Rachael - Maple

lib/max_subarray.py

@@ -2,11 +2,23 @@
 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 not nums:
+        return 0 
+    if not len(nums):
         return 0
-    if len(nums) == 0:
-        return 0
-    pass
+
+    max_so_far = 0
+    max_ending_here = 0
+
+    for num in nums:
+        max_ending_here = max_ending_here + num 
+        if max_ending_here < 0:
+            max_ending_here = 0
+        if max_so_far < max_ending_here:
+            max_so_far = max_ending_here
+
+    return max(nums) if max_so_far == 0 else max_so_far 
+

lib/newman_conway.py

@@ -1,10 +1,15 @@
-
-
-# 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
+    if num <= 0:
+        raise ValueError 
+    elif num == 1:
+        return '1' 
+    else: 
+        memo = [0, 1, 1]
+        for i in range(3, num+1):
+            next_num = memo[memo[-1]] + memo[i-memo[i-1]]
+            memo.append(next_num)
+        return ' '.join([str(i) for i in memo if i])