From 1b10d9c9e9723c577dcebed80594879069f8f53a Mon Sep 17 00:00:00 2001
From: cojenco <icathyouyang@gmail.com>
Date: Fri, 2 Oct 2020 13:01:28 -0700
Subject: [PATCH 1/3] pass tests for newman_conway

---
 lib/newman_conway.rb | 21 +++++++++++++++++++--
 1 file changed, 19 insertions(+), 2 deletions(-)

diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 4c985cd..7a068c3 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,7 +1,24 @@
 
 
-# Time complexity: ?
+# Time complexity: O(n) and actually O(3n) since I'm using shift and join? 
 # Space Complexity: ?
+# P(n) = P(P(n - 1)) + P(n - P(n - 1))
+# P(5) = P(P(4)) + P(5 - P(4))
+#      = P(2) + P(3) = 3
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
+  raise ArgumentError.new("num must be a positive integer") if num <= 0
+  return "1" if num == 1
+  return "1 1" if num == 2
+
+  memo = ["", 1, 1]
+  n = 3
+  while n <= num
+    pre = memo[n-1]
+    res = memo[pre] + memo[n - pre] 
+    memo[n] = res
+    n += 1
+  end
+
+  memo.shift
+  return memo.join(" ")
 end
\ No newline at end of file

From 50645ac5f452d88feba7905cfcbcfc0b66039bfb Mon Sep 17 00:00:00 2001
From: cojenco <icathyouyang@gmail.com>
Date: Fri, 2 Oct 2020 21:13:30 -0700
Subject: [PATCH 2/3] revise newman_conway

---
 lib/newman_conway.rb | 34 ++++++++++++++++++++++------------
 1 file changed, 22 insertions(+), 12 deletions(-)

diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 7a068c3..cf97d5a 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,24 +1,34 @@
-
-
 # Time complexity: O(n) and actually O(3n) since I'm using shift and join? 
-# Space Complexity: ?
+# Space Complexity: O(n) for the additional memo array storing n of the sequence
 # P(n) = P(P(n - 1)) + P(n - P(n - 1))
-# P(5) = P(P(4)) + P(5 - P(4))
-#      = P(2) + P(3) = 3
 def newman_conway(num)
   raise ArgumentError.new("num must be a positive integer") if num <= 0
   return "1" if num == 1
-  return "1 1" if num == 2
 
-  memo = ["", 1, 1]
+  # n starts at 3 per newman_conway property, though all indice in memo[] need to deduct by 1
+  memo = [1, 1]
   n = 3
   while n <= num
-    pre = memo[n-1]
-    res = memo[pre] + memo[n - pre] 
-    memo[n] = res
+    pre = memo[n - 1 - 1]                               # pre = P(n-1)
+    memo[n - 1] = memo[pre - 1] + memo[n - pre - 1]     # P(n) stored at index (n-1) = P(P(n - 1)) + P(n - P(n - 1)) 
     n += 1
   end
 
-  memo.shift
   return memo.join(" ")
-end
\ No newline at end of file
+end
+
+
+# alternative solution w/o shifting indice
+# def newman_conway(num)
+#   raise ArgumentError.new("num must be a positive integer") if num <= 0
+#   return "1" if num == 1
+#   memo = ["", 1, 1]
+#   n = 3
+#   while n <= num
+#     pre = memo[n-1]
+#     memo[n] = memo[pre] + memo[n - pre] 
+#     n += 1
+#   end
+#   memo.shift
+#   return memo.join(" ")
+# end
\ No newline at end of file

From 2c6d399175647734c6f0f61d30e9454f4f0b1277 Mon Sep 17 00:00:00 2001
From: cojenco <icathyouyang@gmail.com>
Date: Sun, 4 Oct 2020 15:56:40 -0700
Subject: [PATCH 3/3] complete max_subarray

---
 lib/max_subarray.rb        | 22 +++++++++++++++++-----
 test/max_sub_array_test.rb |  2 +-
 2 files changed, 18 insertions(+), 6 deletions(-)

diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 5204edb..fe97bdc 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,8 +1,20 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n)
+# Space Complexity: O(1)
 def max_sub_array(nums)
-    return 0 if nums == nil
+    return nil if nums.nil? || nums.empty?
     
-    raise NotImplementedError, "Method not implemented yet!"
-end
+    max_so_far = nums[0]
+    max_ending_here = nums[0]
+
+    i = 1
+    while i < nums.length
+      max_ending_here += nums[i]
+      # assign max to current num if previous accumulated is deducting value (~liability)
+      max_ending_here = nums[i] if max_ending_here < nums[i]
+      max_so_far = max_ending_here if max_so_far < max_ending_here
+      i += 1
+    end
+
+    return max_so_far
+end
\ No newline at end of file
diff --git a/test/max_sub_array_test.rb b/test/max_sub_array_test.rb
index 3253cdf..e27e1ca 100644
--- a/test/max_sub_array_test.rb
+++ b/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]