Whit - Paper

lib/max_subarray.py

@@ -5,8 +5,20 @@ def max_sub_array(nums):
         Time Complexity: ?
         Space Complexity: ?
     """
-    if nums == None:
+    if nums == None or len(nums) == 0:
         return 0
-    if len(nums) == 0:
-        return 0
-    pass
+
+    if len(nums) == 1:
+        return nums[0]
+
+    max_sum = nums[0] + nums[1]
+    max_sum_here =  0
+
+    for i in range(len(nums)):
+        max_sum_here = max_sum_here + nums[i]
+        if max_sum < max_sum_here:
+            max_sum = max_sum_here
+        if max_sum_here < 0:
+            max_sum_here = 0
+
+    return max_sum

lib/newman_conway.py

@@ -4,7 +4,25 @@
 # 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 < 1:
+        raise ValueError("Input must be an integer larger than 0")
+
+    if num == 1:
+        return "1"
+
+    seq = [1, 1]
+    i = 3
+
+    while i <= num:
+        n = seq[seq[i - 2] - 1] + seq[i - seq[i - 2] - 1]
+        seq.append(n)
+        i += 1
+
+    printed_seq = ""
+    for n in seq:
+        printed_seq += str(n) + " "
+
+    return printed_seq[0:-1]