diff --git a/lib/max_subarray.py b/lib/max_subarray.py
index 4e892e0..59d8e98 100644
--- a/lib/max_subarray.py
+++ b/lib/max_subarray.py
@@ -2,11 +2,20 @@
 def max_sub_array(nums):
     """ Returns the max subarray of the given list of numbers.
         Returns 0 if  nums is None or an empty list.
-        Time Complexity: ?
-        Space Complexity: ?
+        Time Complexity: O(n)
+        Space Complexity: O(1)
     """
     if nums == None:
         return 0
     if len(nums) == 0:
         return 0
-    pass
+    #  initialize maxSub -> first nsumber in the array
+    maxSub = nums[0]
+    currentSum = nums[0]
+    for index in range(1, len(nums)):
+        # start at index 1
+        # compare current value with current sum
+        currentSum = max(nums[index], currentSum + nums[index])
+        # assign to the max of itself compared to the currentSum
+        maxSub = max(maxSub, currentSum)
+    return maxSub
diff --git a/lib/newman_conway.py b/lib/newman_conway.py
index 70a3353..6a7ee2e 100644
--- a/lib/newman_conway.py
+++ b/lib/newman_conway.py
@@ -1,10 +1,40 @@
 
-
-# Time complexity: ?
-# Space Complexity: ?
 def newman_conway(num):
     """ Returns a list of the Newman Conway numbers for the given value.
-        Time Complexity: ?
-        Space Complexity: ?
+        Time Complexity: O(n)
+        Space Complexity: O(n) - it adds elements to result variable  while (i <= num)
     """
-    pass
+    # P(1) = 1
+    # P(2) = 1
+    # for all n > 2
+    # P(n) = P(P(n - 1)) + P(n - P(n - 1))
+    # use memoization table to store values for each calcula item
+    if num == 0:
+        raise ValueError()
+    if num == 1:
+        return "1"
+    if num == 2:
+        return "1 1"
+    record = [0] * (num + 1)
+    record[0] = 0
+    record[1] = 1
+    result = []
+    if num > 2:
+        record[2] = 1
+    
+    i = 3
+    # first 3 items
+    while i<=num:
+        record[i]
+        # P(n) = P(P(n - 1)) + P(n - P(n - 1))
+        record[i] = record[record[i-1]] + record[i- record[i-1]]
+        i +=1
+
+    i = 1
+    result = []
+    while (i <= num) :
+        #  Display the sequence element   
+        result.append(record[i])
+        i += 1
+    resultOutput = [str(item) for item in result]
+    return " ".join(resultOutput)