diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 5204edb..f78242d 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,8 +1,31 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n)
+# Space Complexity: O(1)
 def max_sub_array(nums)
-    return 0 if nums == nil
-    
-    raise NotImplementedError, "Method not implemented yet!"
+  max_so_far = nums[0]
+  max_ending_here = nums[0]
+  i = 1
+  while i < nums.length
+      max_ending_here = max_ending_here + nums[i]
+      if max_so_far < max_ending_here
+          max_so_far = max_ending_here
+      end
+      if max_ending_here < 0
+          max_ending_here = 0
+      end
+      i += 1
+  end
+  return max_so_far
 end
+
+# Initialize:
+#     max_so_far = 0
+#     max_ending_here = 0
+
+# Loop for each element of the array
+#   (a) max_ending_here = max_ending_here + a[i]
+#   (b) if(max_ending_here < 0)
+#             max_ending_here = 0
+#   (c) if(max_so_far < max_ending_here)
+#             max_so_far = max_ending_here
+# return max_so_far
\ No newline at end of file
diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 4c985cd..38bbdde 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,7 +1,22 @@
-
-
-# Time complexity: ?
-# Space Complexity: ?
+# Time complexity: O(n)
+# Space Complexity: O(n)
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
-end
\ No newline at end of file
+  raise ArgumentError if num < 1
+  sequence = []
+  n = 1
+  while n <= num 
+    sequence.push(get_newman_num(n))
+    n += 1
+  end
+  return sequence.join(" ")
+end
+
+def get_newman_num(num)
+  if num < 3
+    return 1
+  else
+    num = get_newman_num(get_newman_num(num - 1)) + get_newman_num(num - get_newman_num(num - 1))
+  # P(n) = P(P(n - 1)) + P(n - P(n - 1))
+    return num
+  end
+end
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]