## Cheaplist in Clojure

Following is the implementation of the cheap list data structure from AI Game Programming Wisdom (Lighting-Fast A*), a cheap-list works just like a priority map takes a vector of key val (priority) pairs and produces a sequence with entries sorted by value (priority), the twist is that it will only keep first n entries sorted.

The idea behind the structure is that when implementing A-Star you either keep the open set in a sorted heap structure that gives you fast removal but slow insertion or in a unsorted list which gives you fast insertion but slow removal, in the case of A* you want to have both, fast insertion and fast removal, at every iteration you pop one node but there is potential to insert eight nodes, so you want pop the cheapest node without searching for it, you also want to insert into the list without worrying about the nodes position in the list.

A cheap-list achieves this by keeping 5 nodes that are cheapest (lowest priority) on the list sorted (book uses 15 but in my case 5 works best, any number higher/lower than 5 actually slows it down. YMMV), when we pop from the list all we do is remove the first item on the cheap list, if it is empty we refill it from the rest of the unsorted nodes using lazy quicksort at a cost of O(N + k log N). This way, we don't do any node searching until at least 5 revolutions later.

Whenever we add a node to the list, we first do a check to see if the node is cheap enough to be in the cheap list by checking the node on the end of the cheap list. If it costs more than the cheap list end node, the new node is added to the bulk map. Otherwise, we also do a sorted insert into the cheap list that is 5 nodes deep.

(def que-size 5)

(defn qsort-aux [[pivot & tail] pred]
(when pivot
(let [pred? (partial pred pivot)]
(lazy-cat (qsort-aux (filter pred? tail) pred)
[pivot]
(qsort-aux (remove pred? tail) pred)))))

(defn qsort [xs f] (qsort-aux (seq xs) f))

(deftype CheapList [pred cheap bulk]
Object
(toString [this] (str (seq this)))

clojure.lang.IPersistentVector
(cons [this curr]
(let [[item-curr pri-curr] curr
eol (last cheap)
[item-eol pri-eol] eol]

(cond
;;empty list
(nil? eol)
(CheapList. pred (conj cheap curr) (assoc bulk item-curr pri-curr))

;;list contains item
(bulk item-curr)
(.cons
(CheapList. pred
(filter (fn [[k]]
(not= k item-curr)) cheap)
(dissoc bulk item-curr))
curr)

;;cheaper then the curr most expensive
(pred eol curr)
(if (>= (count cheap) que-size)
(CheapList. pred
(qsort (conj (drop-last cheap) curr) pred)
(assoc bulk item-eol pri-eol))
(CheapList. pred
(qsort (conj cheap curr) pred)
(assoc bulk item-curr pri-curr)))

;;new item
:default (CheapList. pred cheap (assoc bulk item-curr pri-curr)))))

clojure.lang.ISeq
(first [this]
(first cheap))

(more [this]
(if (= (count cheap) 1)
(let [bulk (dissoc bulk (-> cheap first first))]
(CheapList. pred
(take que-size (qsort bulk pred))
bulk))
(CheapList. pred (rest cheap) (dissoc bulk (-> cheap first first)))))

(seq [this]
(when (not (empty? bulk))
(lazy-seq (cons (first this) (rest this)))))

(equiv [this o]
(and (= CheapList (type o))
(= (seq this) (seq o))))

(count [this]
(count bulk))

(empty [this]
(empty? bulk))

clojure.lang.ILookup
(valAt [this key]
(bulk key))

(valAt [this key not-found]
(or (.valAt this key) not-found))

clojure.lang.IFn
(invoke [this key]
(get this key))

(invoke [this key not-found]
(get this key not-found)))

(defn cheap-list
[pred & keyvals]
(reduce conj (CheapList. pred [] {}) keyvals))


Usage,

(def p (cheap-list (fn [[_ a] [_ b]]
(> a b))
[:a 2] [:b 1] [:c 3] [:d 5] [:e 4] [:f 3]))

core=> p
([:b 1] [:a 2] [:f 3] [:c 3] [:e 4] [:d 5])


We can use conj to assign a value (priority) to a new item,

(conj p [:e -5])

([:e -5] [:b 1] [:a 2] [:f 3] [:c 3] [:d 5])


or to assign a new value (priority) to an existing item,

(conj p [:c 4])

([:b 1] [:a 2] [:f 3] [:c 4] [:e 4] [:d 5])


To look up the value (priority) of a given item,

(p :c)
(get p :c)
(get p :not-an-item -6)


Cheap lists are countable,

(count p)


and can also be tested for emptiness,

(empty? p)