From 40d4ab7c422c050daedaf03e9a9767407b09fcd6 Mon Sep 17 00:00:00 2001
From: Lilly <waterlilly169@GMAIL.COM>
Date: Sun, 10 Jul 2022 13:09:24 -0700
Subject: [PATCH] Lilly Pine C16

---
 .vscode/settings.json |  7 +++++++
 lib/max_subarray.py   | 16 +++++++++++++---
 lib/newman_conway.py  | 27 +++++++++++++++++++++++----
 3 files changed, 43 insertions(+), 7 deletions(-)
 create mode 100644 .vscode/settings.json

diff --git a/.vscode/settings.json b/.vscode/settings.json
new file mode 100644
index 0000000..3e99ede
--- /dev/null
+++ b/.vscode/settings.json
@@ -0,0 +1,7 @@
+{
+    "python.testing.pytestArgs": [
+        "."
+    ],
+    "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..fe0b930 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:
         return 0
     if len(nums) == 0:
         return 0
-    pass
+    n = len(nums)
+    max_sum = -10000000000
+    curr_sum = 0
+
+    for i in range(n):
+        curr_sum += nums[i]
+        if curr_sum > max_sum:
+            max_sum = curr_sum
+        if curr_sum < 0:
+            curr_sum = 0
+    return max_sum
diff --git a/lib/newman_conway.py b/lib/newman_conway.py
index 70a3353..0f8dbc9 100644
--- a/lib/newman_conway.py
+++ b/lib/newman_conway.py
@@ -2,9 +2,28 @@
 
 # Time complexity: ?
 # Space Complexity: ?
-def newman_conway(num):
+def newman_conway(nums):
     """ Returns a list of the Newman Conway numbers for the given value.
-        Time Complexity: ?
-        Space Complexity: ?
+        Time Complexity: O(n)
+        Space Complexity: O(n^2)
     """
-    pass
+    if nums == 0:
+        raise ValueError
+
+    if nums == 1:
+        return "1"
+    
+    if nums == 2:
+        return "1 1"
+
+    seq = ""
+    start_list = [0, 1, 1]
+    for i in range(3,nums+1): 
+        start_list.append( start_list[start_list[i - 1]] + start_list[i - start_list[i - 1]]) 
+    
+    for num in start_list[1:]:
+        seq += str(num) + " "
+    return seq.strip()
+
+
+