diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 5204edb..e3d3baa 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,8 +1,24 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n)
+# Space Complexity: O(1) 
 def max_sub_array(nums)
-    return 0 if nums == nil
+    return nil if nums.nil? || nums.empty?
+    return nums[0] if nums.length  == 1 
+
+    highest_peak = nums[0]
+    highest = nums[0]
+    i = 1 
+
+    while i < nums.length 
+        highest_peak += nums[i]
+
+        highest_peak = nums[i] if highest_peak < nums[i]
+        highest = highest_peak if highest < highest_peak
+        i += 1
+    end 
+
+    return highest
     
-    raise NotImplementedError, "Method not implemented yet!"
 end
+
+
diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 4c985cd..a71d2fe 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,7 +1,26 @@
+# Time complexity: O(n)
+# Space Complexity: O(n)
 
-
-# Time complexity: ?
-# Space Complexity: ?
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
-end
\ No newline at end of file
+  raise ArgumentError.new if num == 0
+
+  return "1" if num == 1
+  return "1 1" if num == 2
+
+  array = []
+  array[0] = 0
+  array[1] = 1
+  array[2] = 1
+  tally = "1 1"
+  i = 3
+
+  until i > num
+    array[i] = array[array[i - 1]] + array[i - array[i - 1]]
+    tally += " #{array[i]}"
+    i += 1
+  end
+
+  return tally
+end 
+
+#research source: https://www.geeksforgeeks.org/print-n-terms-newman-conway-sequence/
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]