Leaves - Dominique

Rakefile

@@ -1,5 +1,6 @@
 require 'rake/testtask'
 
+
 Rake::TestTask.new do |t|
   t.libs = ["lib"]
   t.warning = true

lib/recursive-methods.rb

@@ -1,47 +1,119 @@
 # Authoring recursive algorithms. Add comments including time and space complexity for each method.
-
-# Time complexity: ?
-# Space complexity: ?
+require "pry"
+# Time complexity: O(n)
+# Space complexity: O(n)
 def factorial(n)
-    raise NotImplementedError, "Method not implemented"
+  raise ArgumentError, 'Must provide a number greater than 1' unless n >= 0
+
+  if n == 1 || 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"
+
+  return s if s.length <= 1
+
+  last = s[-1]
+
+  rest = s[0...-1]
+
+  return last + reverse(rest)
 end
 
-# Time complexity: ?
-# Space complexity: ?
-def reverse_inplace(s)
-    raise NotImplementedError, "Method not implemented"
+# Time complexity: O(n)
+# Space complexity: O(n)
+def reverse_inplace(string)
+  return _reverse(string, 0, string.length - 1)
 end
 
-# Time complexity: ?
-# Space complexity: ?
+def _reverse(string, i, j)
+  if j - i <= 0
+    return string
+  else
+    swap(string, i, j)
+    return _reverse(string, i += 1, j -=1)
+  end 
+end 
+
+def swap(string, i, j)
+  a = string[i]
+  string[i] = string[j]
+  string[j] = a
+end 
+
+# Time complexity: O(n)
+# Space complexity: O(n)
 def bunny(n)
-    raise NotImplementedError, "Method not implemented"
+  if n == 0
+    return 0
+  elsif n == 1
+    return 2 
+  else
+    2 + bunny(n - 1)
+  end 
 end
 
-# Time complexity: ?
-# Space complexity: ?
-def nested(s)
-    raise NotImplementedError, "Method not implemented"
+# Time complexity: O(n)
+# Space complexity: O(n)
+
+def nested(string)
+  if string.length % 2 != 0
+    return false
+  else 
+    recursion(string, 0, string.length - 1)
+  end 
 end
 
+def recursion(string, start_index, end_index)
+  if start_index > end_index
+    return true
+  elsif string[start_index] == "(" && string[end_index] == ")"
+    return recursion(string, start_index + 1, end_index - 1)
+  else
+    return false
+  end 
+end 
+
 # Time complexity: ?
 # Space complexity: ?
 def search(array, value)
-    raise NotImplementedError, "Method not implemented"
+  if array == []
+    return false
+  else
+    return search_helper(array, value, i)
+  end 
 end
 
-# Time complexity: ?
-# Space complexity: ?
+def search_helper(array, value, i)
+  if array[i] == value
+    return true 
+  else
+    recursion(array, value, i += 1)
+  end 
+end 
+
+# Time complexity: O(n)
+# Space complexity: O(n)
 def is_palindrome(s)
-    raise NotImplementedError, "Method not implemented"
+  return is_palindrome(s, 0, s.length - 1 )
 end
 
+def is_palindrome(s, start_index, end_index)
+  if start_index < end_index
+    return true
+  elsif s[0] != s[s.length - 1]
+    return false
+  else
+    is_palindrome(s, start_index + 1, end_index - 1)
+  end 
+end 
+
 # Time complexity: ?
 # Space complexity: ?
 def digit_match(n, m)