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

- 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

gem install depq

- reference manual
- home page on rubyforge
- project info on rubyforge
- depq on rubygems.org
- source repository on github
- raa entry

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 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

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]]

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.

Tanaka Akira <akr@fsij.org>

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