akr-depq

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

= 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.

pd = Depq.new pd.insert "durian" pd.insert "banana" p pd.delete_min #=> "banana" pd.insert "orange" pd.insert "apple" pd.insert "melon" p pd.delete_min #=> "apple" p pd.delete_min #=> "durian" p pd.delete_min #=> "melon" p pd.delete_min #=> "orange" p pd.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 corresnponds to the values and comparison operator specified for the queue.

pd = Depq.new(:casecmp) # use casecmp instead of <=>. pd.inesrt 1, "Foo" # specify the priority for 1 as "Foo" pd.insert 2, "bar" pd.insert 3, "Baz" p pd.delete_min #=> 2 # "bar" is minimum p pd.delete_min #=> 3 p pd.delete_min #=> 1 # "Foo" is maximum p pd.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.

pd = Depq.new pd.insert "a", 1 # "a", "c" and "e" has same priority: 1 pd.insert "b", 0 # "b", "d" and "f" has same priority: 0 pd.insert "c", 1 pd.insert "d", 0 pd.insert "e", 1 pd.insert "f", 0 p pd.delete_min #=> "b" first element with priority 0 p pd.delete_min #=> "d" p pd.delete_min #=> "f" last element with priority 0 p pd.delete_min #=> "a" first element with priority 1 p pd.delete_min #=> "c" p pd.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.

pd = Depq.new d = pd.insert "durian", 1 m = pd.insert "mangosteen", 2 c = pd.insert "cherry", 3 p m #=> #<Depq::Locator: "mangosteen":2> p m.value #=> "mangosteen" p m.priority #=> 2 p pd.find_min #=> "durian" p pd.find_min_locator #=> #<Depq::Locator: "durian":1> m.update("mangosteen", 0) p pd.find_min #=> "mangosteen" p pd.find_min_locator #=> #<Depq::Locator: "mangosteen":0> pd.delete_element d p pd.delete_min #=> "mangosteen" p pd.delete_min #=> "cherry" p pd.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 and Performance Tips

Depq uses min-heap or max-heap internally. When delete_min is used, min-heap is constructed and max-heap is destructed. When delete_max is used, max-heap is constructed and min-heap is destructed. So mixing delete_min and delete_max causes bad performance. In future, min-max-heap may be implemented to avoid this problem. min-max-heap will be used when delete_min and delete_max is used both. (Because min-max-heap is slower than min-heap/max-heap.)

= Author

Tanaka Akira [e-mail]

= 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)