diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 5204edb..fe97bdc 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,8 +1,20 @@
 
-# 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?
     
-    raise NotImplementedError, "Method not implemented yet!"
-end
+    max_so_far = nums[0]
+    max_ending_here = nums[0]
+
+    i = 1
+    while i < nums.length
+      max_ending_here += nums[i]
+      # assign max to current num if previous accumulated is deducting value (~liability)
+      max_ending_here = nums[i] if max_ending_here < nums[i]
+      max_so_far = max_ending_here if max_so_far < max_ending_here
+      i += 1
+    end
+
+    return max_so_far
+end
\ No newline at end of file
diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 4c985cd..cf97d5a 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,7 +1,34 @@
+# Time complexity: O(n) and actually O(3n) since I'm using shift and join? 
+# Space Complexity: O(n) for the additional memo array storing n of the sequence
+# P(n) = P(P(n - 1)) + P(n - P(n - 1))
+def newman_conway(num)
+  raise ArgumentError.new("num must be a positive integer") if num <= 0
+  return "1" if num == 1
 
+  # n starts at 3 per newman_conway property, though all indice in memo[] need to deduct by 1
+  memo = [1, 1]
+  n = 3
+  while n <= num
+    pre = memo[n - 1 - 1]                               # pre = P(n-1)
+    memo[n - 1] = memo[pre - 1] + memo[n - pre - 1]     # P(n) stored at index (n-1) = P(P(n - 1)) + P(n - P(n - 1)) 
+    n += 1
+  end
 
-# Time complexity: ?
-# Space Complexity: ?
-def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
-end
\ No newline at end of file
+  return memo.join(" ")
+end
+
+
+# alternative solution w/o shifting indice
+# def newman_conway(num)
+#   raise ArgumentError.new("num must be a positive integer") if num <= 0
+#   return "1" if num == 1
+#   memo = ["", 1, 1]
+#   n = 3
+#   while n <= num
+#     pre = memo[n-1]
+#     memo[n] = memo[pre] + memo[n - pre] 
+#     n += 1
+#   end
+#   memo.shift
+#   return memo.join(" ")
+# 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]