Elle

lib/heap_sort.rb

@@ -1,8 +1,26 @@
-
+require_relative "min_heap"
+# require 'pry'
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
-def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
-end
+# Time Complexity:  O(nlogn),where n is the number of items in the list, 
+# because the add and remove methods are O(nlogn)
+# Space Complexity: O(2n), where n is the number of items in the list
+def heapsort(list)
+  return list if list.length < 2
+
+  heap = MinHeap.new
+
+  i = 0
+  list.each do
+    heap.add(list[i])
+    i += 1
+  end
+
+  i = 0
+  until i == list.length
+    list[i] = heap.remove
+    i += 1
+  end
+
+  return list
+end

lib/min_heap.rb

@@ -14,18 +14,24 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(nlogn) because heap_up is nlogn, where n is the number of nodes in the heap
+  # Space Complexity: O(1)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    @store << HeapNode.new(key, value)
+    index = @store.length-1
+    heap_up(index) if @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(nlogn), where n is the number of nodes in the heap
+  # Space Complexity: O(1)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if empty?
+    swap(0, @store.length-1)
+    removed_item = @store.pop
+    heap_down(0) if @store.length > 1
+    return removed_item.value
   end
 
 
@@ -44,28 +50,47 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(1)
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return @store.empty?
   end
 
   private
 
   # This helper method takes an index and
   #  moves it up the heap, if it is less than it's parent node.
   #  It could be **very** helpful for the add method.
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time Complexity: O(nlogn), where n is the number of nodes in the heap
+  # Space Complexity: O(1)
   def heap_up(index)
-
+    return if index == 0
+    parent_index = find_parent_index(index)           # O(1)
+    if @store[parent_index].key > @store[index].key
+      swap(parent_index, index)                       # O(1)
+      heap_up(parent_index)
+    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..."
+  def heap_down(parent_index)
+    left_child_index = find_left_child_index(parent_index)
+    right_child_index = find_right_child_index(parent_index)
+    smallest = 0
+
+    return if !@store[left_child_index]
+
+    if !@store[right_child_index] || @store[left_child_index].key < @store[right_child_index].key
+      smallest = left_child_index
+    else
+      smallest = right_child_index
+    end
+
+    if @store[smallest].key < @store[parent_index].key
+      swap(smallest, parent_index)
+    end
   end
 
   # If you want a swap method... you're welcome
@@ -74,4 +99,19 @@ def swap(index_1, index_2)
     @store[index_1] = @store[index_2]
     @store[index_2] = temp
   end
+
+  # These helper methods find the index of the
+  # current item's parent node, and the indices
+  # of its left and right children
+  def find_parent_index(node_index)
+    return ((node_index-1)/2).floor
+  end
+
+  def find_left_child_index(node_index)
+    return node_index * 2 + 1
+  end
+
+  def find_right_child_index(node_index)
+    return node_index * 2 + 2
+  end
 end

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 = []