Fire - Roshni

lib/max_subarray.rb

@@ -1,8 +1,32 @@
+# Kadane's algorithm
+# Initialize:
+#     max_so_far = 0
+#     max_ending_here = 0
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Loop for each element of the array
+#   (a) max_ending_here = max_ending_here + a[i]
+#   (b) if(max_ending_here < 0)
+#             max_ending_here = 0
+#   (c) if(max_so_far < max_ending_here)
+#             max_so_far = max_ending_here
+# return max_so_far
+# TODO https://leetcode.com/problems/maximum-subarray/ - below solution doesn't work on Leetcode, go back & review
+
+# Time Complexity: O(n) to iterate through the entire nums array 
+# Space Complexity: O(1) given that the space required for max_so_far and max_ending_here do not change with the size of nums
 def max_sub_array(nums)
-    return 0 if nums == nil
+    return nil if nums.empty? 
 
-    raise NotImplementedError, "Method not implemented yet!"
+    max_so_far = nums[0]
+    max_ending_here = 0
+
+    nums.each do |num|
+        max_ending_here += num 
+        if max_so_far < max_ending_here
+            max_so_far = max_ending_here
+        elsif max_ending_here < 0
+            max_ending_here = 0
+        end
+    end
+    return max_so_far
 end

lib/newman_conway.rb

@@ -1,7 +1,17 @@
+# Time complexity: O(n) as the number of iterations required increases as the number grows 
+# Space Complexity: O(n) as the size of the solutions array grows as the size of the number grows 
+def newman_conway(num)
+  raise ArgumentError.new("Number must be at least greater than or equal to 1 to calculate newman conway sequence") if num <= 0 
+  return "1" if num == 1
+  return "1 1" if num == 2
 
+  memo = [0, 1, 1]
+  i = 3 
 
-# Time complexity: ?
-# Space Complexity: ?
-def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
+  while i <= num 
+    memo << memo[memo[i - 1]] + memo[i - memo[i - 1]]
+    i += 1 
+  end
+
+  return memo[1..-1].join(" ")
 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]