Depq - Feature Rich Double-Ended Priority Queue.
Features
-
queue - you can insert and delete values
-
priority - you can get a value with minimum priority
-
double-ended - you can get a value with maximum priority too
-
stable - you don’t need to maintain timestamps yourself
-
update priority - usable for Dijkstra’s shortest path algorithm and various graph algorithms
-
implicit binary heap - most operations are O(log n) at worst
Install
gem install depq
Links
-
((<reference manual|URL:depq.rubyforge.org/rdoc/classes/Depq.html>))
-
((<home page on rubyforge|URL:depq.rubyforge.org/>))
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((<project info on rubyforge|URL:rubyforge.org/projects/depq/>))
-
((<source repository on github|URL:github.com/akr/depq>))
-
((<raa entry|URL:raa.ruby-lang.org/project/depq/>))
Introduction
Simple Insertion/Deletion
You can insert values into a Depq object. You can deletes the values from the object from ascending/descending order. delete_min deletes the minimum value. It is used for ascending order.
q = Depq.new
q.insert "durian"
q.insert "banana"
p q.delete_min #=> "banana"
q.insert "orange"
q.insert "apple"
q.insert "melon"
p q.delete_min #=> "apple"
p q.delete_min #=> "durian"
p q.delete_min #=> "melon"
p q.delete_min #=> "orange"
p q.delete_min #=> nil
delete_max is similar to delete_min except it deletes maximum element instead of minimum. It is used for descending order.
The Order
The order is defined by the priorities corresponds to the values and comparison operator specified for the queue.
q = Depq.new(:casecmp) # use casecmp instead of <=>.
q.insert 1, "Foo" # specify the priority for 1 as "Foo"
q.insert 2, "bar"
q.insert 3, "Baz"
p q.delete_min #=> 2 # "bar" is minimum
p q.delete_min #=> 3
p q.delete_min #=> 1 # "Foo" is maximum
p q.delete_min #=> nil
If there are multiple values with same priority, subpriority is used to compare them. subpriority is an integer which can be specified by 3rd argument of insert. If it is not specified, total number of inserted elements is used. So Depq is “stable” with delete_min. The element inserted first is minimum and deleted first.
q = Depq.new
q.insert "a", 1 # "a", "c" and "e" has same priority: 1
q.insert "b", 0 # "b", "d" and "f" has same priority: 0
q.insert "c", 1
q.insert "d", 0
q.insert "e", 1
q.insert "f", 0
p q.delete_min #=> "b" first element with priority 0
p q.delete_min #=> "d"
p q.delete_min #=> "f" last element with priority 0
p q.delete_min #=> "a" first element with priority 1
p q.delete_min #=> "c"
p q.delete_min #=> "e" last element with priority 1
Note that delete_max is also stable. This means delete_max deletes the element with maximum priority with “minimum” subpriority.
Update Element
An inserted element can be modified and/or deleted. This is done using Depq::Locator object. It is returned by insert, find_min_locator, etc.
q = Depq.new
d = q.insert "durian", 1
m = q.insert "mangosteen", 2
c = q.insert "cherry", 3
p m #=> #<Depq::Locator: "mangosteen":2>
p m.value #=> "mangosteen"
p m.priority #=> 2
p q.find_min #=> "durian"
p q.find_min_locator #=> #<Depq::Locator: "durian":1>
m.update("mangosteen", 0)
p q.find_min #=> "mangosteen"
p q.find_min_locator #=> #<Depq::Locator: "mangosteen":0>
q.delete_element d
p q.delete_min #=> "mangosteen"
p q.delete_min #=> "cherry"
p q.delete_min #=> nil
For example, this feature can be used for graph algorithms such as Dijkstra’s shortest path finding algorithm, A* search algorithm, etc.
def dijkstra_shortest_path(start, edges)
h = {}
edges.each {|v1, v2, w|
(h[v1] ||= []) << [v2, w]
}
h.default = []
q = Depq.new
visited = {start => q.insert([start], 0)}
until q.empty?
path, w1 = q.delete_min_priority
v1 = path.last
h[v1].each {|v2, w2|
if !visited[v2]
visited[v2] = q.insert(path+[v2], w1 + w2)
elsif w1 + w2 < visited[v2].priority
visited[v2].update(path+[v2], w1 + w2) # update val/prio
end
}
end
result = []
visited.each_value {|loc|
result << [loc.value, loc.priority]
}
result
end
E = [
['A', 'B', 2],
['A', 'C', 4],
['B', 'C', 1],
['C', 'B', 2],
['B', 'D', 3],
['C', 'D', 1],
]
p dijkstra_shortest_path('A', E)
#=> [[["A"], 0],
# [["A", "B"], 2],
# [["A", "B", "C"], 3],
# [["A", "B", "C", "D"], 4]]
Internal Heap Algorithm
Depq uses min-heap, max-heap or interval-heap internally. When delete_min is used, min-heap is constructed. When delete_max is used, max-heap is constructed. When delete_min and delete_max is used, interval-heap is constructed.
Author
Tanaka Akira <[email protected]>
License
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
(1) Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
(2) Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
(3) The name of the author may not be used to endorse or promote products
derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE AUTHOR “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
(The modified BSD licence)