Leaves - Sabrina

lib/fibonacci.rb

@@ -1,8 +1,30 @@
 # Improved Fibonacci
 
-# Time Complexity - ?
-# Space Complexity - ?  (should be O(n))
+# Time Complexity - O(n)
+# Space Complexity - O(n)
+#   you only keep the last two solutions, so the solutions array does not grow,
+#   but you're still effectiving the stack by adding recursive calls
 # Hint, you may want a recursive helper method
 def fibonacci(n)
-
+  if n < 0
+    raise ArgumentError.new('Number cannot be less than zero')
+  end
+
+  return fib_helper([0, 1], 2, n)
+end
+
+def fib_helper(solutions, current, n)
+  if n == 0 || n == 1
+    return n
+  end
+
+  last_solution = solutions[-1]
+  new_solution = solutions[0] + solutions[1]
+
+  if current == n    
+    return new_solution
+  end
+
+  solutions = [last_solution, new_solution]
+  return fib_helper(solutions, current + 1, n)
 end

lib/super_digit.rb

@@ -1,15 +1,31 @@
 # Superdigit
 
-# Time Complexity - ?
-# Space Complexity - ?
+# Time Complexity - O(n) where n is the number of digits in the input number
+# Space Complexity - O(log n)
 def super_digit(n)
-
+  if (n / 10) == 0
+    return n
+  else
+    sum = 0
+    while ((n / 10.0) > 0)
+      sum += (n % 10)
+      n = (n / 10)
+    end
+    return super_digit(sum)
+  end
 end
-
 
-# Time Complexity - ?
-# Space Complexity - ?
+# Time Complexity - O(n)
+#     because the while loop to create the concatenated number
+#     and the while loop adding the digits of the number are not nested.
+# Space Complexity - O(log k * n)
 def refined_super_digit(n, k)
-
+  concatenated_n = ''
+  while k > 0
+    concatenated_n += n.to_s
+    k -= 1
+  end
+
+  concatenated_n = concatenated_n.to_i
+  return super_digit(concatenated_n)
 end
-

test/fibonacci_test.rb

@@ -41,10 +41,10 @@
   end
   it "will return 5 for fib(5)" do
     # Act
-    answer = fibonacci(4)
+    answer = fibonacci(5)
 
     # Assert
-    expect(answer).must_equal 3
+    expect(answer).must_equal 5
   end
   it "will return 55 for fib(10)" do
     # Act

test/super_digit_test.rb

@@ -1,61 +1,69 @@
 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)
-
+    
     # Assert
     expect(answer).must_equal 2
   end
-
+  
   it "will return 5 for super_digit(5)" do
     # Act
     answer = super_digit(5)
-
+    
     # Assert
     expect(answer).must_equal 5
-   end
-
+  end
+  
   it "will return 6 for super_digit(123)" do
     # Act
     answer = super_digit(123)
-
+    
     # Assert
     expect(answer).must_equal 6
   end
-
+  
   it "will return 6 for super_digit(12327)" do
     # Act
     answer = super_digit(12327)
-
+    
     # Assert
     expect(answer).must_equal 6
   end
-
+
+  it "will return 9 for super_digit(999_999_999_999)" do
+    # Act
+    answer = super_digit(999_999_999_999)
+
+    # Assert
+    expect(answer).must_equal 9
+  end
+
   describe "refined superdigit" do 
     it "will return 1 for n = 1 and k = 1" do
       # Act
       answer = refined_super_digit(1, 1)
-
+      
       # Assert
       expect(answer).must_equal 1      
     end
-
+    
     it "will return 8 for n=9875 and k = 4" do
       # Act
       answer = refined_super_digit(9875, 4)
-
+      
       # Assert
       expect(answer).must_equal 8
     end
-
+    
     it "will return 3 for n=148 and k = 3" do
-        # Act
-        answer = refined_super_digit(148, 3)
-
-        # Assert
-        expect(answer).must_equal 3
+      # Act
+      answer = refined_super_digit(148, 3)
+      
+      # Assert
+      expect(answer).must_equal 3
     end
   end
 end