Paper: Dynamic Programming

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 len(nums) == 0:
-        return 0
-    pass
+    if max(nums) < 0: 
+        return max(nums)
+
+   #Implementation of Kadane's Algorithm
+
+    maxSum = 0
+    currSum = 0 
+
+    for i in range(len(nums)): 
+        currSum = currSum + nums[i]
+        if(currSum > maxSum): 
+            maxSum = currSum
+        if(currSum < 0):
+            currSum = 0
+    return maxSum

lib/newman_conway.py

@@ -1,10 +1,24 @@
 
 
-# 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("Integer cannot be zero")
+
+    if num == 1:
+        return "1"
+
+    if num == 2:
+        return "1 1"
+
+    nums = [0, 1, 1]
+
+    for i in range (3, num + 1):
+        nums.append( nums[nums[i-1]] + nums[i - nums[i-1]])
+
+    return " ".join([str(item) for item in nums[1:num+1]])