From f7202bcae7ae76e9251a587b1cd4a374dd698df8 Mon Sep 17 00:00:00 2001
From: Kelsey Krippaehne <kelseykripp@gmail.com>
Date: Sun, 29 Mar 2020 15:33:33 -0700
Subject: [PATCH] Added newman_conway and max_subarray working methods

---
 lib/max_subarray.rb        | 27 +++++++++++++++++---
 lib/newman_conway.rb       | 28 ++++++++++++++++++---
 test/max_sub_array_test.rb | 50 +++++++++++++++++++-------------------
 3 files changed, 73 insertions(+), 32 deletions(-)

diff --git a/lib/max_subarray.rb b/lib/max_subarray.rb
index 5204edb..c5b9307 100644
--- a/lib/max_subarray.rb
+++ b/lib/max_subarray.rb
@@ -1,8 +1,27 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n), only going through the array of nums once
+# Space Complexity: O(1), constant, only creating a couple of variables
+
 def max_sub_array(nums)
-    return 0 if nums == nil
+  return 0 if nums == nil
+  return nil if nums.length == 0
+  
+  curr_max_sum = nums[0]
+  max_sum = nums[0]
+  i = 1
+  while i < nums.length
+    if (curr_max_sum + nums[i]) <= nums[i] 
+      curr_max_sum = nums[i]
+    elsif (curr_max_sum + nums[i]) >= nums[i]
+      curr_max_sum += nums[i]
+    end
     
-    raise NotImplementedError, "Method not implemented yet!"
+    if (curr_max_sum > max_sum)
+      max_sum = curr_max_sum
+    end
+    i += 1
+  end
+  
+  return max_sum
+  
 end
diff --git a/lib/newman_conway.rb b/lib/newman_conway.rb
index 4c985cd..9a32e69 100644
--- a/lib/newman_conway.rb
+++ b/lib/newman_conway.rb
@@ -1,7 +1,29 @@
 
 
-# Time complexity: ?
-# Space Complexity: ?
+# Time complexity: O(n)
+# Space Complexity: O(n)
+
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
+  if num == 0
+    throw ArgumentError, "no value for 0 in the Newman-Conway sequence"
+  end
+  
+  seq = []
+  # holding seq[0] as nil
+  # this keeps the index number 'n' equal to the argument 'num'
+  # tiny space sacrifice to keep those numbers the same
+  seq[1] = 1
+  seq[2] = 1
+  
+  if num == 1 || num == 2
+    return seq[1..num].join(' ')
+  end
+  
+  n = 3
+  while n <= num
+    seq[n] = seq[seq[n - 1]] + seq[n- seq[n-1]]
+    n += 1
+  end
+  
+  return seq[1..num].join(' ')
 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..5f930ef 100644
--- a/test/max_sub_array_test.rb
+++ b/test/max_sub_array_test.rb
@@ -1,70 +1,70 @@
 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]
-
+    
     # Act
     answer = max_sub_array(input)
-
+    
     # Assert
     expect(answer).must_equal 6
   end
-
+  
   it "will work with a totally negative array" do
     # Arrange
     input = [-3, -4, -5, -6, -7]
-
+    
     # Act
     answer = max_sub_array(input)
-
+    
     # Assert
     expect(answer).must_equal(-3)
   end
-
+  
   it "will work with a totally negative array with the largest element at the rear" do
     # Arrange
     input = [ -4, -5, -6, -7, -3]
-
+    
     # Act
     answer = max_sub_array(input)
-
+    
     # Assert
     expect(answer).must_equal(-3)
   end
-
+  
   it "will work with a 1-element array" do
     # Arrange
     input = [3]
-
+    
     # Act
     answer = max_sub_array(input)
-
+    
     # Assert
     expect(answer).must_equal 3
   end
-
+  
   it "will return nil for an empty array" do
-   # Arrange
-   input = []
-
-   # Act
-   answer = max_sub_array(input)
-
-   # Assert
-   expect(answer).must_be_nil
+    # Arrange
+    input = []
+    
+    # Act
+    answer = max_sub_array(input)
+    
+    # Assert
+    expect(answer).must_be_nil
   end
-
+  
   it "will work for [50, -50, 50]" do
     # Arrange
     input = [50, -50, 50]
-
+    
     # Act
     answer = max_sub_array(input)
-
+    
     # Assert
     expect(answer).must_equal 50
   end
-
+  
 end
\ No newline at end of file