From 193dc1b9bfe0c2287fe9640d5d39767e20037432 Mon Sep 17 00:00:00 2001
From: Eve Le <nguyenthao.lee@gmail.com>
Date: Mon, 18 Nov 2019 16:57:38 -0800
Subject: [PATCH 1/4] Implemented fibonacci method

---
 lib/fibonacci.rb | 20 +++++++++++++++++---
 1 file changed, 17 insertions(+), 3 deletions(-)

diff --git a/lib/fibonacci.rb b/lib/fibonacci.rb
index 7465c25..2415499 100644
--- a/lib/fibonacci.rb
+++ b/lib/fibonacci.rb
@@ -1,8 +1,22 @@
 # Improved Fibonacci
 
-# Time Complexity - ?
-# Space Complexity - ?  (should be O(n))
+# Time Complexity - O(n)
+# Space Complexity - O(n) stack space
 # Hint, you may want a recursive helper method
 def fibonacci(n)
- 
+  return fib_helper([0, 1], 2, n)
 end
+
+def fib_helper(results, current, n)
+  raise ArgumentError if n < 0
+  return results[n] if n == 0 || n == 1
+  
+  if current == n
+    return results[0] + results[1]
+  end
+  
+  temp = results[0] + results[1]
+  results[0] = results[1]
+  results[1] = temp
+  return fib_helper(results, current + 1, n)
+end
\ No newline at end of file

From 3b6501faae4a59d3baf2ba35dae490b93e52a8c1 Mon Sep 17 00:00:00 2001
From: Eve Le <nguyenthao.lee@gmail.com>
Date: Mon, 18 Nov 2019 21:38:47 -0800
Subject: [PATCH 2/4] Implemented super_digit method

---
 lib/super_digit.rb       | 14 ++++++++++----
 test/super_digit_test.rb |  4 ++--
 2 files changed, 12 insertions(+), 6 deletions(-)

diff --git a/lib/super_digit.rb b/lib/super_digit.rb
index 33e367f..b78e71c 100644
--- a/lib/super_digit.rb
+++ b/lib/super_digit.rb
@@ -3,13 +3,19 @@
 # Time Complexity - ?
 # Space Complexity - ?
 def super_digit(n)
-   
+    return n if n/10 == 0
+
+    sum = n % 10
+    while n/10 != 0
+        n = n/10
+        sum += n % 10
+    end
+    return super_digit(sum)
 end
-  
+
 
 # Time Complexity - ?
 # Space Complexity - ?
 def refined_super_digit(n, k)
-    
+
 end
-    
\ No newline at end of file
diff --git a/test/super_digit_test.rb b/test/super_digit_test.rb
index 60da3a1..20973f1 100644
--- a/test/super_digit_test.rb
+++ b/test/super_digit_test.rb
@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "super_digit" do
+describe "super_digit" do
   it "will return 2 for super_digit(9875)" do
     # Act
     answer = super_digit(9875)
@@ -33,7 +33,7 @@
     expect(answer).must_equal 6
   end
 
-  describe "refined superdigit" do 
+  xdescribe "refined superdigit" do 
     it "will return 1 for n = 1 and k = 1" do
       # Act
       answer = refined_super_digit(1, 1)

From 29cc616d7f7c1581704022f877d00b2c1e6fbc43 Mon Sep 17 00:00:00 2001
From: Eve Le <nguyenthao.lee@gmail.com>
Date: Mon, 18 Nov 2019 22:16:11 -0800
Subject: [PATCH 3/4] Implemented refined_super_digit

---
 lib/super_digit.rb       | 15 ++++++++++-----
 test/super_digit_test.rb |  2 +-
 2 files changed, 11 insertions(+), 6 deletions(-)

diff --git a/lib/super_digit.rb b/lib/super_digit.rb
index b78e71c..a853cbd 100644
--- a/lib/super_digit.rb
+++ b/lib/super_digit.rb
@@ -1,7 +1,7 @@
 # Superdigit
 
-# Time Complexity - ?
-# Space Complexity - ?
+# Time Complexity - O(logn) n is the number itself
+# Space Complexity - O(logn)
 def super_digit(n)
     return n if n/10 == 0
 
@@ -14,8 +14,13 @@ def super_digit(n)
 end
 
 
-# Time Complexity - ?
-# Space Complexity - ?
+# Time Complexity - O(logn) n is the number itself
+# Space Complexity - O(logn)
 def refined_super_digit(n, k)
-
+    return n if k == 1 && n/10 == 0
+    sum = 0
+    k.times do
+        sum += super_digit(n)
+    end
+    return super_digit(sum)
 end
diff --git a/test/super_digit_test.rb b/test/super_digit_test.rb
index 20973f1..8eb6475 100644
--- a/test/super_digit_test.rb
+++ b/test/super_digit_test.rb
@@ -33,7 +33,7 @@
     expect(answer).must_equal 6
   end
 
-  xdescribe "refined superdigit" do 
+  describe "refined superdigit" do 
     it "will return 1 for n = 1 and k = 1" do
       # Act
       answer = refined_super_digit(1, 1)

From 55a0e7fdb80626439fad4a3de9b43aaa546d5d54 Mon Sep 17 00:00:00 2001
From: Eve Le <nguyenthao.lee@gmail.com>
Date: Tue, 19 Nov 2019 22:26:51 -0800
Subject: [PATCH 4/4] Simplified refined_super_digit

---
 lib/super_digit.rb | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/lib/super_digit.rb b/lib/super_digit.rb
index a853cbd..a21339d 100644
--- a/lib/super_digit.rb
+++ b/lib/super_digit.rb
@@ -4,7 +4,7 @@
 # Space Complexity - O(logn)
 def super_digit(n)
     return n if n/10 == 0
-
+    
     sum = n % 10
     while n/10 != 0
         n = n/10
@@ -19,8 +19,6 @@ def super_digit(n)
 def refined_super_digit(n, k)
     return n if k == 1 && n/10 == 0
     sum = 0
-    k.times do
-        sum += super_digit(n)
-    end
+    sum += super_digit(n) * k
     return super_digit(sum)
 end