Tiffany Harper :: Max SubArray and NewmanConway

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
+
+    max_sum = nums[0]
+    temp_sum = nums[0]
+
+    for i in range(1, len(nums)):
+        current = nums[i]
+        temp_sum = max(current, current + temp_sum)
+        max_sum = max(temp_sum, max_sum)
+
+    return max_sum

lib/newman_conway.py

@@ -7,4 +7,24 @@ def newman_conway(num):
         Time Complexity: ?
         Space Complexity: ?
     """
-    pass
+    # P(n) = P(P(n - 1)) + P(n - P(n - 1)) - Newman Conway Sequence
+    if num == 0:
+        raise ValueError()
+
+    if num == 1:
+        return "1"
+    if num == 2:
+        return "1 1"
+    starter_arr = [0, 1, 1]
+
+    i = 3
+    while i <= num:
+        starter_arr.append(
+            starter_arr[starter_arr[i-1]] + starter_arr[i - starter_arr[i-1]])
+        i += 1
+
+    newman_string = ""
+    for i in range(1, len(starter_arr)):
+        newman_string += str(starter_arr[i]) + " "
+
+    return newman_string[:-1]