Class: Containers::Heap

Inherits:
Object
  • Object
show all
Includes:
Enumerable
Defined in:
lib/containers/heap.rb

Overview

rdoc

A Heap is a container that satisfies the heap property that nodes are always smaller in
value than their parent node.

The Containers::Heap class is flexible and upon initialization, takes an optional block
that determines how the items are ordered. Two versions that are included are the
Containers::MaxHeap and Containers::MinHeap that return the largest and smallest items on
each invocation, respectively.

This library implements a Fibonacci heap, which allows O(1) complexity for most methods.

MIT License

Copyright (c) 2009 Kanwei Li

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

Direct Known Subclasses

MaxHeap, MinHeap

Defined Under Namespace

Classes: Node

Instance Method Summary collapse

Constructor Details

#initialize(ary = [], &block) ⇒ Heap

call-seq:

Heap.new(optional_array) { |x, y| optional_comparison_fn } -> new_heap

If an optional array is passed, the entries in the array are inserted into the heap with equal key and value fields. Also, an optional block can be passed to define the function that maintains heap property. For example, a min-heap can be created with:

minheap = Heap.new { |x, y| (x <=> y) == -1 }
minheap.push(6)
minheap.push(10)
minheap.pop #=> 6

Thus, smaller elements will be parent nodes. The heap defaults to a min-heap if no block is given.



60
61
62
63
64
65
66
67
 
# File 'lib/containers/heap.rb', line 60

def initialize(ary=[], &block)
  @compare_fn = block || lambda { |x, y| (x <=> y) == -1 }
  @next = nil
  @size = 0
  @stored = {}

  ary.each { |n| push(n) } unless ary.empty?
end

Instance Method Details

#change_key(key, new_key, delete = false) ⇒ Object

call-seq:

change_key(key, new_key) -> [new_key, value]
change_key(key, new_key) -> nil

Changes the key from one to another. Doing so must not violate the heap property or an exception will be raised. If the key is found, an array containing the new key and value pair is returned, otherwise nil is returned.

In the case of duplicate keys, an arbitrary key is changed. This will be investigated more in the future.

Complexity: amortized O(1)

minheap = MinHeap.new([1, 2])
minheap.change_key(2, 3) #=> raise error since we can't increase the value in a min-heap
minheap.change_key(2, 0) #=> [0, 2]
minheap.pop #=> 2
minheap.pop #=> 1



284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
 
# File 'lib/containers/heap.rb', line 284

def change_key(key, new_key, delete=false)
  return if @stored[key].nil? || @stored[key].empty? || (key == new_key)

  # Must maintain heap property
  raise "Changing this key would not maintain heap property!" unless (delete || @compare_fn[new_key, key])
  node = @stored[key].shift
  if node
    node.key = new_key
    @stored[new_key] ||= []
    @stored[new_key] << node
    parent = node.parent
    if parent
      # if heap property is violated
      if delete || @compare_fn[new_key, parent.key]
        cut(node, parent)
        cascading_cut(parent)
      end
    end
    if delete || @compare_fn[node.key, @next.key]
      @next = node
    end
    return [node.key, node.value]
  end
  nil
end

#clear ⇒ Object

call-seq:

clear -> nil

Removes all elements from the heap, destructively.

Complexity: O(1)



165
166
167
168
169
170
 
# File 'lib/containers/heap.rb', line 165

def clear
  @next = nil
  @size = 0
  @stored = {}
  nil
end

#delete(key) ⇒ Object

call-seq:

delete(key) -> value
delete(key) -> nil

Deletes the item with associated key and returns it. nil is returned if the key is not found. In the case of nodes with duplicate keys, an arbitrary one is deleted.

Complexity: amortized O(log n)

minheap = MinHeap.new([1, 2])
minheap.delete(1) #=> 1
minheap.size #=> 1



322
323
324
 
# File 'lib/containers/heap.rb', line 322

def delete(key)
  pop if change_key(key, nil, true)
end

#empty? ⇒ Boolean

call-seq:

empty? -> true or false

Returns true if the heap is empty, false otherwise.

Returns:

  • (Boolean) 


176
177
178
 
# File 'lib/containers/heap.rb', line 176

def empty?
  @next.nil?
end

#has_key?(key) ⇒ Boolean

call-seq:

has_key?(key) -> true or false

Returns true if heap contains the key.

Complexity: O(1)

minheap = MinHeap.new([1, 2])
minheap.has_key?(2) #=> true
minheap.has_key?(4) #=> false

Returns:

  • (Boolean) 


123
124
125
 
# File 'lib/containers/heap.rb', line 123

def has_key?(key)
  @stored[key] && !@stored[key].empty? ? true : false
end

#merge!(otherheap) ⇒ Object

call-seq:

merge!(otherheap) -> merged_heap

Does a shallow merge of all the nodes in the other heap.

Complexity: O(1)

heap = MinHeap.new([5, 6, 7, 8])
otherheap = MinHeap.new([1, 2, 3, 4])
heap.merge!(otherheap)
heap.size #=> 8
heap.pop #=> 1

Raises:

  • (ArgumentError) 


192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
 
# File 'lib/containers/heap.rb', line 192

def merge!(otherheap)
  raise ArgumentError, "Trying to merge a heap with something not a heap" unless otherheap.kind_of? Containers::Heap
  other_root = otherheap.instance_variable_get("@next")
  if other_root
    @stored = @stored.merge(otherheap.instance_variable_get("@stored")) { |key, a, b| (a << b).flatten }
    # Insert othernode's @next node to the left of current @next
    @next.left.right = other_root
    ol = other_root.left
    other_root.left = @next.left
    ol.right = @next
    @next.left = ol

    @next = other_root if @compare_fn[other_root.key, @next.key]
  end
  @size += otherheap.size
end

#next ⇒ Object

call-seq:

next -> value
next -> nil

Returns the value of the next item in heap order, but does not remove it.

Complexity: O(1)

minheap = MinHeap.new([1, 2])
minheap.next #=> 1
minheap.size #=> 2



138
139
140
 
# File 'lib/containers/heap.rb', line 138

def next
  @next && @next.value
end

#next_key ⇒ Object

call-seq:

next_key -> key
next_key -> nil

Returns the key associated with the next item in heap order, but does not remove the value.

Complexity: O(1)

minheap = MinHeap.new
minheap.push(1, :a)
minheap.next_key #=> 1



154
155
156
 
# File 'lib/containers/heap.rb', line 154

def next_key
  @next && @next.key
end

#pop ⇒ Object Also known as: next!

call-seq:

pop -> value
pop -> nil

Returns the value of the next item in heap order and removes it from the heap.

Complexity: O(1)

minheap = MinHeap.new([1, 2])
minheap.pop #=> 1
minheap.size #=> 1



220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
 
# File 'lib/containers/heap.rb', line 220

def pop
  return nil unless @next
  popped = @next
  if @size == 1
    clear
    return popped.value
  end
  # Merge the popped's children into root node
  if @next.child
    @next.child.parent = nil

    # get rid of parent
    sibling = @next.child.right
    until sibling == @next.child
      sibling.parent = nil
      sibling = sibling.right
    end

    # Merge the children into the root. If @next is the only root node, make its child the @next node
    if @next.right == @next
      @next = @next.child
    else
      next_left, next_right = @next.left, @next.right
      current_child = @next.child
      @next.right.left = current_child
      @next.left.right = current_child.right
      current_child.right.left = next_left
      current_child.right = next_right
      @next = @next.right
    end
  else
    @next.left.right = @next.right
    @next.right.left = @next.left
    @next = @next.right
  end
  consolidate

  unless @stored[popped.key].delete(popped)
    raise "Couldn't delete node from stored nodes hash"
  end
  @size -= 1

  popped.value
end

#push(key, value = key) ⇒ Object Also known as: <<

call-seq:

push(key, value) -> value
push(value) -> value

Inserts an item with a given key into the heap. If only one parameter is given, the key is set to the value.

Complexity: O(1)

heap = MinHeap.new
heap.push(1, "Cat")
heap.push(2)
heap.pop #=> "Cat"
heap.pop #=> 2

Raises:

  • (ArgumentError) 


83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
 
# File 'lib/containers/heap.rb', line 83

def push(key, value=key)
  raise ArgumentError, "Heap keys must not be nil." unless key
  node = Node.new(key, value)
  # Add new node to the left of the @next node
  if @next
    node.right = @next
    node.left = @next.left
    node.left.right = node
    @next.left = node
    if @compare_fn[key, @next.key]
      @next = node
    end
  else
    @next = node
  end
  @size += 1

  arr = []
  w = @next.right
  until w == @next do
    arr << w.value
    w = w.right
  end
  arr << @next.value
  @stored[key] ||= []
  @stored[key] << node
  value
end

#size ⇒ Object Also known as: length

call-seq:

size -> int

Return the number of elements in the heap.



41
42
43
 
# File 'lib/containers/heap.rb', line 41

def size
  @size
end