diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..98ce5f6 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,23 @@
 
-
+require_relative 'min_heap'
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity: O (n log (n))
+# Space Complexity: O(n)
 def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  return [] if list.nil?
+  return list if list.length == 1
+  
+  heap = MinHeap.new 
+  
+  list.each do |node|
+    heap.add(node)
+  end
+  
+  sorted_heap = []
+  
+  list.length.times do 
+    node = heap.remove 
+    sorted_heap << node
+  end
+  return sorted_heap
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..056b23e 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -1,6 +1,6 @@
 class HeapNode
   attr_reader :key, :value
-
+  
   def initialize(key, value)
     @key = key
     @value = value
@@ -8,66 +8,108 @@ def initialize(key, value)
 end
 
 class MinHeap
-
+  
   def initialize
     @store = []
   end
-
+  
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log(n))
+  # Space Complexity: O(1)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    newNode = HeapNode.new(key, value)
+    @store << newNode
+    
+    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))
+  # Space Complexity: O(1)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if @store.empty?
+    
+    length = @store.length 
+    swap(0, length -1)
+    
+    removed_node = @store.pop
+    heap_down(0)
+    
+    return removed_node.value
   end
-
-
+  
+  
   # Used for Testing
   def to_s
     return "[]" if @store.empty?
-
+    
     output = "["
     (@store.length - 1).times do |index|
       output += @store[index].value + ", "
     end
-
+    
     output += @store.last.value + "]"
-      
+    
     return output
   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..."
+    if @store.length == 0
+      return true
+    else 
+      return false
+    end
   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(log (n))
+  # Space complexity: O(1)
   def heap_up(index)
+    parent = (index - 1) / 2
     
+    if @store[parent].key > @store[index].key
+      swap(parent, index)
+    end    
+    
+    while parent > 0 
+      return 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].nil? && @store[right_child].nil?
+    
+    if @store[left_child].nil?
+      smallest_child = right_child
+    elsif @store[right_child].nil?
+      smallest_child = left_child
+    elsif @store[left_child].key < @store[right_child].key 
+      smallest_child = left_child
+    else  
+      smallest_child = right_child
+    end
+    
+    if @store[index].key > @store[smallest_child].key 
+      swap(index, smallest_child)
+    end
+    
+    return heap_down(smallest_child)
   end
-
+  
   # If you want a swap method... you're welcome
   def swap(index_1, index_2)
     temp = @store[index_1]