Paper - Nandita G.

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:
         return 0
     if len(nums) == 0:
         return 0
-    pass
+    if len(nums) == 1:
+        return nums[0]
+
+    max_so_far = nums[0]
+    max_ending_here = 0
+
+    for i in range(len(nums)):
+        if max_ending_here < 0:
+            max_ending_here = 0
+        max_ending_here += nums[i]
+        if max_so_far < max_ending_here:
+            max_so_far = max_ending_here
+    return max_so_far

lib/newman_conway.py

@@ -1,10 +1,25 @@
 
 
-# Time complexity: ?
-# Space Complexity: ?
+# Time complexity: O(n)
+# Space Complexity: O(n)
 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("num cannot be less than 1")
+    memo = [0] * (num+1)
+    memo[0] = 0
+    memo[1] = 1
+    if num > 1:
+        memo[2] = 1
+
+    x = 3
+    while x <= num:
+        memo[x] = memo[memo[x - 1]] + memo[x - memo[x - 1]]
+        x += 1
+
+    memo.pop(0)
+    memo = [str(int) for int in memo]
+    return " ".join(memo)