Michelle Morales - Spruce

lib/max_subarray.py

@@ -2,11 +2,19 @@
 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(n)
     """
     if nums == None:
         return 0
     if len(nums) == 0:
         return 0
-    pass
+
+    ans = nums[0]
+    subarr_sum = nums[0]
+
+    for i in range(1, len(nums)):
+        subarr_sum = max(nums[i], nums[i] + subarr_sum)
+        ans = max(ans, subarr_sum)
+
+    return ans

lib/newman_conway.py

@@ -1,10 +1,35 @@
-
-
 # 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)
+Newman-Conway Sequence is the one which generates the following integer sequence. 
+1 1 2 2 3 4 4 4 5 6 7 7…
+In mathematical terms, the sequence P(n) of Newman-Conway numbers is defined by recurrence relation 
+
+P(n) = P(P(n - 1)) + P(n - P(n - 1)) 
+with seed values P(1) = 1 and P(2) = 1
+Given a number n, print n-th number in Newman-Conway Sequence.
     """
-    pass
+    if num == 0:
+        raise ValueError
+    elif num == 1:
+        return "1"
+    elif num == 2:
+        return "1 1"
+
+    memo_list = [0,1,1]
+
+    for n in range(3, num +1):
+        new_num = memo_list[memo_list[n-1]] + memo_list[n - memo_list[n-1]]
+        memo_list.append(new_num)
+    memo_list.pop(0)
+    memo_list = " ".join([str(x) for x in memo_list])
+    return memo_list
+
+
+
+
+
+