Earth - Beauttie

lib/heap_sort.rb

@@ -1,8 +1,12 @@
 
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
-def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+# Time Complexity:  O(n log n); adding n nodes to a heap is O(n log n), 
+# while removing n nodes from the heap is O(n log n) => O(nlog n + nlog n)
+# Space Complexity: O(n) because of heap with up to n nodes
+def heapsort(list)
+  min_heap = MinHeap.new
+  list.each { |key| min_heap.add(key) }
+  list.length.times { |i| list[i] = min_heap.remove }
+  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(log n)
+  # Space Complexity: O(1)
   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)
+  # Space Complexity: O(1)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if @store.empty?
+
+    swap(0, @store.length - 1)
+    result = @store.pop
+    heap_down(0)
+    return result.value
   end
 
 
@@ -44,28 +50,49 @@ 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(log n)
+  # Space complexity: O(1)
   def heap_up(index)
-
+    parent_index = (index - 1) / 2
+    if index == 0
+      return
+    elsif @store[index].key < @store[parent_index].key
+      swap(parent_index, index)
+      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..."
+    left_child_index = 2 * index + 1
+    right_child_index = 2 * index + 2
+    last_index = @store.length - 1
+    if left_child_index > last_index
+      return
+    elsif right_child_index <= last_index && @store[right_child_index].key < @store[left_child_index].key
+      if @store[right_child_index].key < @store[index].key
+        swap(index, right_child_index)
+        heap_down(right_child_index)
+      end
+    else
+      if @store[left_child_index].key < @store[index].key
+        swap(index, left_child_index)
+        heap_down(left_child_index)
+      end
+    end
   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 = []