diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index 6b692e4..99b921d 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,19 @@
 
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity:  O(n log(n))
+# Space Complexity: O(n)
 def heapsort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+
+  heap = MinHeap.new
+
+  list.each  do |num|
+    heap.add(num)
+  end
+  result = []
+  until heap.empty?
+    result << heap.remove
+  end
+  return result
+
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..32bbd90 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,32 @@ def initialize
   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..."
+    new_element = HeapNode.new(key, value)
+    next_index = @store.length
+    @store[next_index] = new_element
+    heap_up(next_index)
+
   end
 
   # This method removes and returns an element from the heap
-  #   maintaining the heap structure
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # maintaining the heap structure
+  # Time Complexity: O(log(n))
+  # Space Complexity: O(1)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return if @store.empty?
+
+    last_index = @store.length - 1
+    swap(0, last_index)
+
+    temp = @store[last_index]
+    @store.delete_at(last_index)
+    heap_down(0)
+
+    return temp.value
+
   end
 
 
@@ -39,33 +53,73 @@ def to_s
     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..."
+    return @store.length == 0
   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)
-    
+    return if index == 0  # if index is 0 it means its a parent so no need to perform heap up
+
+    if index % 2 == 0 # if index is even number it means its a right chile as right_child = 2*(i) + 2 <-- and this is always even number
+      parent_index = (index - 2) / 2
+    else
+      parent_index = (index - 1) / 2
+    end
+
+    if @store[index].key < @store[parent_index].key
+      swap(index, parent_index)
+      heap_up(parent_index)
+    else
+      return
+    end
+
   end
 
-  # This helper method takes an index and 
+  # This helper method takes an index and
   #  moves it up the heap if it's smaller
   #  than it's parent node.
+  # Time complexity: O(log(n))
+  # Space complexity: O(1)
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    return if @store.empty?
+    last_index = @store.length - 1
+    return if index == last_index # if index is the last one, we have reached the right most node
+
+    right_child_idx = (2 * index) + 2
+    left_child_idx = (2 * index) + 1
+
+    return if left_child_idx > last_index #  if we reach the end of/edge of the tree return
+
+    # only swap when current parent is greater than either of the child nodes then find the smallest of the two dscendants
+    # only check the reight child if the right_child_index is less than the max valid index of the array.
+    if (right_child_idx <= last_index && @store[index].key > @store[right_child_idx].key) || @store[index].key > @store[left_child_idx].key
+      if (right_child_idx <= last_index &&  @store[right_child_idx].key < @store[left_child_idx].key)
+        swap(right_child_idx, index) # swap only when value is greater than child
+        heap_down(right_child_idx)
+      else
+        swap(left_child_idx, index) # swap only when value is greater than child
+        heap_down(left_child_idx)
+      end
+    else
+      return
+    end
+
   end
 
   # If you want a swap method... you're welcome
diff --git a/test/heapsort_test.rb b/test/heapsort_test.rb
index 34402ac..fb7fa84 100644
--- a/test/heapsort_test.rb
+++ b/test/heapsort_test.rb
@@ -1,8 +1,8 @@
 require_relative "test_helper"
 
-xdescribe "heapsort" do
+describe "heapsort" do
   it "sorts an empty array" do
-    # Arrange 
+    # Arrange
     list = []
 
     # Act
@@ -13,7 +13,7 @@
   end
 
   it "can sort a 1-element array" do
-    # Arrange 
+    # Arrange
     list = [5]
 
     # Act
@@ -22,9 +22,9 @@
     # Assert
     expect(result).must_equal [5]
   end
-  
+
   it "can sort a 5-element array" do
-    # Arrange 
+    # Arrange
     list = [5, 27, 3, 16, -50]
 
     # Act
@@ -32,5 +32,5 @@
 
     # Assert
     expect(result).must_equal [-50, 3, 5, 16, 27]
-  end  
+  end
 end
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