Track-Best Library
Track-Best is a Common Lisp library used to track the N best of some series of items. One creates a tracker and then adds scored items to it. The tracker keeps the N best items and returns them at the end.
The main entry point is the function WITH-TRACK-BEST
macro.
(with-track-best (keyword-args)
...body...)
The body
can call (track item score &optional tracker)
as often as
desired. In the end, the with-track-best
will return two values:
the list of best items and the list of their scores.
The keyword-args
can be any of the following:
:NAME variable-name
--- A symbol used as the variable name for the tracker. This is only needed if you will explicitly refer to the tracker in thebody
statements.:KEEP number-to-keep
--- The number of items to track. This defaults to1
item.:KEEP-TIES whether-to-keep-ties
--- If true, then items with the same score will all be kept until there are KEEP items with better scores. This defaults to 'NIL'.:ORDER-BY-FN function-to-compare-scores
--- The function used to determine if one score is larger or smaller than another score. The default for this argument is#'>
:ALWAYS-RETURN-LIST t-or-nil
--- Ifalways-return-list
is true, thenWITH-TRACK-BEST
will return a list even whenKEEP
is1
. Ifalways-return-list
is not true, thenWITH-TRACK-BEST
will return the single item whenKEEP
is1
. The default for this argument isNIL
.:RETURN-BEST t-or-nil
--- ifreturn-best
isNIL
, then the form returns the value(s) from the last expression in thebody
rather than the best items. This argument defaults toT
. Note: This argument is evaluated at macroexpansion time, not at runtime.
The other useful entry point is the MAP-BEST
which takes a function
and an optional tracker. It calls the function for each item
currently in the best list of the tracker (from best to worst).
MAP-BEST
passes two parameters to the function: the item and its
score. The MAP-BEST
function returns a list of the results of those
function calls.
(with-track-best (:keep 3 :return-best nil)
(dolist (v '(-5 -3 -1 0 2 4))
(track v (abs v)))
(map-best #'(lambda (item score)
(* item score))))
=> '(-25 16 -9)
Example: Finding the longest matching substring in two strings
Given two strings S1
and S2
, find the longest substring they have
in common.
(let ((s1 "Keep playing cards on Friday. Get smart.")
(s2 "Thank G-d it's Friday!"))
(with-track-best ()
(dotimes (len (length s1))
(dotimes (offset (- (length s1) len -1))
(let ((needle (subseq s1 offset (+ offset len))))
(when (search needle s2 :test #'string=)
(track needle len)))))))
The outer DOTIMES
loop determines the length substring of S1
to
look for in S2
. The inner DOTIMES
loop picks the offset to start
the substring of S1
. Then, if the substring is found in S2
, it is
tracked with its score being its length.
Example: Finding the farthest vertex from a point
Given a list of vertexes VERTEX-LIST
, find the vertex farthest from
a TARGET
vertex based on a given DISTANCE
function.
(defun find-farthest (target vertex-list distance-fn)
(with-track-best ()
(dolist (v vertex-list)
(track v (funcall distance-fn v target))))))
Example: Finding the three closest vertexes to a point
Given a list of vertexes VERTEX-LIST
, find the three that are closest
to a TARGET
vertex based on a given DISTANCE
function.
(defun find-three-closest (target vertex-list distance-fn)
(with-track-best (:keep 3 :order-by-fn #'<)
(dolist (v vertex-list)
(track v (funcall distance-fn v target))))))
The :ORDER-BY-FN
function here specifies that the best vectors are
the ones with the smallest score. The scores used here are the
distance from the TARGET
as given by the DISTANCE-FN
.
Example: The lowest highest point
Suppose you had a list of various states. For each state you had a list of different cities and their altitude. Find the highest altitude in each state and find the state with the lowest high.
(let ((data '(("Alabama" ("Birmingham" 664)
("Mobile" 218)
("Montegomery" 221))
("Alaska" ("Anchorage" 144)
("Fairbanks" 531))
("Arizona" ("Grand Canyon" 6606)
("Phoenix" 1132)
("Tuscon" 2641)))))
(with-track-best (:order-by-fn #'<)
(dolist (state-info data)
(multiple-value-bind (city altitude)
(with-track-best ()
(dolist (city-info (rest state-info))
(track (first city-info) (second city-info))))
(track (list (first state-info) city) altitude)))))
=> (values '("Alaska" "Fairbanks") 531)
The inner WITH-TRACK-BEST
here tracks the highest city in a given
state. The outer WITH-TRACK-BEST
trackes the lowest of the highest
cities.
Example: Finding the lowest and highest numbers in a list
Given a list of numbers, return a list containing the lowest number and highest number from the list.
(with-track-best (:name lowest
:order-by-fn #'<
:return-best nil)
(with-track-best (:name highest
:return-best nil)
(dolist (v '(2 4 6 8 10 1 3 5 7 9))
(track v v lowest)
(track v v highest))
(list (caar (map-best #'cons lowest))
(caar (map-best #'cons highest)))))
In this example, we used the :NAME
to specify two different
trackers. In our loop, we tracked each value with both trackers. In
the end, we also used the :RETURN-RESULTS NIL
directive so that the
returned value would be our LIST
expression rather than the best
result from the LOWEST
tracker.
Example: Keeping ties
If the :KEEP-TIES
parameter is not NIL, then all items with the best
score will be returned. The order of these items is not guaranteed.
(with-track-best (:keep-ties t)
(dolist (c '((:FIVE 5) (:EIGHT 8)
(:CINQO 5) (:OCHO 8)
(:CINQ 5) (:HUIT 8)))
(track (first c) (second c))))
=> (values '(:EIGHT :HUIT :OCHO) '(8 8 8))
Warning about how ties are handled
If the :KEEP
parameter is 1
, the first item tracked with the best
score will be returned. If the :KEEP
parameter is greater than one,
there is no guarantee about which items are kept when multiple items
of the same score are found. For example, the following form will
definitely return (VALUES :EIGHT 8)
.
(with-track-best ()
(dolist (c '((:FIVE 5) (:EIGHT 8)
(:CINQO 5) (:OCHO 8)
(:CINQ 5) (:HUIT 8)))
(track (first c) (second c))))
=> (values :EIGHT 8)
On the other hand, this snippet will not guarantee the order in which
:EIGHT
, :OCHO
, and :HUIT
appear nor which of :FIVE
, :CINQO
,
or :CINQ
will be included.
(with-track-best (:keep 4)
(dolist (c '((:FIVE 5) (:EIGHT 8)
(:CINQO 5) (:OCHO 8)
(:CINQ 5) (:HUIT 8)))
(track (first c) (second c))))
=> (values ??? '(8 8 8 5))
To be sure, the answer is deterministic. Given the same inputs in the same order, the same output will be generated. There are two caveats to this:
- Where a tie gets inserted amongst its peers is highly sensitive to the number of items being kept and where its peers are in the list at the time of insertion.
- More importantly, I make no guarantee that this order will be
preserved across releases. You should not depend on particular
behavior when
:KEEP
is greater than one and ':KEEP-TIES' is NIL.