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..e1a9f24 100644
--- a/lib/max_subarray.py
+++ b/lib/max_subarray.py
@@ -1,12 +1,25 @@
 
+from json.encoder import INFINITY
+
+
 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
+
+    maximum = - INFINITY
+    current_max = 0
+
+    for num in nums:
+        current_max += num
+        if current_max > maximum:
+            maximum = current_max
+        if current_max < 0:
+            current_max = 0
+    return maximum
diff --git a/lib/newman_conway.py b/lib/newman_conway.py
index 70a3353..20e92be 100644
--- a/lib/newman_conway.py
+++ b/lib/newman_conway.py
@@ -4,7 +4,31 @@
 # 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)
+
+        P(1) = 1
+        P(2) = 1
+        for all n > 2
+        P(n) = P(P(n - 1)) + P(n - P(n - 1))
     """
-    pass
+
+    # make a dict with key as n, and the value as P(n) (aka the output)
+
+    outputs = {}
+
+    res = []
+    if num <= 0:
+        raise ValueError
+    
+    for n in range(1, num + 1):
+        if n == 1 or n == 2:
+            outputs[n] = 1
+            res.append("1")
+            continue
+        # P(n -1) -> outputs[ n - 1]
+        value = outputs[outputs[n - 1]] + outputs[n - outputs[n - 1]]
+        outputs[n] = value
+        res.append(str(value))
+    
+    return " ".join(res)