diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 5204edb..1618086 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,8 +1,26 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n) because we have do our if/else operations on every element in the array
+# Space Complexity: O(1) because we are re-using the same variable
 def max_sub_array(nums)
     return 0 if nums == nil
-    
-    raise NotImplementedError, "Method not implemented yet!"
+    return nil if nums.empty?
+    return nums[0] if nums.length == 1
+
+    max_so_far = max_ending_here = nums[0]
+
+    nums[1..-1].each do |number|
+
+        if max_ending_here + number < number
+            max_ending_here = number
+        else
+            max_ending_here += number
+        end
+
+        if max_so_far < max_ending_here
+            max_so_far = max_ending_here
+        end
+    end
+
+    return max_so_far
+
 end
diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 4c985cd..403a677 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,7 +1,33 @@
 
 
-# Time complexity: ?
-# Space Complexity: ?
+# Time complexity: O(n) because we need to perform our "what is the p?" steps n times
+# Space Complexity: also O(n) because we are adding an element to the sequence array for every n
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
+  raise ArgumentError, "Argument must be an integer greater than zero." if num <= 0 
+
+  if num == 1
+    return "1"
+  elsif num == 2
+    return "1 1"
+  else
+    p_helper(num, [1, 1])
+  end 
+end
+
+def p_helper(num, sequence)
+
+  # BASE CASE: stop when count of numbers in sequence array is the same as `num`
+  return sequence.join(" ") if num == sequence.length
+
+  # REGRESSIVE CASE: add p for next integer in sequence
+  # forumula: p(num) = p(p(num - 1)) + p(num - p(num - 1))
+  next_integer = sequence.length + 1
+  # if num is 4 previous_p is at index 2 (value: 2)
+  previous_p = sequence[next_integer - 2]
+  # now we need to look up p of the previous_p value
+  p_previous_p = sequence[previous_p - 1]
+  # find p of number minus previous number's p, then add it to p_previous_p
+  p = p_previous_p + sequence[(next_integer - previous_p) - 1]
+  sequence << p
+  return p_helper(num, sequence)
 end
\ No newline at end of file
diff --git a/test/max_sub_array_test.rb b/test/max_sub_array_test.rb
index 3253cdf..e27e1ca 100644
--- a/test/max_sub_array_test.rb
+++ b/test/max_sub_array_test.rb
@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "max subarray" do
+describe "max subarray" do
   it "will work for [-2,1,-3,4,-1,2,1,-5,4]" do
     # Arrange
     input = [-2,1,-3,4,-1,2,1,-5,4]