From 3c46a903ef480afac654c6b4aab1e46ff46d6dbc Mon Sep 17 00:00:00 2001
From: Parseluni <deliagaiaglow@gmail.com>
Date: Sat, 25 Dec 2021 20:57:53 -0800
Subject: [PATCH] Completed

---
 .vscode/settings.json |  5 +++++
 lib/max_subarray.py   | 22 ++++++++++++++++------
 lib/newman_conway.py  | 25 ++++++++++++++++++++++---
 3 files changed, 43 insertions(+), 9 deletions(-)
 create mode 100644 .vscode/settings.json

diff --git a/.vscode/settings.json b/.vscode/settings.json
new file mode 100644
index 0000000..d969f96
--- /dev/null
+++ b/.vscode/settings.json
@@ -0,0 +1,5 @@
+{
+  "python.testing.pytestArgs": ["tests"],
+  "python.testing.unittestEnabled": false,
+  "python.testing.pytestEnabled": true
+}
diff --git a/lib/max_subarray.py b/lib/max_subarray.py
index 4e892e0..60f15b0 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)
+        Space Complexity: O(1)
     """
-    if nums == None:
+    if nums == None or len(nums) == 0:
         return 0
-    if len(nums) == 0:
-        return 0
-    pass
+
+    partial_sum = nums[0]
+    max_sum = nums[0]
+    
+    for i in range(1, len(nums)):
+        if partial_sum + nums[i] < nums[i]:
+            partial_sum = nums[i]
+        else:
+            partial_sum += nums[i]
+            
+        max_sum = max(max_sum, partial_sum)
+        
+    return max_sum
diff --git a/lib/newman_conway.py b/lib/newman_conway.py
index 70a3353..25b8891 100644
--- a/lib/newman_conway.py
+++ b/lib/newman_conway.py
@@ -4,7 +4,26 @@
 # Space Complexity: ?
 def newman_conway(num):
     """ Returns a list of the Newman Conway numbers for the given value.
-        Time Complexity: ?
-        Space Complexity: ?
+        Recursive formula:
+        P(1) = 1
+        P(2) = 1
+        for all n > 2
+        P(n) = P(P(n - 1)) + P(n - P(n - 1))
+
+        Time Complexity: O(n)
+        Space Complexity: O(n)
     """
-    pass
+    if num == 0:
+        raise ValueError
+
+    if num == 1:
+        return "1"
+
+    seq = [0, 1, 1] 
+
+    for i in range(3,num+1): 
+        seq.append( seq[seq[i - 1]] + seq[i - seq[i - 1]]) 
+
+
+    final_string = ' '.join([str(item) for item in seq[1:]])
+    return final_string