Module binaryheap
Binary heap implementation
A binary heap (or binary tree) is a sorting algorithm.
The 'plain binary heap' is managed by positions. Which are hard to get once
an element is inserted. It can be anywhere in the list because it is resorted
upon insertion/deletion of items. The array with values is stored in field
values
:
peek = heap.values[1]
A 'unique binary heap' is where the payload is unique and the payload itself also stored (as key) in the heap with the position as value, as in;
heap.reverse[payload] = [pos]
Due to this setup the reverse search, based on payload, is now a much faster operation because instead of traversing the list/heap, you can do;
pos = heap.reverse[payload]
This means that deleting elements from a 'unique binary heap' is faster than from a plain heap.
All management functions in the 'unique binary heap' take payload
instead of pos
as argument.
Note that the value of the payload must be unique!
Fields of heap object:
 values  array of values
 payloads  array of payloads (unique binary heap only)
 reverse  map from payloads to indices (unique binary heap only)
Basic heap
binaryHeap (swap, erase, lt)  Creates a new binary heap. 
Plain heap
heap:insert (value)  Inserts an element in the heap. 
heap:peek ()  Returns the element at the top of the heap, without removing it. 
heap:pop ()  Removes the top of the heap and returns it. 
heap:remove (pos)  Removes an element from the heap. 
heap:size ()  Returns the number of elements in the heap. 
heap:update (pos, newValue)  Updates the value of an element in the heap. 
maxHeap (gt)  Creates a new maxheap, where the largest value is at the top. 
minHeap (lt)  Creates a new minheap, where the smallest value is at the top. 
Unique heap
heap:size ()  Returns the number of elements in the heap. 
maxUnique (gt)  Creates a new maxheap with unique payloads. 
minUnique (lt)  Creates a new minheap with unique payloads. 
unique:insert (value, payload)  Inserts an element in the heap. 
unique:peek ()  Returns the element at the top of the heap, without removing it. 
unique:peekValue ()  Returns the element at the top of the heap, without removing it. 
unique:pop ()  Removes the top of the heap and returns it. 
unique:remove (payload)  Removes an element from the heap. 
unique:update (payload, newValue)  Updates the value of an element in the heap. 
unique:valueByPayload (payload)  Returns the value associated with the payload 
Basic heap
 binaryHeap (swap, erase, lt)

Creates a new binary heap.
This is the core of all heaps, the others
are built upon these sorting functions.
Parameters:
 swap
(function)
swap(heap, idx1, idx2)
swaps values atidx1
andidx2
in the heapsheap.values
andheap.payloads
lists (see return value below).  erase
(function)
swap(heap, position)
raw removal  lt
(function) in
lt(a, b)
returnstrue
whena < b
(for a minheap)
Returns:

table with two methods;
heap:bubbleUp(pos)
andheap:sinkDown(pos)
that implement the sorting algorithm and two fields;heap.values
andheap.payloads
being lists, holding the values and payloads respectively.  swap
(function)
Plain heap
nil
), as long as the comparison function used to create
the heap can handle it.
 heap:insert (value)

Inserts an element in the heap.
Parameters:
 value the value used for sorting this element
Returns:

nothing, or throws an error on bad input
 heap:peek ()

Returns the element at the top of the heap, without removing it.
Returns:

value at the top, or
nil
if there is none  heap:pop ()

Removes the top of the heap and returns it.
Returns:

value at the top, or
nil
if there is none  heap:remove (pos)

Removes an element from the heap.
Parameters:
 pos the position to remove
Returns:

value, or nil if a bad
pos
value was provided  heap:size ()

Returns the number of elements in the heap.
Returns:

number of elements
 heap:update (pos, newValue)

Updates the value of an element in the heap.
Parameters:
 pos the position which value to update
 newValue the new value to use for this payload
 maxHeap (gt)

Creates a new maxheap, where the largest value is at the top.
Parameters:
 gt (optional) comparison function (greaterthan), see binaryHeap.
Returns:

the new heap
 minHeap (lt)

Creates a new minheap, where the smallest value is at the top.
Parameters:
 lt (optional) comparison function (lessthan), see binaryHeap.
Returns:

the new heap
Unique heap
 The
value
, this is used for ordering the heap. It can be any type (exceptnil
), as long as the comparison function used to create the heap can handle it.  The
payload
, this can be any type (exceptnil
), but it MUST be unique.
With the 'unique heap' it is easier to remove elements from the heap.
 heap:size ()

Returns the number of elements in the heap.
Returns:

number of elements
 maxUnique (gt)

Creates a new maxheap with unique payloads.
A maxheap is where the largest value is at the top.
NOTE: All management functions in the 'unique binary heap' take
payload
instead ofpos
as argument.Parameters:
 gt (optional) comparison function (greaterthan), see binaryHeap.
Returns:

the new heap
 minUnique (lt)

Creates a new minheap with unique payloads.
A minheap is where the smallest value is at the top.
NOTE: All management functions in the 'unique binary heap' take
payload
instead ofpos
as argument.Parameters:
 lt (optional) comparison function (lessthan), see binaryHeap.
Returns:

the new heap
 unique:insert (value, payload)

Inserts an element in the heap.
Parameters:
 value the value used for sorting this element
 payload the payload attached to this element
Returns:

nothing, or throws an error on bad input
 unique:peek ()

Returns the element at the top of the heap, without removing it.
Returns:

payload, value, or
nil
if there is none  unique:peekValue ()

Returns the element at the top of the heap, without removing it.
Returns:

value at the top, or
nil
if there is noneUsage:
 simple timer based heap example while true do sleep(heap:peekValue()  gettime())  assume LuaSocket gettime function coroutine.resume((heap:pop()))  assumes payload to be a coroutine,  double parens to drop extra return value end
 unique:pop ()

Removes the top of the heap and returns it.
When used with timers, pop will return the payload that is due.
Note: this function returns
payload
as the first result to prevent extra locals when retrieving thepayload
.Returns:

payload, value, or
nil
if there is none  unique:remove (payload)

Removes an element from the heap.
Parameters:
 payload the payload to remove
Returns:

value, payload or nil if not found
 unique:update (payload, newValue)

Updates the value of an element in the heap.
Parameters:
 payload the payoad whose value to update
 newValue the new value to use for this payload
Returns:

nothing, or throws an error on bad input
 unique:valueByPayload (payload)

Returns the value associated with the payload
Parameters:
 payload the payload to lookup
Returns:

value or nil if no such payload exists