Branches - Eve

lib/heap_sort.rb

@@ -1,8 +1,48 @@
-
+require_relative 'min_heap'
 
 # 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(nlogn)
+# Space Complexity: O(1)
+def heapsort(list)
+  size = list.length()
+  size.times do |index|
+    heap_up(list, index)
+  end
+
+  size.times do |index|
+    swap(list, 0, size - 1 - index)
+    heap_down(list, size - 1 - index)
+  end
+  return list
+end
+
+def heap_up(list, index)
+  current = index
+  parent_index = (current % 2 == 0) ? current/2 - 1 : current/2
+  while current > 0 && list[current] > list[parent_index]
+    swap(list, current, parent_index)
+    current = parent_index
+    parent_index = (current % 2 == 0) ? current/2 - 1 : current/2
+  end
+end
+
+def heap_down(list, last)
+  current = 0
+  left = 1
+  while (current < last) && (left < last)
+    bigger = left
+    right = left + 1
+    bigger = right if right < last && list[right] > list[left]
+
+    break if list[current] > list[bigger]
+    swap(list, current,  bigger)
+    current = bigger
+    left = 2*current + 1
+  end
+end
+
+def swap(list, index_1, index_2)
+  temp = list[index_1]
+  list[index_1] = list[index_2]
+  list[index_2] = temp
 end

lib/min_heap.rb

@@ -1,73 +1,96 @@
 class HeapNode
   attr_reader :key, :value
-
+  
   def initialize(key, value)
     @key = key
     @value = value
   end
 end
 
 class MinHeap
-
+  
   def initialize
     @store = []
   end
-
+  
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(logn)
+  # Space Complexity: O(1)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    new_node = HeapNode.new(key, value)
+    @store << new_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(logn)
+  # Space Complexity: O(1)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    swap(0, @store.length - 1)
+    element = @store.pop()
+    heap_down(0)
+    return element.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..."
+    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(logn)
+  # Space complexity: O(1)
   def heap_up(index)
-
+    parent = (index % 2 == 0) ? index/2 - 1 : index/2
+    while index > 0 && @store[index].key < @store[parent].key
+      swap(index, parent)
+      index = parent
+      parent = (index % 2 == 0) ? index/2 - 1 : index/2
+    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..."
-  end
+  #  moves it down the heap if it's larger
+  #  than it's child node.
+  def heap_down(current)
+    left = 1
+    size = @store.length
+    while (current < size) && (left < size)
+      smaller = left
+      right = left + 1
+
+      smaller = right if right < size && @store[right].key < @store[left].key
 
+      break if @store[current].key < @store[smaller].key
+      swap(current, smaller)
+      current = smaller
+      left = 2*current + 1
+    end
+  end
+
   # If you want a swap method... you're welcome
   def swap(index_1, index_2)
     temp = @store[index_1]

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 = []
@@ -33,4 +33,15 @@
     # Assert
     expect(result).must_equal [-50, 3, 5, 16, 27]
   end  
+
+  it "can sort a big array" do
+    # Arrange 
+    list = [1, 12, 13, -50, 235, 2, 0, 9, -6, 7, 20, -12, 8, 31]
+
+    # Act
+    result = heapsort(list)
+
+    # Assert
+    expect(result).must_equal [-50, -12, -6, 0, 1, 2, 7, 8, 9, 12, 13, 20, 31, 235]
+  end  
 end