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..aa44177 100644
--- a/lib/max_subarray.py
+++ b/lib/max_subarray.py
@@ -2,11 +2,17 @@
 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
+    maxSub = nums[0]
+    currentSum = nums[0]
+    for index in range(1, len(nums)):
+        currentSum = max(nums[index], currentSum + nums[index])
+        maxSub = max(maxSub, currentSum)
+    return maxSub
diff --git a/lib/newman_conway.py b/lib/newman_conway.py
index 70a3353..0001017 100644
--- a/lib/newman_conway.py
+++ b/lib/newman_conway.py
@@ -1,10 +1,39 @@
-
-
-# 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)
     """
-    pass
+ # P(1) = 1
+    # P(2) = 1
+    # for all n > 2
+    # P(n) = P(P(n - 1)) + P(n - P(n - 1))
+    # use memoization
+    if num == 0:
+        raise ValueError()
+    if num == 1:
+        return "1"
+    if num == 2:
+        return "1 1"
+    new_seq = [0] * (num + 1)
+    new_seq[0] = 0
+    new_seq[1] = 1
+    result = []
+    if num > 2:
+        new_seq[2] = 1
+
+    i = 3
+    # first 3 items
+    while i<=num:
+        new_seq[i]
+        # P(n) = P(P(n - 1)) + P(n - P(n - 1))
+        new_seq[i] = new_seq[new_seq[i-1]] + new_seq[i- new_seq[i-1]]
+        i +=1
+
+    i = 1
+    result = []
+    while (i <= num) :
+        #  Display the sequence element   
+        result.append(new_seq[i])
+        i += 1
+    resultOutput = [str(item) for item in result]
+    return " ".join(resultOutput)
\ No newline at end of file