Space - Lee

lib/heap_sort.rb

@@ -1,8 +1,22 @@
-
+require_relative "min_heap"
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity: O(n log n), where n is the number of nodes and because this method adds the elements to a heap, then places them back in the array in order
+# Space Complexity: O(log n), due to recursive calls of the heap_up and heap_down methods within the add and remove methods
 def heapsort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  return list if list.empty? || list.length < 2
+
+  min_heap = MinHeap.new
+  list.each do |value|
+    min_heap.add(value)
+  end
+
+  i = 0
+
+  while i < list.length
+    list[i] = min_heap.remove
+    i += 1
+  end
+
+  return list
 end

lib/min_heap.rb

@@ -14,18 +14,25 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n), where n is the number of nodes in a heap (a complete binary tree has log n levels)
+  # Space Complexity: O(log n), due to recursive calls of the heap_up method
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    @store << HeapNode.new(key, value)
+    heap_up(@store.length - 1)
   end
 
   # This method removes and returns an element from the heap
   #   maintaining the heap structure
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n), where n is the number of nodes in a heap (a complete binary tree has log n levels)
+  # Space Complexity: O(log n), due to recursive calls of the heap_down method
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return if @store.empty? 
+
+    swap(0, @store.length - 1)
+    result = @store.pop
+
+    heap_down(0) unless @store.empty?
+    return result.value
   end
 
 
@@ -44,10 +51,10 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(n), where n is the number of nodes
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return @store.empty?
   end
 
   private
@@ -58,14 +65,35 @@ def empty?
   # Time complexity: ?
   # Space complexity: ?
   def heap_up(index)
-
+    return if !index || !@store[index]
+
+    parent = (index - 1) / 2
+
+    if @store[index].key < @store[parent].key
+      swap(index, parent)
+      return if parent == 0
+      heap_up(parent)
+    end
   end
 
   # This helper method takes an index and 
   #  moves it up the heap if it's smaller
   #  than it's parent node.
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    left_child = index * 2 + 1
+    right_child = index * 2 + 2
+    return if !@store[left_child] 
+
+    min_child = @store[right_child] ? find_min_child(left_child, right_child) : left_child 
+
+    if @store[index].key > @store[min_child].key
+      swap(index, min_child)
+      heap_down(min_child)
+    end
+  end
+
+  def find_min_child(left_child, right_child)
+    @store[left_child].key <= @store[right_child].key ? left_child : right_child
   end
 
   # If you want a swap method... you're welcome

test/heapsort_test.rb

@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "heapsort" do
+describe "heapsort" do
   it "sorts an empty array" do
     # Arrange 
     list = []