diff --git a/.vscode/settings.json b/.vscode/settings.json
new file mode 100644
index 0000000..9b38853
--- /dev/null
+++ b/.vscode/settings.json
@@ -0,0 +1,7 @@
+{
+    "python.testing.pytestArgs": [
+        "tests"
+    ],
+    "python.testing.unittestEnabled": false,
+    "python.testing.pytestEnabled": true
+}
\ No newline at end of file
diff --git a/lib/max_subarray.py b/lib/max_subarray.py
index 4e892e0..24cec20 100644
--- a/lib/max_subarray.py
+++ b/lib/max_subarray.py
@@ -2,11 +2,21 @@
 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), iterates through relative to the size of the list given.
+        Space Complexity: ? O(1), we will only ever make 2 
     """
+    #guard clauses
     if nums == None:
         return 0
     if len(nums) == 0:
         return 0
-    pass
+    
+    # initialize /memoize:
+    max_subarray_so_far = nums[0]
+    max_this_subarray = nums[0]
+
+    for i in range(1, len(nums)): # O(n)
+        max_this_subarray = max(max_this_subarray + nums[i], nums[i])
+        max_subarray_so_far = max(max_this_subarray, max_subarray_so_far) 
+
+    return max_subarray_so_far 
\ No newline at end of file
diff --git a/lib/newman_conway.py b/lib/newman_conway.py
index 70a3353..91e77b1 100644
--- a/lib/newman_conway.py
+++ b/lib/newman_conway.py
@@ -1,10 +1,30 @@
-
-
-# Time complexity: ?
-# Space Complexity: ?
+''' 
+P(1) = 1
+P(2) = 1
+for all n > 2
+P(n) = P(P(n - 1)) + P(n - P(n - 1)) 
+'''
 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)
     """
-    pass
+    # base case guard clauses
+    if num < 1:
+        raise ValueError('newman conway number cant be zero nums long')
+    elif num == 1:
+        return '1'
+
+    memo = [0,1,1]
+    count = 3
+ 
+    while count <= num: 
+        #            P(P(n - 1))        +    P (n - P(n - 1)) 
+        memo.append(memo[memo[count-1]] + memo[count - memo[count-1]])
+        count += 1
+
+    NCnums = []
+    for num in memo:
+        NCnums.append(str(num))
+    # print(NCnums[1:])
+    return " ".join(NCnums[1:])
\ No newline at end of file