Cyndi

lib/heap_sort.rb

@@ -1,8 +1,40 @@
 
 
 # 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(n logn)
+# Space Complexity: O(1)
+def heapsort(list)
+  n = list.length
+  (n / 2).downto(0) do |i|
+    heapify(list, i, n)
+  end
+  n -= 1
+  while n > 0
+    swap(list, 0, n)
+    n -= 1
+    heapify(list, 0, n)
+  end
+  return list
+end
+
+def heapify(array, index, len)
+  greatest = index
+  left_child = 2 * index + 1
+  right_child = 2 * index + 2
+  if left_child < len && array[left_child] > array[index]
+    greatest = left_child
+  end
+  if right_child < len && array[right_child] > array[greatest]
+    greatest = right_child
+  end
+  if greatest != index
+    swap(array, greatest, index)
+    heapify(array, greatest, len)
+  end
+end
+
+def swap(array, index_1, index_2)
+  temp = array[index_1]
+  array[index_1] = array[index_2]
+  array[index_2] = temp
+end

lib/min_heap.rb

@@ -8,27 +8,30 @@ 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(n)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    new_heap_node = HeapNode.new(key, value)
+    @store.append(new_heap_node)
+    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..."
+    swap(0, @store.length - 1)
+    result = @store.pop
+    heap_down(0) unless @store.empty?
+    return result.value
   end
 
-
   # Used for Testing
   def to_s
     return "[]" if @store.empty?
@@ -39,33 +42,66 @@ 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(n)
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return true if @store == []
   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 = find_parent_index(index)
+    while @store[index].key < @store[parent_index].key && parent_index >= 0
+      swap(parent_index, index)
+      index = parent_index
+      parent_index = find_parent_index(index)
+    end
+  end
+
+  def find_parent_index(child_index)
+    if child_index % 2 == 0
+      parent_index = (child_index - 2) / 2
+    else
+      parent_index = (child_index - 1) / 2
+    end
+    return parent_index
   end
 
-  # This helper method takes an index and 
-  #  moves it up the heap if it's smaller
-  #  than it's parent node.
+  # This helper method takes an index and
+  #  moves it down the heap if it's bigger
+  #  than it's child's node.
+   # Time complexity: O(log n)
+  # Space complexity: O(1)
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    child_index = find_minimum_child_index(index)
+    while child_index <= @store.length - 1 && @store[index].key > @store[child_index].key
+      swap(index, child_index)
+      index = child_index
+      child_index = find_minimum_child_index(index)
+    end
+  end
+
+  def find_minimum_child_index(index)
+    child_index1 = 2 * index + 1
+    child_index2 = 2 * index + 2
+    return child_index1 if child_index1 > @store.length - 1
+    if @store[child_index1].key <= @store[child_index2].key
+      min_child_index = child_index1
+    else
+      min_child_index = child_index2
+    end
+    return min_child_index
   end
 
   # If you want a swap method... you're welcome
@@ -74,4 +110,4 @@ def swap(index_1, index_2)
     @store[index_1] = @store[index_2]
     @store[index_2] = temp
   end
-end
+end

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
@@ -22,15 +22,15 @@
     # Assert
     expect(result).must_equal [5]
   end
-  
+
   it "can sort a 5-element array" do
-    # Arrange 
+    # Arrange
     list = [5, 27, 3, 16, -50]
 
     # Act
     result = heapsort(list)
 
     # Assert
     expect(result).must_equal [-50, 3, 5, 16, 27]
-  end  
-end
+  end
+end