Depq - Double-Ended Priority Queue

depq is double-ended stable priority queue with priority update operation implemented using implicit heap.

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 will get the value inserted first with minimum/maximum priority
priority update - usable for Dijkstra's shortest path algorithm and various graph algorithms
implicit heap - compact heap representation using array. most operations are O(log n) at worst
several utility methods: nlargest, nsmallest, merge, astar_search

Install

gem install depq

Introduction

Simple Insertion/Deletion

You can insert values into a Depq object. You can delete 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" which means that the element inserted first is 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

delete_max is also stable. This means delete_max deletes the element with maximum priority with "minimum" subpriority.

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_max     #=> "a"         first element with priority 1
p q.delete_max     #=> "c"
p q.delete_max     #=> "e"         last element with priority 1
p q.delete_max     #=> "b"         first element with priority 0
p q.delete_max     #=> "d"
p q.delete_max     #=> "f"         last element with priority 0

Update Element

An inserted element can be modified and/or deleted. The element to be modified is specified by 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 <akr@fsij.org>

License

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
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.
The name of the author may not be used to endorse or promote products derived from this software without specific prior written permission.

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(The modified BSD licence)