From ecba7dd478cc3d08bc787134e165f6d84843f890 Mon Sep 17 00:00:00 2001
From: C Gutierrez <gutierrez.clara.es@gmail.com>
Date: Tue, 31 Mar 2020 00:45:06 -0700
Subject: [PATCH 1/4] newman_conway

---
 lib/newman_conway.rb | 51 +++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 50 insertions(+), 1 deletion(-)

diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 4c985cd..379b18e 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -2,6 +2,55 @@
 
 # Time complexity: ?
 # Space Complexity: ?
+
+
+
+def newman_conway_helper(num) 
+  if num == 0
+    return 0
+  elsif 
+    num == 1 || num == 2
+    return 1
+  else
+    temp = num - 1
+    return temp
+  end
+  
+end
+
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
+  
+  if num == 0 || num == nil
+    raise ArgumentError
+  elsif num == 1
+    return "1"
+  elsif num == 2
+    return "1 1"
+  end
+  
+  if num >= 3
+    return_array = [1, 1]
+  end
+  
+  i = 3
+  
+  until i > num do
+    
+    # P(n) = P(P(n - 1)) + P(n - P(n - 1))
+    
+    temp_a = return_array[(return_array[i-2])-1]
+    
+    temp_b = return_array[(i-(return_array[i-2]))-1]
+    
+    temp = temp_a + temp_b
+    
+    i += 1
+    
+    return_array.push temp
+  end
+  
+  return_string = return_array.join(" ")
+  
+  return return_string
+  
 end
\ No newline at end of file

From 4cbf94106c0b80ab5c7d6fd410b9f4f6c24c5271 Mon Sep 17 00:00:00 2001
From: C Gutierrez <gutierrez.clara.es@gmail.com>
Date: Tue, 31 Mar 2020 00:47:57 -0700
Subject: [PATCH 2/4] newman_conway clean-up with complexities and removal of
 abandoned method

---
 lib/newman_conway.rb | 21 ++++-----------------
 1 file changed, 4 insertions(+), 17 deletions(-)

diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 379b18e..c5f4910 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,22 +1,9 @@
 
 
-# Time complexity: ?
-# Space Complexity: ?
-
-
-
-def newman_conway_helper(num) 
-  if num == 0
-    return 0
-  elsif 
-    num == 1 || num == 2
-    return 1
-  else
-    temp = num - 1
-    return temp
-  end
-  
-end
+# Time complexity: O(n)
+## As the number goes to infinity, its values have to be assessed relative to whatever's already in the array, but because it's based on an array, the look-up cost is very low given that an index value is being passed in. 
+# Space Complexity: O(n)
+## As the number goes to infinity, the amount of space will grow at the same rate
 
 def newman_conway(num)
   

From 41dadb58c3c5fb33bce2ef66ab7b4734a7ca3cf1 Mon Sep 17 00:00:00 2001
From: C Gutierrez <gutierrez.clara.es@gmail.com>
Date: Tue, 31 Mar 2020 01:20:03 -0700
Subject: [PATCH 3/4] max_subarray basic functionality

---
 lib/max_subarray.rb | 32 +++++++++++++++++++++++++++++---
 1 file changed, 29 insertions(+), 3 deletions(-)

diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 5204edb..3ef8603 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,8 +1,34 @@
 
 # Time Complexity: ?
 # Space Complexity: ?
-def max_sub_array(nums)
-    return 0 if nums == nil
+def max_sub_array(number_array)
+    length = number_array.length
+    if length == 0 
+        return nil
+    elsif length == 1
+        return number_array[0]
+    end
+    
+    max_so_far = number_array[0]
+    max_ending_here = 0
+    
+    i = 0
+    
+    until i == length do
+        
+        max_ending_here = max_ending_here + number_array[i]
+        
+        if max_so_far < max_ending_here
+            max_so_far = max_ending_here
+            i += 1
+        elsif max_ending_here < 0
+            max_ending_here = 0
+            i += 1
+        else
+            i+= 1
+        end
+    end
+    
+    return max_so_far
     
-    raise NotImplementedError, "Method not implemented yet!"
 end

From 101bb67cd294fdf5c150f7308c9774198c0a4b88 Mon Sep 17 00:00:00 2001
From: C Gutierrez <gutierrez.clara.es@gmail.com>
Date: Tue, 31 Mar 2020 01:21:37 -0700
Subject: [PATCH 4/4] max_subarray with complexities

---
 lib/max_subarray.rb | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 3ef8603..c694158 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,6 +1,10 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n)
+## The method iterates over the entire array but does so only once
+
+# Space Complexity: O(1)
+## There are a limited number of variables that are constantly being re-assessed, so as the input goes to infitity the space requirements do not grow. 
+
 def max_sub_array(number_array)
     length = number_array.length
     if length == 0