Persistent Weighted Sets

Air supports, in additon to the standard persistent set type PSet, a weighted set PWSet (and PWIdSet). These types are broadly similar to PSet and PIdSet except that their entries additionally have non-negative numeric weights. These sets act as (1) persistent sets, (2) priority queues, and (3) discrete random variables.

Examples

Elements are given with their weights as pairs, and are ordered from highest to lowest weight:

julia> using Air, Random

julia> s = PWSet{Symbol}(:a => 0.1, :b => 0.2, :c => 0.3)
PWSet{Symbol, Float64}([:c, :b, :a])

julia> collect(s)
3-element Vector{Symbol}:
 :c
 :b
 :a

A weighted set supports the usual set operations:

julia> :b in s
true

julia> length(s)
3

julia> delete(s, :b)
PWSet{Symbol, Float64}([:c, :a])

It also supports the weighted extras:

julia> first(s)          # the element with the highest weight
:c

julia> pop(s)            # a copy without that element
PWSet{Symbol, Float64}([:b, :a])

julia> getweight(s, :b)
0.2

julia> setweight(s, :a, 9.9)   # a copy with one weight changed
PWSet{Symbol, Float64}([:a, :c, :b])

julia> rand(s)           # draws an element with probability proportional to weight
:c