water - mackenzie

lib/max_subarray.rb

@@ -1,8 +1,32 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n!)? You only go throught the each with index n times, but the inner loop completes decrementing number of loops... 
+# Space Complexity: O(1), no additional data structures created outside of 2 variables each times
 def max_sub_array(nums)
     return 0 if nums == nil
-
-    raise NotImplementedError, "Method not implemented yet!"
+    return nil if nums == []
+    return nums[0] if nums.length == 1 
+
+    max_so_far = nums[0]
+    max_ending_here = 0
+
+    nums.each_with_index do |num, index| 
+        i = index + 1 
+
+        if num > max_so_far
+            max_so_far = num
+        end
+
+        max_ending_here = num 
+
+        while  i < nums.length do 
+            max_ending_here = max_ending_here + nums[i]
+                if (max_so_far < max_ending_here)
+                    max_so_far = max_ending_here
+                end
+            i+=1
+        end
+    end
+
+
+    return max_so_far
 end

lib/newman_conway.rb

@@ -1,7 +1,31 @@
 
 
-# Time complexity: ?
-# Space Complexity: ?
+# Time complexity: O(n)
+# Space Complexity: O(n), always creating 1 array num + 1 length long and 1 string proprtionate to n 
+# P(1) = 1
+# P(2) = 1
+# for all n > 2
+# P(n) = P(P(n - 1)) + P(n - P(n - 1))
+# 1 1 2 2 3 4 4 4 5 6 7 7….
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
+  raise ArgumentError, "num must be > 0" if num < 1
+
+  return "1" if num == 1
+  return "1 1" if num == 2
+
+  ncs_numbers = Array.new(num + 1)
+  ncs_numbers[1] = 1
+  ncs_numbers[2] = 1
+
+  n = 3
+
+  ncs_string = "1 1"
+  while n <= num
+    ncs_numbers[n] = ncs_numbers[ncs_numbers[n-1]] + ncs_numbers[n - ncs_numbers[n-1]]
+    ncs_string << " " 
+    ncs_string << ncs_numbers[n].to_s
+    n += 1
+  end
+
+  return ncs_string
 end

test/max_sub_array_test.rb

@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "max subarray" do
+describe "max subarray" do
   it "will work for [-2,1,-3,4,-1,2,1,-5,4]" do
     # Arrange
     input = [-2,1,-3,4,-1,2,1,-5,4]