Heaps

Heaps are data structures that efficiently maintain the minimum (or maximum) for a set of data that may dynamically change.

All heaps in this package are derived from AbstractHeap, and provide the following interface:

# Let h be a heap, i be a handle, and v be a value.

length(h)         # returns the number of elements

isempty(h)        # returns whether the heap is empty

push!(h, v)       # add a value to the heap

top(h)            # return the top value of a heap

pop!(h)           # removes the top value, and returns it

Mutable heaps (values can be changed after being pushed to a heap) are derived from AbstractMutableHeap <: AbstractHeap, and additionally provides the following interface:

i = push!(h, v)              # adds a value to the heap and and returns a handle to v

update!(h, i, v)             # updates the value of an element (referred to by the handle i)

v, i = top_with_handle(h)    # returns the top value of a heap and its handle

Currently, both min/max versions of binary heap (type BinaryHeap) and mutable binary heap (type MutableBinaryHeap) have been implemented.

Examples of constructing a heap:

h = binary_minheap(Int)
h = binary_maxheap(Int)            # create an empty min/max binary heap of integers

h = binary_minheap([1,4,3,2])
h = binary_maxheap([1,4,3,2])      # create a min/max heap from a vector

h = mutable_binary_minheap(Int)
h = mutable_binary_maxheap(Int)    # create an empty mutable min/max heap

h = mutable_binary_minheap([1,4,3,2])
h = mutable_binary_maxheap([1,4,3,2])    # create a mutable min/max heap from a vector

Functions using heaps

Heaps can be used to extract the largest or smallest elements of an array without sorting the entire array first:

nlargest(3, [0,21,-12,68,-25,14]) # => [68,21,14]
nsmallest(3, [0,21,-12,68,-25,14]) # => [-25,-12,0]

nlargest(n, a) is equivalent to sort(a, lt = >)[1:min(n, end)], and nsmallest(n, a) is equivalent to sort(a, lt = <)[1:min(n, end)].