65,7 @@
   * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/maths/add_digits.rb)
   * [Aliquot Sum](https://github.com/TheAlgorithms/Ruby/blob/master/maths/aliquot_sum.rb)
   * [Aliquot Sum Test](https://github.com/TheAlgorithms/Ruby/blob/master/maths/aliquot_sum_test.rb)
+  * [Average Mean](https://github.com/TheAlgorithms/Ruby/blob/master/maths/average_mean.rb)
   * [Binary To Decimal](https://github.com/TheAlgorithms/Ruby/blob/master/maths/binary_to_decimal.rb)
   * [Ceil](https://github.com/TheAlgorithms/Ruby/blob/master/maths/ceil.rb)
   * [Ceil Test](https://github.com/TheAlgorithms/Ruby/blob/master/maths/ceil_test.rb)

From 9fbd75fa66dd64a7766fa250075e37bcd26c406f Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 10 Apr 2021 09:56:05 -0700
Subject: [PATCH 56/83] Add hash table approach

---
 data_structures/arrays/arrays_intersection.rb | 55 +++++++++++++++++++
 1 file changed, 55 insertions(+)
 create mode 100644 data_structures/arrays/arrays_intersection.rb

diff --git a/data_structures/arrays/arrays_intersection.rb b/data_structures/arrays/arrays_intersection.rb
new file mode 100644
index 0000000..cf1c1dc
--- /dev/null
+++ b/data_structures/arrays/arrays_intersection.rb
@@ -0,0 +1,55 @@
+# Given three integer arrays arr1, arr2 and arr3 sorted in strictly increasing order, return a sorted array of only the integers that appeared in all three arrays.
+#
+# Example 1:
+#
+# Input: arr1 = [1,2,3,4,5], arr2 = [1,2,5,7,9], arr3 = [1,3,4,5,8]
+# Output: [1,5]
+# Explanation: Only 1 and 5 appeared in the three arrays.
+#
+# Example 2:
+#
+# Input: arr1 = [197,418,523,876,1356], arr2 = [501,880,1593,1710,1870], arr3 = [521,682,1337,1395,1764]
+# Output: []
+#
+#
+
+#
+# Approach: Hash table
+#
+
+# Complexity Analysis
+
+# Time Complexity: O(n) - n is the total length of
+# all of the input arrays.
+# Space Complexity: O(n) - n is the total length of all of the
+# input arrays. This is because we adopted a Hash table to store all
+# numbers and their number of appearances as values.
+
+def arrays_intersection(arr1, arr2, arr3)
+  hash = Hash.new(0)
+
+  add_to_hash(arr1, hash)
+  add_to_hash(arr2, hash)
+  add_to_hash(arr3, hash)
+
+  hash.select { |key, value| value == 3 }.keys
+end
+
+def add_to_hash(arr, hash)
+  arr.each_with_index do |value, index|
+   hash[value] += 1
+  end
+end
+
+arr1 = [1,2,3,4,5]
+arr2 = [1,2,5,7,9]
+arr3 = [1,3,4,5,8]
+print arrays_intersection(arr1, arr2, arr3)
+# Output: [1,5]
+# Explanation: Only 1 and 5 appeared in the three arrays.
+
+arr1 = [197,418,523,876,1356]
+arr2 = [501,880,1593,1710,1870]
+arr3 = [521,682,1337,1395,1764]
+print arrays_intersection(arr1, arr2, arr3)
+# Output: []

From 21e8bb04ef3d4346e1ba94dfb093fb7e1ed3cba3 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sat, 10 Apr 2021 16:56:19 +0000
Subject: [PATCH 57/83] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index a34b83d..bd38b0d 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -14,6 +14,7 @@
 ## Data Structures
   * Arrays
     * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/add_digits.rb)
+    * [Arrays Intersection](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/arrays_intersection.rb)
     * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_all_duplicates_in_an_array.rb)
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)

From fe4e56e8a4a04b3fc317477ad6a16e369f50bf1a Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 10 Apr 2021 09:57:25 -0700
Subject: [PATCH 58/83] Move to correct path

---
 data_structures/{arrays => hash_table}/arrays_intersection.rb | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename data_structures/{arrays => hash_table}/arrays_intersection.rb (100%)

diff --git a/data_structures/arrays/arrays_intersection.rb b/data_structures/hash_table/arrays_intersection.rb
similarity index 100%
rename from data_structures/arrays/arrays_intersection.rb
rename to data_structures/hash_table/arrays_intersection.rb

From d6e7b9f1d8411d02a81664f517dbec81b56f9e27 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sat, 10 Apr 2021 16:57:53 +0000
Subject: [PATCH 59/83] updating DIRECTORY.md

---
 DIRECTORY.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index bd38b0d..daeb2cc 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -14,7 +14,6 @@
 ## Data Structures
   * Arrays
     * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/add_digits.rb)
-    * [Arrays Intersection](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/arrays_intersection.rb)
     * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_all_duplicates_in_an_array.rb)
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
@@ -38,6 +37,7 @@
     * [Preorder Traversal](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/binary_trees/preorder_traversal.rb)
   * Hash Table
     * [Anagram Checker](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/anagram_checker.rb)
+    * [Arrays Intersection](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/arrays_intersection.rb)
     * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/find_all_duplicates_in_an_array.rb)
     * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/richest_customer_wealth.rb)
     * [Two Sum](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/hash_table/two_sum.rb)

From 745b66227bb05231d401d51e558a00aae42d3a39 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 10 Apr 2021 10:04:40 -0700
Subject: [PATCH 60/83] Minor changes

---
 .../hash_table/arrays_intersection.rb         | 19 ++++++++++---------
 1 file changed, 10 insertions(+), 9 deletions(-)

diff --git a/data_structures/hash_table/arrays_intersection.rb b/data_structures/hash_table/arrays_intersection.rb
index cf1c1dc..7d270fc 100644
--- a/data_structures/hash_table/arrays_intersection.rb
+++ b/data_structures/hash_table/arrays_intersection.rb
@@ -32,24 +32,25 @@ def arrays_intersection(arr1, arr2, arr3)
   add_to_hash(arr2, hash)
   add_to_hash(arr3, hash)
 
-  hash.select { |key, value| value == 3 }.keys
+  hash.select { |_key, value| value == 3 }.keys
 end
 
 def add_to_hash(arr, hash)
-  arr.each_with_index do |value, index|
-   hash[value] += 1
+  arr.count.times do |pointer|
+    value = arr[pointer]
+    hash[value] += 1
   end
 end
 
-arr1 = [1,2,3,4,5]
-arr2 = [1,2,5,7,9]
-arr3 = [1,3,4,5,8]
+arr1 = [1, 2, 3, 4, 5]
+arr2 = [1, 2, 5, 7, 9]
+arr3 = [1, 3, 4, 5, 8]
 print arrays_intersection(arr1, arr2, arr3)
 # Output: [1,5]
 # Explanation: Only 1 and 5 appeared in the three arrays.
 
-arr1 = [197,418,523,876,1356]
-arr2 = [501,880,1593,1710,1870]
-arr3 = [521,682,1337,1395,1764]
+arr1 = [197, 418, 523, 876, 1356]
+arr2 = [501, 880, 1593, 1710, 1870]
+arr3 = [521, 682, 1337, 1395, 1764]
 print arrays_intersection(arr1, arr2, arr3)
 # Output: []

From 2197a587fb4d6405adc425adfa81bf06922c550b Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 10 Apr 2021 10:15:00 -0700
Subject: [PATCH 61/83] Update arrays_intersection.rb

---
 data_structures/hash_table/arrays_intersection.rb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/hash_table/arrays_intersection.rb b/data_structures/hash_table/arrays_intersection.rb
index 7d270fc..f100e37 100644
--- a/data_structures/hash_table/arrays_intersection.rb
+++ b/data_structures/hash_table/arrays_intersection.rb
@@ -32,7 +32,7 @@ def arrays_intersection(arr1, arr2, arr3)
   add_to_hash(arr2, hash)
   add_to_hash(arr3, hash)
 
-  hash.select { |_key, value| value == 3 }.keys
+  hash.select { |key, value| value == 3 }.keys
 end
 
 def add_to_hash(arr, hash)

From ce0d1863a292cb69ab7ab01b4145e8e462058f29 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 10 Apr 2021 10:38:43 -0700
Subject: [PATCH 62/83] Next greater element

---
 .../arrays/next_greater_element.rb            | 55 +++++++++++++++++++
 1 file changed, 55 insertions(+)
 create mode 100644 data_structures/arrays/next_greater_element.rb

diff --git a/data_structures/arrays/next_greater_element.rb b/data_structures/arrays/next_greater_element.rb
new file mode 100644
index 0000000..fc71766
--- /dev/null
+++ b/data_structures/arrays/next_greater_element.rb
@@ -0,0 +1,55 @@
+# You are given two integer arrays nums1 and nums2 both of unique elements, where nums1 is a subset of nums2.
+#
+# Find all the next greater numbers for nums1's elements in the corresponding places of nums2.
+#
+# The Next Greater Number of a number x in nums1 is the first greater number to its right in nums2. If it does not exist, return -1 for this number.
+
+# Example 1:
+#
+# Input: nums1 = [4,1,2], nums2 = [1,3,4,2]
+# Output: [-1,3,-1]
+#
+# Explanation:
+# For number 4 in the first array, you cannot find the next greater number for it in the second array, so output -1.
+# For number 1 in the first array, the next greater number for it in the second array is 3.
+# For number 2 in the first array, there is no next greater number for it in the second array, so output -1.
+#
+# Example 2:
+#
+# Input: nums1 = [2,4], nums2 = [1,2,3,4]
+# Output: [3,-1]
+# 
+# Explanation:
+# For number 2 in the first array, the next greater number for it in the second array is 3.
+# For number 4 in the first array, there is no next greater number for it in the second array, so output -1.
+
+# @param {Integer[]} nums1
+# @param {Integer[]} nums2
+# @return {Integer[]}
+def next_greater_element(nums1, nums2)
+  nums1.each_with_index do |value, pointer1|
+    max = 0
+    pos_nums2 = nums2.find_index(value)
+
+    nums2[pos_nums2..nums2.count].each do |value|
+      if value > nums1[pointer1]
+        max = value
+        break
+      end
+    end
+
+    nums1[pointer1] = (nums1[pointer1] < max ? max : -1)
+  end
+
+  nums1
+end
+
+nums1 = [4, 1, 2]
+nums2 = [1, 3, 4, 2]
+print next_greater_element(nums1, nums2)
+# Output: [-1,3,-1]
+
+nums1 = [2, 4]
+nums2 = [1, 2, 3, 4]
+print next_greater_element(nums1, nums2)
+# Output: [3,-1]

From 1c9a26f389a5d62b60a10a7879c0eed848ec8c0f Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 10 Apr 2021 10:41:01 -0700
Subject: [PATCH 63/83] Minor changes

---
 data_structures/arrays/next_greater_element.rb | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/data_structures/arrays/next_greater_element.rb b/data_structures/arrays/next_greater_element.rb
index fc71766..0790ab1 100644
--- a/data_structures/arrays/next_greater_element.rb
+++ b/data_structures/arrays/next_greater_element.rb
@@ -18,7 +18,7 @@
 #
 # Input: nums1 = [2,4], nums2 = [1,2,3,4]
 # Output: [3,-1]
-# 
+#
 # Explanation:
 # For number 2 in the first array, the next greater number for it in the second array is 3.
 # For number 4 in the first array, there is no next greater number for it in the second array, so output -1.
@@ -27,18 +27,18 @@
 # @param {Integer[]} nums2
 # @return {Integer[]}
 def next_greater_element(nums1, nums2)
-  nums1.each_with_index do |value, pointer1|
+  nums1.each_with_index do |nums1_value, pointer1|
     max = 0
-    pos_nums2 = nums2.find_index(value)
+    pos_nums2 = nums2.find_index(nums1_value)
 
-    nums2[pos_nums2..nums2.count].each do |value|
-      if value > nums1[pointer1]
-        max = value
+    nums2[pos_nums2..nums2.count].each do |nums2_value|
+      if nums2_value > nums1_value
+        max = nums2_value
         break
       end
     end
 
-    nums1[pointer1] = (nums1[pointer1] < max ? max : -1)
+    nums1[pointer1] = (nums1_value < max ? max : -1)
   end
 
   nums1

From 4e0d914d63c1eb4c4ea2eb436325b3e2992623cf Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sat, 10 Apr 2021 17:41:17 +0000
Subject: [PATCH 64/83] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index c94db91..763e907 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -18,6 +18,7 @@
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
     * [Get Products Of All Other Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/get_products_of_all_other_elements.rb)
+    * [Next Greater Element](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/next_greater_element.rb)
     * [Remove Elements](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/remove_elements.rb)
     * [Richest Customer Wealth](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/richest_customer_wealth.rb)
     * [Shuffle Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/shuffle_array.rb)

From 4d9d7ca1cdad47591163d384c8de5f891f23c2a8 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 10 Apr 2021 10:46:55 -0700
Subject: [PATCH 65/83] add complexity analysis

---
 data_structures/arrays/next_greater_element.rb | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/data_structures/arrays/next_greater_element.rb b/data_structures/arrays/next_greater_element.rb
index 0790ab1..ffe957e 100644
--- a/data_structures/arrays/next_greater_element.rb
+++ b/data_structures/arrays/next_greater_element.rb
@@ -23,6 +23,15 @@
 # For number 2 in the first array, the next greater number for it in the second array is 3.
 # For number 4 in the first array, there is no next greater number for it in the second array, so output -1.
 
+# 
+# Approach: Brute Force
+# 
+
+# Complexity Analysis
+# 
+# Time complexity : O(m*n). The complete nums1 array (of size n) needs to be scanned for all the m elements of nums2 in the worst case.
+# Space complexity : O(1). No additional space since we're swapping elements in nums1 and returning the input array.
+
 # @param {Integer[]} nums1
 # @param {Integer[]} nums2
 # @return {Integer[]}

From 20d5ea3b6d419bd3b9fc62f07c3863607ff1c167 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 10 Apr 2021 10:49:41 -0700
Subject: [PATCH 66/83] Update next_greater_element.rb

---
 data_structures/arrays/next_greater_element.rb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/data_structures/arrays/next_greater_element.rb b/data_structures/arrays/next_greater_element.rb
index ffe957e..92b3344 100644
--- a/data_structures/arrays/next_greater_element.rb
+++ b/data_structures/arrays/next_greater_element.rb
@@ -29,8 +29,8 @@
 
 # Complexity Analysis
 # 
-# Time complexity : O(m*n). The complete nums1 array (of size n) needs to be scanned for all the m elements of nums2 in the worst case.
-# Space complexity : O(1). No additional space since we're swapping elements in nums1 and returning the input array.
+# Time complexity: O(m*n). The complete nums1 array (of size n) needs to be scanned for all the m elements of nums2 in the worst case.
+# Space complexity: O(1). No additional space since we're swapping elements in nums1 and returning the input array.
 
 # @param {Integer[]} nums1
 # @param {Integer[]} nums2

From f94eafd15a76817545647c5c408af416fd21ee15 Mon Sep 17 00:00:00 2001
From: maxbarsukov <maximbarsukov@bk.ru>
Date: Sun, 11 Apr 2021 14:39:22 +0300
Subject: [PATCH 67/83] The Searches folder is renamed to lowercase just like
 the other folders

---
 {Searches => searches}/binary_search.rb                  | 0
 {Searches => searches}/depth_first_search.rb             | 0
 {Searches => searches}/double_linear_search.rb           | 0
 {Searches => searches}/jump_search.rb                    | 0
 {Searches => searches}/linear_search.rb                  | 0
 {Searches => searches}/recursive_double_linear_search.rb | 0
 {Searches => searches}/recursive_linear_search.rb        | 0
 {Searches => searches}/ternary_search.rb                 | 0
 8 files changed, 0 insertions(+), 0 deletions(-)
 rename {Searches => searches}/binary_search.rb (100%)
 rename {Searches => searches}/depth_first_search.rb (100%)
 rename {Searches => searches}/double_linear_search.rb (100%)
 rename {Searches => searches}/jump_search.rb (100%)
 rename {Searches => searches}/linear_search.rb (100%)
 rename {Searches => searches}/recursive_double_linear_search.rb (100%)
 rename {Searches => searches}/recursive_linear_search.rb (100%)
 rename {Searches => searches}/ternary_search.rb (100%)

diff --git a/Searches/binary_search.rb b/searches/binary_search.rb
similarity index 100%
rename from Searches/binary_search.rb
rename to searches/binary_search.rb
diff --git a/Searches/depth_first_search.rb b/searches/depth_first_search.rb
similarity index 100%
rename from Searches/depth_first_search.rb
rename to searches/depth_first_search.rb
diff --git a/Searches/double_linear_search.rb b/searches/double_linear_search.rb
similarity index 100%
rename from Searches/double_linear_search.rb
rename to searches/double_linear_search.rb
diff --git a/Searches/jump_search.rb b/searches/jump_search.rb
similarity index 100%
rename from Searches/jump_search.rb
rename to searches/jump_search.rb
diff --git a/Searches/linear_search.rb b/searches/linear_search.rb
similarity index 100%
rename from Searches/linear_search.rb
rename to searches/linear_search.rb
diff --git a/Searches/recursive_double_linear_search.rb b/searches/recursive_double_linear_search.rb
similarity index 100%
rename from Searches/recursive_double_linear_search.rb
rename to searches/recursive_double_linear_search.rb
diff --git a/Searches/recursive_linear_search.rb b/searches/recursive_linear_search.rb
similarity index 100%
rename from Searches/recursive_linear_search.rb
rename to searches/recursive_linear_search.rb
diff --git a/Searches/ternary_search.rb b/searches/ternary_search.rb
similarity index 100%
rename from Searches/ternary_search.rb
rename to searches/ternary_search.rb

From b2fc530555f38f2da5f3fe173e5ae6f97b406ee3 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sun, 11 Apr 2021 22:56:29 +0000
Subject: [PATCH 68/83] updating DIRECTORY.md

---
 DIRECTORY.md | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index a34b83d..45e03fa 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -104,14 +104,14 @@
     * [Sol1](https://github.com/TheAlgorithms/Ruby/blob/master/project_euler/problem_5/sol1.rb)
 
 ## Searches
-  * [Binary Search](https://github.com/TheAlgorithms/Ruby/blob/master/Searches/binary_search.rb)
-  * [Depth First Search](https://github.com/TheAlgorithms/Ruby/blob/master/Searches/depth_first_search.rb)
-  * [Double Linear Search](https://github.com/TheAlgorithms/Ruby/blob/master/Searches/double_linear_search.rb)
-  * [Jump Search](https://github.com/TheAlgorithms/Ruby/blob/master/Searches/jump_search.rb)
-  * [Linear Search](https://github.com/TheAlgorithms/Ruby/blob/master/Searches/linear_search.rb)
-  * [Recursive Double Linear Search](https://github.com/TheAlgorithms/Ruby/blob/master/Searches/recursive_double_linear_search.rb)
-  * [Recursive Linear Search](https://github.com/TheAlgorithms/Ruby/blob/master/Searches/recursive_linear_search.rb)
-  * [Ternary Search](https://github.com/TheAlgorithms/Ruby/blob/master/Searches/ternary_search.rb)
+  * [Binary Search](https://github.com/TheAlgorithms/Ruby/blob/master/searches/binary_search.rb)
+  * [Depth First Search](https://github.com/TheAlgorithms/Ruby/blob/master/searches/depth_first_search.rb)
+  * [Double Linear Search](https://github.com/TheAlgorithms/Ruby/blob/master/searches/double_linear_search.rb)
+  * [Jump Search](https://github.com/TheAlgorithms/Ruby/blob/master/searches/jump_search.rb)
+  * [Linear Search](https://github.com/TheAlgorithms/Ruby/blob/master/searches/linear_search.rb)
+  * [Recursive Double Linear Search](https://github.com/TheAlgorithms/Ruby/blob/master/searches/recursive_double_linear_search.rb)
+  * [Recursive Linear Search](https://github.com/TheAlgorithms/Ruby/blob/master/searches/recursive_linear_search.rb)
+  * [Ternary Search](https://github.com/TheAlgorithms/Ruby/blob/master/searches/ternary_search.rb)
 
 ## Sorting
   * [Bogo Sort](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/bogo_sort.rb)

From 0f3441c0882faa759dcfcccb021631e0f5b45dd0 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Wed, 14 Apr 2021 23:41:50 +0000
Subject: [PATCH 69/83] updating DIRECTORY.md

---
 DIRECTORY.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 4f8a0a7..df4f340 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -65,10 +65,12 @@
 ## Maths
   * [Abs](https://github.com/TheAlgorithms/Ruby/blob/master/maths/abs.rb)
   * [Abs Test](https://github.com/TheAlgorithms/Ruby/blob/master/maths/abs_test.rb)
+  * [Add](https://github.com/TheAlgorithms/Ruby/blob/master/maths/add.rb)
   * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/maths/add_digits.rb)
   * [Aliquot Sum](https://github.com/TheAlgorithms/Ruby/blob/master/maths/aliquot_sum.rb)
   * [Aliquot Sum Test](https://github.com/TheAlgorithms/Ruby/blob/master/maths/aliquot_sum_test.rb)
   * [Average Mean](https://github.com/TheAlgorithms/Ruby/blob/master/maths/average_mean.rb)
+  * [Average Median](https://github.com/TheAlgorithms/Ruby/blob/master/maths/average_median.rb)
   * [Binary To Decimal](https://github.com/TheAlgorithms/Ruby/blob/master/maths/binary_to_decimal.rb)
   * [Ceil](https://github.com/TheAlgorithms/Ruby/blob/master/maths/ceil.rb)
   * [Ceil Test](https://github.com/TheAlgorithms/Ruby/blob/master/maths/ceil_test.rb)

From 50e6dc6f86993d9ad93fdf4760d4204fcc49fd9c Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 15 Apr 2021 17:25:30 -0700
Subject: [PATCH 70/83] Arrays intersection: two-pointer approach

---
 data_structures/arrays/arrays_intersection.rb | 67 +++++++++++++++++++
 1 file changed, 67 insertions(+)
 create mode 100644 data_structures/arrays/arrays_intersection.rb

diff --git a/data_structures/arrays/arrays_intersection.rb b/data_structures/arrays/arrays_intersection.rb
new file mode 100644
index 0000000..63db80e
--- /dev/null
+++ b/data_structures/arrays/arrays_intersection.rb
@@ -0,0 +1,67 @@
+# Given three integer arrays arr1, arr2 and arr3 sorted in strictly increasing order, return a sorted array of only the integers that appeared in all three arrays.
+#
+# Example 1:
+#
+# Input: arr1 = [1,2,3,4,5], arr2 = [1,2,5,7,9], arr3 = [1,3,4,5,8]
+# Output: [1,5]
+# Explanation: Only 1 and 5 appeared in the three arrays.
+#
+# Example 2:
+#
+# Input: arr1 = [197,418,523,876,1356], arr2 = [501,880,1593,1710,1870], arr3 = [521,682,1337,1395,1764]
+# Output: []
+#
+#
+
+#
+# Approach: Two-pointer
+#
+
+# Complexity Analysis
+#
+# Time Complexity: O(n), where n is the total length of all of the
+# input arrays.
+# Space Complexity: O(1), as we only initiate three integer variables
+# using constant space.
+
+# @param {Integer[]} arr1
+# @param {Integer[]} arr2
+# @param {Integer[]} arr3
+# @return {Integer[]}
+def arrays_intersection(arr1, arr2, arr3)
+  result = []
+
+  # prepare three pointers to iterate through three arrays
+  # p1, p2, and p3 point to the beginning of arr1, arr2, and arr3 accordingly
+  p1 = p2 = p3 = 0
+
+  while (p1 < arr1.count) && (p2 < arr2.count) && (p3 < arr3.count)
+    if arr1[p1] == arr2[p2] && arr1[p1] == arr3[p3]
+      result.push(arr1[p1])
+
+      p1 += 1
+      p2 += 1
+      p3 += 1
+    elsif arr1[p1] < arr2[p2]
+      p1 += 1
+    elsif arr2[p2] < arr3[p3]
+      p2 += 1
+    else
+      p3 += 1
+    end
+  end
+
+  result
+end
+
+arr1 = [1, 2, 3, 4, 5]
+arr2 = [1, 2, 5, 7, 9]
+arr3 = [1, 3, 4, 5, 8]
+print(arrays_intersection(arr1, arr2, arr3))
+# Output: [1,5]
+
+arr1 = [197, 418, 523, 876, 1356]
+arr2 = [501, 880, 1593, 1710, 1870]
+arr3 = [521, 682, 1337, 1395, 1764]
+print(arrays_intersection(arr1, arr2, arr3))
+# Output: []

From 6a076bde0750af89a078e98a49c0e7c0b4735f33 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Fri, 16 Apr 2021 00:25:50 +0000
Subject: [PATCH 71/83] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index df4f340..4c08933 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -14,6 +14,7 @@
 ## Data Structures
   * Arrays
     * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/add_digits.rb)
+    * [Arrays Intersection](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/arrays_intersection.rb)
     * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_all_duplicates_in_an_array.rb)
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)

From da89bae9314f1dc838ec299556324908a479f1f3 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 15 Apr 2021 17:27:27 -0700
Subject: [PATCH 72/83] Update arrays_intersection.rb

---
 data_structures/arrays/arrays_intersection.rb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/data_structures/arrays/arrays_intersection.rb b/data_structures/arrays/arrays_intersection.rb
index 63db80e..c9780e0 100644
--- a/data_structures/arrays/arrays_intersection.rb
+++ b/data_structures/arrays/arrays_intersection.rb
@@ -14,7 +14,7 @@
 #
 
 #
-# Approach: Two-pointer
+# Approach: Two-pointers
 #
 
 # Complexity Analysis

From b101ef25d7aec58f631293f0ff91c355c298120a Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Thu, 15 Apr 2021 18:00:29 -0700
Subject: [PATCH 73/83] Update and rename arrays_intersection.rb to
 sorted_arrays_intersection.rb

---
 ...arrays_intersection.rb => sorted_arrays_intersection.rb} | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)
 rename data_structures/arrays/{arrays_intersection.rb => sorted_arrays_intersection.rb} (90%)

diff --git a/data_structures/arrays/arrays_intersection.rb b/data_structures/arrays/sorted_arrays_intersection.rb
similarity index 90%
rename from data_structures/arrays/arrays_intersection.rb
rename to data_structures/arrays/sorted_arrays_intersection.rb
index c9780e0..a48a7c2 100644
--- a/data_structures/arrays/arrays_intersection.rb
+++ b/data_structures/arrays/sorted_arrays_intersection.rb
@@ -28,7 +28,7 @@
 # @param {Integer[]} arr2
 # @param {Integer[]} arr3
 # @return {Integer[]}
-def arrays_intersection(arr1, arr2, arr3)
+def sorted_arrays_intersection(arr1, arr2, arr3)
   result = []
 
   # prepare three pointers to iterate through three arrays
@@ -57,11 +57,11 @@ end
 arr1 = [1, 2, 3, 4, 5]
 arr2 = [1, 2, 5, 7, 9]
 arr3 = [1, 3, 4, 5, 8]
-print(arrays_intersection(arr1, arr2, arr3))
+print(sorted_arrays_intersection(arr1, arr2, arr3))
 # Output: [1,5]
 
 arr1 = [197, 418, 523, 876, 1356]
 arr2 = [501, 880, 1593, 1710, 1870]
 arr3 = [521, 682, 1337, 1395, 1764]
-print(arrays_intersection(arr1, arr2, arr3))
+print(sorted_arrays_intersection(arr1, arr2, arr3))
 # Output: []

From b1131f996a577f874dd3470d373daed7cf302c83 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Fri, 16 Apr 2021 01:00:45 +0000
Subject: [PATCH 74/83] updating DIRECTORY.md

---
 DIRECTORY.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 4c08933..1028fcd 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -14,7 +14,6 @@
 ## Data Structures
   * Arrays
     * [Add Digits](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/add_digits.rb)
-    * [Arrays Intersection](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/arrays_intersection.rb)
     * [Find All Duplicates In An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_all_duplicates_in_an_array.rb)
     * [Find The Highest Altitude](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/find_the_highest_altitude.rb)
     * [Fizz Buzz](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/fizz_buzz.rb)
@@ -25,6 +24,7 @@
     * [Shuffle Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/shuffle_array.rb)
     * [Single Number](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/single_number.rb)
     * [Sort Squares Of An Array](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sort_squares_of_an_array.rb)
+    * [Sorted Arrays Intersection](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/sorted_arrays_intersection.rb)
     * Strings
       * [Anagram Checker](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/anagram_checker.rb)
       * [Jewels And Stones](https://github.com/TheAlgorithms/Ruby/blob/master/data_structures/arrays/strings/jewels_and_stones.rb)

From 2c11993806af4b8d91228274faf2576c325dc283 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Fri, 16 Apr 2021 14:12:30 -0700
Subject: [PATCH 75/83] Add brute force solution

---
 data_structures/arrays/intersection.rb | 29 ++++++++++++++++++++++----
 1 file changed, 25 insertions(+), 4 deletions(-)

diff --git a/data_structures/arrays/intersection.rb b/data_structures/arrays/intersection.rb
index bd826a0..9633d7b 100644
--- a/data_structures/arrays/intersection.rb
+++ b/data_structures/arrays/intersection.rb
@@ -7,17 +7,38 @@
 # @return {Integer[]}
 
 #
-# Approach 1:
+# Approach 1: Brute Force
 #
-# Time Complexity:
+# Time Complexity: O(n^2)
 #
 def intersect(arr1, arr2)
+  result = []
+
+  if arr1.length < arr2.length
+    shorter = arr1
+    longer = arr2
+  else
+    shorter = arr2
+    longer = arr1
+  end
+
+  shorter.each do |matcher|
+    longer.each do |number|
+      next if number != matcher
+      result.push(number)
+      break
+    end
+  end
+
+  result
 end
+
 nums1 = [1, 2, 2, 1]
 nums2 = [2, 2]
-intersect(nums1, nums2)
+puts intersect(nums1, nums2)
 # => [2,2]
+
 nums1 = [4, 9, 5]
 nums2 = [9, 4, 9, 8, 4]
-intersect(nums1, nums2)
+puts intersect(nums1, nums2)
 # => [4,9]
\ No newline at end of file

From 7b20bca2f82d02d9bc7046bc7d386a11f7389c84 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Fri, 16 Apr 2021 16:21:49 -0700
Subject: [PATCH 76/83] Add hash solution

---
 data_structures/arrays/intersection.rb | 32 ++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)

diff --git a/data_structures/arrays/intersection.rb b/data_structures/arrays/intersection.rb
index 9633d7b..a59f58c 100644
--- a/data_structures/arrays/intersection.rb
+++ b/data_structures/arrays/intersection.rb
@@ -38,6 +38,38 @@ nums2 = [2, 2]
 puts intersect(nums1, nums2)
 # => [2,2]
 
+nums1 = [4, 9, 5]
+nums2 = [9, 4, 9, 8, 4]
+puts intersect(nums1, nums2)
+# => [4,9]
+
+#
+# Approach 2: Hash
+#
+# Time Complexity: O(n)
+#
+def intersect(arr1, arr2)
+  result = []
+
+  hash = Hash.new(0)
+
+  arr2.each {|num| hash[num] += 1 }
+
+  arr1.each do |num|
+    if hash.has_key?(num)
+      result << num if hash[num] >= 1
+      hash[num] -= 1
+    end
+  end
+  
+  result
+end
+
+nums1 = [1, 2, 2, 1]
+nums2 = [2, 2]
+puts intersect(nums1, nums2)
+# => [2,2]
+
 nums1 = [4, 9, 5]
 nums2 = [9, 4, 9, 8, 4]
 puts intersect(nums1, nums2)

From b0287375a44d9c55bf992fae05028f0ccf51efcb Mon Sep 17 00:00:00 2001
From: Jessica Kwok <jessicatckwok@gmail.com>
Date: Fri, 16 Apr 2021 16:33:19 -0700
Subject: [PATCH 77/83] Add two pointers solution

---
 data_structures/arrays/intersection.rb | 41 +++++++++++++++++++++++++-
 1 file changed, 40 insertions(+), 1 deletion(-)

diff --git a/data_structures/arrays/intersection.rb b/data_structures/arrays/intersection.rb
index a59f58c..b0091bc 100644
--- a/data_structures/arrays/intersection.rb
+++ b/data_structures/arrays/intersection.rb
@@ -61,7 +61,7 @@ def intersect(arr1, arr2)
       hash[num] -= 1
     end
   end
-  
+
   result
 end
 
@@ -70,6 +70,45 @@ nums2 = [2, 2]
 puts intersect(nums1, nums2)
 # => [2,2]
 
+nums1 = [4, 9, 5]
+nums2 = [9, 4, 9, 8, 4]
+puts intersect(nums1, nums2)
+# => [4,9]
+
+#
+# Approach 3: Two Pointers
+#
+# Time Complexity: O(n log n)
+#
+def intersect(nums1, nums2)
+  result = []
+  p1 = 0
+  p2 = 0
+  nums1 = nums1.sort
+  nums2 = nums2.sort
+  while p1 < nums1.length && p2 < nums2.length
+    if nums1[p1] < nums2[p2]
+      p1 += 1
+    elsif nums1[p1] > nums2[p2]
+      p2 += 1
+    elsif nums1[p1] == nums2[p2]
+      result << nums1[p1]
+      p1 += 1
+      p2 += 1
+    end
+  end
+  
+  result
+end
+nums1 = [1, 2, 2, 1]
+nums2 = [2, 2]
+intersect(nums1, nums2)
+
+nums1 = [1, 2, 2, 1]
+nums2 = [2, 2]
+puts intersect(nums1, nums2)
+# => [2,2]
+
 nums1 = [4, 9, 5]
 nums2 = [9, 4, 9, 8, 4]
 puts intersect(nums1, nums2)

From db2d1b74a299e15038b71b8d77a76d5791a88e59 Mon Sep 17 00:00:00 2001
From: Jessica Kwok <60627484+jsca-kwok@users.noreply.github.com>
Date: Mon, 19 Apr 2021 15:54:48 -0700
Subject: [PATCH 78/83] Update data_structures/arrays/intersection.rb

Co-authored-by: Vitor Oliveira <vbrazo@gmail.com>
---
 data_structures/arrays/intersection.rb | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/data_structures/arrays/intersection.rb b/data_structures/arrays/intersection.rb
index b0091bc..a3cb29c 100644
--- a/data_structures/arrays/intersection.rb
+++ b/data_structures/arrays/intersection.rb
@@ -78,7 +78,10 @@ puts intersect(nums1, nums2)
 #
 # Approach 3: Two Pointers
 #
-# Time Complexity: O(n log n)
+# Complexity analysis:
+
+# Time Complexity: O(nlogn + mlogm), where n and m are the lengths of the arrays. We sort two arrays independently and then do a linear scan.
+# Space Complexity: from O(logn+logm) to O(n+m), depending on the implementation of the sorting algorithm.
 #
 def intersect(nums1, nums2)
   result = []
@@ -112,4 +115,4 @@ puts intersect(nums1, nums2)
 nums1 = [4, 9, 5]
 nums2 = [9, 4, 9, 8, 4]
 puts intersect(nums1, nums2)
-# => [4,9]
\ No newline at end of file
+# => [4,9]

From 5c1580fc10038963e124a6b7fc3878aeacbf188d Mon Sep 17 00:00:00 2001
From: Jessica Kwok <60627484+jsca-kwok@users.noreply.github.com>
Date: Mon, 19 Apr 2021 15:55:22 -0700
Subject: [PATCH 79/83] Update data_structures/arrays/intersection.rb

Co-authored-by: Vitor Oliveira <vbrazo@gmail.com>
---
 data_structures/arrays/intersection.rb | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/data_structures/arrays/intersection.rb b/data_structures/arrays/intersection.rb
index a3cb29c..dfcd49b 100644
--- a/data_structures/arrays/intersection.rb
+++ b/data_structures/arrays/intersection.rb
@@ -46,7 +46,14 @@ puts intersect(nums1, nums2)
 #
 # Approach 2: Hash
 #
-# Time Complexity: O(n)
+# Complexity Analysis
+#
+# Time Complexity: O(n+m), where n and m are the lengths of the arrays.
+# We iterate through the first, and then through the second array; insert
+# and lookup operations in the hash map take a constant time.
+#
+# Space Complexity: O(min(n,m)). We use hash map to store numbers (and their
+# counts) from the smaller array.
 #
 def intersect(arr1, arr2)
   result = []

From 9f7e58c574648fce4bc4e5b9a4af1717df8f4a79 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 24 Apr 2021 23:19:41 -0700
Subject: [PATCH 80/83] Sort color algorhtm

---
 sorting/sort_color.rb | 63 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100644 sorting/sort_color.rb

diff --git a/sorting/sort_color.rb b/sorting/sort_color.rb
new file mode 100644
index 0000000..e1cb3a1
--- /dev/null
+++ b/sorting/sort_color.rb
@@ -0,0 +1,63 @@
+# Given an array nums with n objects colored red, white, or blue, sort them in-place so that objects of the same color are adjacent, with the colors in the order red, white, and blue.
+#
+# We will use the integers 0, 1, and 2 to represent the color red, white, and blue, respectively.
+#
+# Example 1:
+#
+# Input: nums = [2,0,2,1,1,0]
+# Output: [0,0,1,1,2,2]
+#
+# Example 2:
+#
+# Input: nums = [2,0,1]
+# Output: [0,1,2]
+#
+# Example 3:
+#
+# Input: nums = [0]
+# Output: [0]
+#
+# Example 4:
+#
+# Input: nums = [1]
+# Output: [1]
+
+# @param {Integer[]} nums
+# @return {Void} Do not return anything, modify nums in-place instead.
+def sort_colors(nums)
+  bubble_sort(nums)
+end
+
+def bubble_sort(array)
+  array_length = array.size
+  return array if array_length <= 1
+
+  loop do
+    swapped = false
+    (array_length - 1).times do |i|
+      if array[i] > array[i + 1]
+        array[i], array[i + 1] = array[i + 1], array[i]
+        swapped = true
+      end
+    end
+    break unless swapped
+  end
+
+  array
+end
+
+nums = [2,0,2,1,1,0]
+puts sort_colors(nums)
+# Output: [0,0,1,1,2,2]
+
+nums = [2,0,1]
+puts sort_colors(nums)
+# Output: [0,1,2]
+
+nums = [0]
+puts sort_colors(nums)
+# Output: [0]
+
+nums = [1]
+puts sort_colors(nums)
+# Output: [1]

From 812a8e42afa4c3c01e5f387b496b4cc7cfc69f35 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sun, 25 Apr 2021 06:19:56 +0000
Subject: [PATCH 81/83] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index df4f340..59eb222 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -138,4 +138,5 @@
   * [Selection Sort Test](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/selection_sort_test.rb)
   * [Shell Sort](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/shell_sort.rb)
   * [Shell Sort Test](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/shell_sort_test.rb)
+  * [Sort Color](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/sort_color.rb)
   * [Sort Tests](https://github.com/TheAlgorithms/Ruby/blob/master/sorting/sort_tests.rb)

From 42dafdfe7aec3ada31cb7b2d1aeee562b04c2cd1 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 24 Apr 2021 23:21:08 -0700
Subject: [PATCH 82/83] enter

---
 sorting/sort_color.rb | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/sorting/sort_color.rb b/sorting/sort_color.rb
index e1cb3a1..fd428ee 100644
--- a/sorting/sort_color.rb
+++ b/sorting/sort_color.rb
@@ -34,12 +34,14 @@ def bubble_sort(array)
 
   loop do
     swapped = false
+
     (array_length - 1).times do |i|
       if array[i] > array[i + 1]
         array[i], array[i + 1] = array[i + 1], array[i]
         swapped = true
       end
     end
+
     break unless swapped
   end
 

From fe6d8489c354b2f030b74630b84159f80a50fbc9 Mon Sep 17 00:00:00 2001
From: Vitor Oliveira <vbrazo@gmail.com>
Date: Sat, 24 Apr 2021 23:26:02 -0700
Subject: [PATCH 83/83] Fix lint

---
 sorting/sort_color.rb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/sorting/sort_color.rb b/sorting/sort_color.rb
index fd428ee..441679e 100644
--- a/sorting/sort_color.rb
+++ b/sorting/sort_color.rb
@@ -48,11 +48,11 @@ def bubble_sort(array)
   array
 end
 
-nums = [2,0,2,1,1,0]
+nums = [2, 0, 2, 1, 1, 0]
 puts sort_colors(nums)
 # Output: [0,0,1,1,2,2]
 
-nums = [2,0,1]
+nums = [2, 0, 1]
 puts sort_colors(nums)
 # Output: [0,1,2]