diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 5204edb..c694158 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,8 +1,38 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
-def max_sub_array(nums)
-    return 0 if nums == nil
+# Time Complexity: O(n)
+## The method iterates over the entire array but does so only once
+
+# Space Complexity: O(1)
+## There are a limited number of variables that are constantly being re-assessed, so as the input goes to infitity the space requirements do not grow. 
+
+def max_sub_array(number_array)
+    length = number_array.length
+    if length == 0 
+        return nil
+    elsif length == 1
+        return number_array[0]
+    end
+    
+    max_so_far = number_array[0]
+    max_ending_here = 0
+    
+    i = 0
+    
+    until i == length do
+        
+        max_ending_here = max_ending_here + number_array[i]
+        
+        if max_so_far < max_ending_here
+            max_so_far = max_ending_here
+            i += 1
+        elsif max_ending_here < 0
+            max_ending_here = 0
+            i += 1
+        else
+            i+= 1
+        end
+    end
+    
+    return max_so_far
     
-    raise NotImplementedError, "Method not implemented yet!"
 end
diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 4c985cd..c5f4910 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,7 +1,43 @@
 
 
-# Time complexity: ?
-# Space Complexity: ?
+# Time complexity: O(n)
+## As the number goes to infinity, its values have to be assessed relative to whatever's already in the array, but because it's based on an array, the look-up cost is very low given that an index value is being passed in. 
+# Space Complexity: O(n)
+## As the number goes to infinity, the amount of space will grow at the same rate
+
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
+  
+  if num == 0 || num == nil
+    raise ArgumentError
+  elsif num == 1
+    return "1"
+  elsif num == 2
+    return "1 1"
+  end
+  
+  if num >= 3
+    return_array = [1, 1]
+  end
+  
+  i = 3
+  
+  until i > num do
+    
+    # P(n) = P(P(n - 1)) + P(n - P(n - 1))
+    
+    temp_a = return_array[(return_array[i-2])-1]
+    
+    temp_b = return_array[(i-(return_array[i-2]))-1]
+    
+    temp = temp_a + temp_b
+    
+    i += 1
+    
+    return_array.push temp
+  end
+  
+  return_string = return_array.join(" ")
+  
+  return return_string
+  
 end
\ No newline at end of file