diff --git a/algorithm b/algorithm
new file mode 100644
index 0000000..2d346a2
--- /dev/null
+++ b/algorithm
@@ -0,0 +1,16 @@
+def square_of_two(n)
+  if n == 0
+    return 1
+  end
+  temp = square_of_two(n / 2)
+  if n % 2 == 0
+    return temp * temp
+  elsif n % 2 == 1
+    return 2 * temp * temp
+  end
+end
+
+p square_of_two(2)
+p square_of_two(4)
+p square_of_two(5)
+p square_of_two(0)
\ No newline at end of file
diff --git a/lib/recursive-methods.rb b/lib/recursive-methods.rb
index fbf6faa..f02f763 100644
--- a/lib/recursive-methods.rb
+++ b/lib/recursive-methods.rb
@@ -1,49 +1,108 @@
 # Authoring recursive algorithms. Add comments including time and space complexity for each method.
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n)
+# Space complexity: O(n)
 def factorial(n)
-    raise NotImplementedError, "Method not implemented"
+  if n < 0
+    raise ArgumentError
+  end
+  if n == 0
+    return 1
+  else
+    return n * factorial(n - 1)
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n)
+# Space complexity: O(n)
 def reverse(s)
-    raise NotImplementedError, "Method not implemented"
+  if s.empty?
+    return ""
+  end
+  if s.length == 1
+    return s[0]
+  else
+    return s[s.length - 1] + reverse(s[0..s.length - 2])
+  end
+end
+
+# Time complexity: O(n)
+# Space complexity: O(1)
+def reverse!(s, b, e)
+  if b >= e
+    return
+  else
+    temp = s[b]
+    s[b] = s[e]
+    s[e] = temp
+    reverse!(s, b + 1, e - 1)
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
 def reverse_inplace(s)
-    raise NotImplementedError, "Method not implemented"
+  if s.empty?
+    return ""
+  end
+  if s.length == 1
+    return s[0]
+  end
+  b = 0
+  e = s.length - 1
+  reverse!(s, b, e)
 end
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n)
+# Space complexity: O(n)
 def bunny(n)
-    raise NotImplementedError, "Method not implemented"
+  if n == 0
+    return 0
+  else
+    return 2 + bunny(n - 1)
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n)
+# Space complexity: O(n)
 def nested(s)
-    raise NotImplementedError, "Method not implemented"
+  if s.length == 0
+    return true
+  elsif s.length == 1
+    return false
+  end
+  return s[0] == "(" && s[s.length - 1] == ")" && nested(s[1..s.length - 2])
 end
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n)
+# Space complexity: O(n)
 def search(array, value)
-    raise NotImplementedError, "Method not implemented"
+  if array.empty?
+    return false
+  end
+  if array[0] == value
+    return true
+  else
+    return search(array[1..array.length - 1], value)
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n)
+# Space complexity: O(n)
 def is_palindrome(s)
-    raise NotImplementedError, "Method not implemented"
+  if s.length <= 1
+    return true
+  end
+  return s[0] == s[s.length - 1] && is_palindrome(s[1..s.length - 2])
 end
 
 # Time complexity: ?
 # Space complexity: ?
 def digit_match(n, m)
-    raise NotImplementedError, "Method not implemented"
-end
\ No newline at end of file
+  if m == 0 || n == 0
+    return 0
+  end
+  if m % 10 == n % 10
+    return digit_match(n / 10, m / 10) + 1
+  else
+    return digit_match(n / 10, m / 10) + 0
+  end
+end
diff --git a/specs/recursion_writing_spec.rb b/specs/recursion_writing_spec.rb
index d8fb1ed..ba5258f 100644
--- a/specs/recursion_writing_spec.rb
+++ b/specs/recursion_writing_spec.rb
@@ -1,7 +1,7 @@
-require 'minitest/autorun'
-require 'minitest/reporters'
+require "minitest/autorun"
+require "minitest/reporters"
 require "minitest/skip_dsl"
-require_relative '../lib/recursive-methods'
+require_relative "../lib/recursive-methods"
 
 describe "factorial" do
   it "will find the factorial of 0" do
@@ -23,8 +23,7 @@
     answer = factorial(num)
 
     # Assert
-    expect(answer).must_equal 5*4*3*2*1
-
+    expect(answer).must_equal 5 * 4 * 3 * 2 * 1
   end
 
   it "will raise an ArgumentError if given a number not >= 0" do
@@ -38,7 +37,7 @@
   end
 end
 
-xdescribe "reverse" do
+describe "reverse" do
   it "will reverse 'cat'" do
     # Arrange
     string = "cat"
@@ -83,17 +82,16 @@
   end
 end
 
-
-xdescribe "reverse_in_place" do
+describe "reverse_in_place" do
   it "will reverse 'cat'" do
     # Arrange
     string = "cat"
 
     # Act
-    answer = reverse_inplace(string)
+    reverse_inplace(string)
 
     # Assert
-    expect(answer).must_equal "tac"
+    expect(string).must_equal "tac"
   end
 
   it "will reverse 'a'" do
@@ -122,14 +120,14 @@
     string = "apple"
 
     # Act
-    answer = reverse_inplace(string)
+    reverse_inplace(string)
 
     # Assert
-    expect(answer).must_equal "elppa"
+    expect(string).must_equal "elppa"
   end
 end
 
-xdescribe "bunny" do
+describe "bunny" do
   it "returns 0 for 0 bunnies" do
     # Arrange
     count = 0
@@ -164,7 +162,7 @@
   end
 end
 
-xdescribe "nested" do
+describe "nested" do
   it "will return true for empystring" do
     # Arrange
     string = ""
@@ -210,7 +208,7 @@
   end
 end
 
-xdescribe "search" do
+describe "search" do
   it "will return false for empty array" do
     # Arrange
     item = "a"
@@ -224,43 +222,43 @@
   end
 
   it "will return true when looking for something in the array" do
-  # Arrange
-  item = "a"
-  array = ["b", "c", "a"]
+    # Arrange
+    item = "a"
+    array = ["b", "c", "a"]
 
-  # Act
-  answer = search(array, item)
+    # Act
+    answer = search(array, item)
 
-  # Assert
-  expect(answer).must_equal true
+    # Assert
+    expect(answer).must_equal true
   end
 
   it "will return false when looking for something not in the array" do
     # Arrange
     item = "x"
     array = ["b", "c", "a"]
-  
+
     # Act
     answer = search(array, item)
-  
+
     # Assert
     expect(answer).must_equal false
-    end
-
-    it "will return true when finding something at the front of the array" do
-      # Arrange
-      item = "b"
-      array = ["b", "c", "a"]
-    
-      # Act
-      answer = search(array, item)
-    
-      # Assert
-      expect(answer).must_equal true
-    end      
+  end
+
+  it "will return true when finding something at the front of the array" do
+    # Arrange
+    item = "b"
+    array = ["b", "c", "a"]
+
+    # Act
+    answer = search(array, item)
+
+    # Assert
+    expect(answer).must_equal true
+  end
 end
 
-xdescribe "is_palindrome" do
+describe "is_palindrome" do
   it "will return true for emptystring" do
     # Arrange
     string = ""
@@ -295,7 +293,7 @@
   end
 end
 
-xdescribe "digit_match" do
+describe "digit_match" do
   it "returns 4 for 1072503891 and 62530841" do
     # Arrange
     num1 = 1072503891
@@ -304,8 +302,8 @@
     # Act
     answer = digit_match(num1, num2)
 
-     # Assert
-     expect(answer).must_equal 4
+    # Assert
+    expect(answer).must_equal 4
   end
 
   it "returns 0 for nonmatching numbers" do
@@ -316,8 +314,8 @@
     # Act
     answer = digit_match(num1, num2)
 
-     # Assert
-     expect(answer).must_equal 0
+    # Assert
+    expect(answer).must_equal 0
   end
 
   it "returns 3 for 841 and 62530841" do
@@ -328,7 +326,7 @@
     # Act
     answer = digit_match(num1, num2)
 
-     # Assert
-     expect(answer).must_equal 3
+    # Assert
+    expect(answer).must_equal 3
   end
-end
\ No newline at end of file
+end