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Medication contraindications

You probably know this, but here's some background so we're all on the same page. Some medicines shouldn't be taken in combination. When two medications shouldn't be taken together, it's called a contraindication.

(def patient-medications [{:name "Blythenal"
                           :rxNorm "blyth"}
                          {:name "Masbutol"
                           :rxNorm "masbut"}
                          {:name "Welbutril"
                           :rxNorm "welb"}])

(def contraindication-pairs [["nr913ng" "blyth"]
                             ["masbut"  "87f2h139049f"]
                             ["nr913ng" "j1j81f0"]
                             ["blyth" "welb"]
                             ["masbut"  "welb"]])

Your task is to take the list of medications a patient has and a list of contraindication pairs, and determine what pairs of medications (if any) they are prescribed that don't mix well.

;;  complete this function
(defn contraindications [meds pairs]

It should return nil if there are no contraindications and a collection of the contraindications (pairs) if there are any.

Bonus: Make it a linear algorithm (linear in the number of the patient medications and the number of the contraindication pairs).

Email submissions to eric@purelyfunctional.tv until June 8, 2020. You can discuss the submissions in the comments below.

(ns tst.demo.core
(:use tupelo.core tupelo.test)
(:require [schema.core :as s]
[clojure.set :as set]))
(def patient-medications [{:name "Blythenal"
:rxNorm "blyth"}
{:name "Masbutol"
:rxNorm "masbut"}
{:name "Welbutril"
:rxNorm "welb"}])
(def contraindication-pairs [["nr913ng" "blyth"]
["masbut" "87f2h139049f"]
["nr913ng" "j1j81f0"]
["blyth" "welb"]
["masbut" "welb"]])
(s/defn patient-meds-set :- #{s/Str}
[arg :- [{s/Keyword s/Str}]]
(set (mapv #(grab :rxNorm %) arg)))
(s/defn contra-pair-sets :- #{#{s/Str}}
[arg :- [[s/Str]]]
(set (mapv (fn [pair-vec]
(set pair-vec))
arg)))
(defn contraindications [meds-in pairs-in]
(let [patient-meds (patient-meds-set meds-in)
contra-pairs (contra-pair-sets pairs-in)
result (filterv #(= 2 (count %))
(forv [contra-pair contra-pairs]
(set/intersection patient-meds contra-pair)))]
result))
(dotest
(is= (contra-pair-sets contraindication-pairs)
#{#{"j1j81f0" "nr913ng"}
#{"masbut" "welb"}
#{"nr913ng" "blyth"}
#{"welb" "blyth"}
#{"masbut" "87f2h139049f"}})
(is= (patient-meds-set patient-medications) #{"masbut" "welb" "blyth"})
(is= (contraindications patient-medications contraindication-pairs)
[#{"masbut" "welb"} #{"welb" "blyth"}]))
(defn contraindications
[meds pairs]
;; one loop thru the list of meds to make an map to facilitate quick lookups
(let [medmap (into {} (map (fn [{:keys [name rxNorm]}] [rxNorm name]) meds))]
;; one loop thru the list of pairs. quickly check if each pair is
;; in list of meds
(loop [pair (first pairs) pairs (rest pairs) result #{}]
(if pair
(let [[p1 p2] pair]
(if (get medmap p1)
(if (get medmap p2)
(recur (first pairs) (rest pairs) (conj result pair))
(recur (first pairs) (rest pairs) result))
(recur (first pairs) (rest pairs) result)))
(if (empty? result) nil result)))))
(defn contraindications [meds pairs]
(let [rx (set (let [m (map :rxNorm meds)]
(for [x1 m x2 m :when (not= x1 x2)] [x1 x2])))
cp (set pairs)
contra (clojure.set/intersection cp rx)]
(if (= #{} contra)
nil
(vec contra))))
(defn contraindications [meds pairs]
(let [medset (set (map :rxNorm meds))]
(not-empty (filter #(and (contains? medset (first %))
(contains? medset (second %)))
pairs))))
(defn contraindications [meds pairs]
(let [contraindication-pairs (map (juxt first identity) pairs)
contraindication-map (into {} contraindication-pairs)
med-ids (map :rxNorm meds)]
(->> med-ids
(map contraindication-map)
(remove nil?)
seq)))
(ns functional-tv-puzzles.-2020.contraindications-380
"Solution which can use several strategies, mainly iterating either over
pairs of contra-indications in linear time, or over generated pairs
from a list of meds in quadratic time, when meds is much smaller than contras.
The decision is taken algorithmically, unless input parameters are overriden. "
(:require [clojure.set :as set])
(:require [clojure.core.reducers :as r]))
(defn dominated?
"Returns true if n is larger than m^2/2 by a given margin"
[m n margin]
(< (-> (* m m) (/ 2) (+ margin)) n))
(defn all-1x1 [xs]
(let [indexed (map-indexed #(vector (inc %) %2)
xs)]
(for [[xi x :as xix] indexed
[yi y :as yiy] indexed
:when (< xi yi)]
#{x y})))
(defn concurrent [pred xs]
(->> xs (r/fold
(r/monoid #(concat %1 %2) (fn [] nil))
(fn [acc pair]
(if (pred pair)
(conj acc (set pair))
acc)))))
(defn ->rx [meds]
(->> meds (map :rxNorm)))
(defn ->sets [pairs]
(->> pairs (map set) (into #{})))
(defn using-sets [meds pairs]
(let [ps (->sets pairs)]
(->> meds ->rx all-1x1 set (set/intersection ps))))
(defn over-meds [meds pairs]
(let [ps (->sets pairs)]
(->> (all-1x1 (->rx meds))
(concurrent (fn [p] (ps p))))))
(defn over-contras [meds pairs]
(let [ms (into #{} (->rx meds))]
(->> pairs
(concurrent (fn [[rx1 rx2]]
(and (ms rx1) (ms rx2)))))))
(defn contraindications
"Returns a coll of all duples of :rxNorm values in `meds`,
which are also found in `pairs`. Option
:override [:meds | :pairs | :sets]
imposes a single strategy of iterating over pairs (linear
performance), meds or sets - the later two involving
preprocessing with quadratic cost.
Otherwise the decision for iterating over meds vs pairs
can be influenced by options :factor and :margin
(defaults 2 and 0 resp.). Increasing these will increase
favoring iterating over pairs.
"
[meds pairs & {:keys [factor margin override]
:or {factor 2 margin 0}}]
(let [msiz (count meds)
psiz (count pairs)
f (or (get {:meds over-meds
:pairs over-contras
:sets using-sets} override)
(if (dominated? msiz psiz
(-> (* factor msiz) (+ margin)))
over-meds
over-contras))]
(f meds pairs)))
(defn contraindications [meds pairs]
(seq (filter #(not-any? nil? (map (set (map :rxNorm meds)) %)) pairs)))
(defn contraindications [meds pairs]
(let [meds-set (reduce #(conj %1 (:rxNorm %2)) #{} meds)]
(not-empty (->> pairs
(filter (fn [[first second]]
(and (contains? meds-set first)
(contains? meds-set second))))))))
(defn contraindications [meds pairs]
(let [meds-set (set (map :rxNorm meds))
contains-pair? (partial every? meds-set)]
(->> pairs (filter contains-pair?) not-empty)))
;;;
;;; Note that while the problem description asked only for handling
;;; "contra-indicated pairs" of medications, it is not meaningfully harder
;;; to handle N medications that shouldn't be taken together.
;;; This code does that, and has one test to demonstrate a "triplet".
;;
;; Examine a collection of medications prescribed to a given patient
;; and a collection of medication-tuples that are "conta-indicated", i.e.
;; that the given collection of medications should not be taken together.
;;
;; Examine the medications the patient is taking and report any combinations
;; that are contra-indicated.
;;
(defn contraindications [meds bad-combos]
(let [prescribed? (fn [med] (contains? (set (map :rxNorm meds)) med))
problem? (fn [bad-combo] (every? prescribed? bad-combo))]
(filter problem? bad-combos)))
(def meds1 [{:name "Blythenal"
:rxNorm "blyth"}
{:name "Masbutol"
:rxNorm "masbut"}
{:name "Welbutril"
:rxNorm "welb"}])
(def meds2 [{:rxNorm "foo"}
{:rxNorm "bar"}
{:rxNorm "baz"}])
(def contraindication-pairs [["nr913ng" "blyth"]
["masbut" "87f2h139049f"]
["nr913ng" "j1j81f0"]
["blyth" "welb"]
["masbut" "welb"]])
(def contraindication-tups [["masbut" "87f2h139049f"]
["nr913ng" "j1j81f0"]
["blyth" "welb" "foo"]
["blyth" "welb" "masbut"]])
(contraindications meds1 contraindication-pairs)
; ==> (["blyth" "welb"] ["masbut" "welb"])
(contraindications meds2 contraindication-pairs)
; ==> ()
(contraindications meds1 contraindication-tups)
; ==> (["blyth" "welb" "masbut"])
(defn contraindications [meds pairs]
(seq (filter #(every? (set (map :rxNorm meds)) %) pairs)))
@cloojure
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cloojure commented Jun 1, 2020

I assume you were going for something like the following, but since set/intersection also contains a loop internally you may really have to call it "quadratic-lite" or something:

(ns tst.demo.core
  (:use tupelo.core tupelo.test)
  (:require [schema.core :as s]
            [clojure.set :as set]))

(def patient-medications [{:name   "Blythenal"
                           :rxNorm "blyth"}
                          {:name   "Masbutol"
                           :rxNorm "masbut"}
                          {:name   "Welbutril"
                           :rxNorm "welb"}])

(def contraindication-pairs [["nr913ng" "blyth"]
                             ["masbut" "87f2h139049f"]
                             ["nr913ng" "j1j81f0"]
                             ["blyth" "welb"]
                             ["masbut" "welb"]])

(s/defn patient-meds-set :- #{s/Str}
  [arg :- [{s/Keyword s/Str}]]
  (set (mapv #(grab :rxNorm %) arg)))

(s/defn contra-pair-sets :- #{#{s/Str}}
  [arg :- [[s/Str]]]
  (set (mapv (fn [pair-vec]
               (set pair-vec))
         arg)))

(defn contraindications [meds-in pairs-in]
  (let [patient-meds (patient-meds-set meds-in)
        contra-pairs (contra-pair-sets pairs-in)
        result       (filterv #(= 2 (count %))
                       (forv [contra-pair contra-pairs]
                         (set/intersection patient-meds contra-pair)))]
    result))

(dotest
  (is= (contra-pair-sets contraindication-pairs)
    #{#{"j1j81f0" "nr913ng"}
      #{"masbut" "welb"}
      #{"nr913ng" "blyth"}
      #{"welb" "blyth"}
      #{"masbut" "87f2h139049f"}})

  (is= (patient-meds-set patient-medications) #{"masbut" "welb" "blyth"})

  (is= (contraindications patient-medications contraindication-pairs)
    [#{"masbut" "welb"} #{"welb" "blyth"}]))

@KingCode
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KingCode commented Jun 1, 2020

My first crack at it. Thus far I don't see a way to have linearity, i.e. without the inner loop traversing the meds - unless meds is always much smaller than the pairs, which would make it negligible...am I missing something?

(defn contraindications [meds pairs]
  (let [meds (->> meds
                  (map :rxNorm)
                  set)]
    (reduce (fn [acc pair]
              (if (every? meds pair)
                (conj acc pair)
                acc))
            nil
            pairs)))

@miner
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miner commented Jun 1, 2020

@KingCode I had the same thought as you. BTW, Eric wrote that the non-contra case should return nil.

(defn contraindications [meds pairs]
  (let [medset (into #{} (map :rxNorm) meds)]
    (into nil (filter #(every? medset %)) pairs)))

@orchid-mantis
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orchid-mantis commented Jun 1, 2020

Hello everyone,
what about this?

(defn contraindications [meds pairs]
  (let [meds-set (reduce #(conj %1 (:rxNorm %2)) #{} meds)]
    (not-empty (->> pairs
                    (filter (fn [[first second]]
                              (and (contains? meds-set first)
                                   (contains? meds-set second))))))))

https://clojuredocs.org/clojure.core/contains_q
'contains?' operates constant or logarithmic time

Is destructuring linear time operation?

@mchampine
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mchampine commented Jun 2, 2020

@miner, I submitted an almost identical solution, slightly shorter without the let, and using seq and set instead of intos. On the other hand I used "not-any? nil?" for the filter; your way is better. Combining best of both yields:

(defn contraindications [meds pairs]
  (seq (filter #(every? (set (map :rxNorm meds)) %) pairs)))

NB: I'd like to make a plea that we go back to waiting for Eric to publish submitted solutions, which is what he's asked for. IMO, solution synthesis and golf should wait until after we've seen the variety of approaches. (If I'm an outlier on this, I'll be quiet and accept the new norm..)

@miner
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miner commented Jun 2, 2020

@mchampine The let should make your solution a bit faster as it caches the set result rather than recalculating every time in the filter expression. From now on, I agree to hold my comments until Eric publishes the submitted solutions. Sorry for any spoilers.

@mchampine
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mchampine commented Jun 2, 2020

@miner No worries. True, the let produces faster code!

@KingCode
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KingCode commented Jun 3, 2020

@miner Thanks for your comment and correction! I have made the change in my previous solution.
I hope no one will mind me, but here is another possibility, assuming that meds is small, and that set operations on large lists are cheap:

(defn contraindications [meds pairs]
  (let [meds (map :rxNorm meds) 
        med-pairs (set (for [m1 meds
                             m2 meds
                               :when (not= m1 m2)]
                           [m1 m2]))]
    (into nil (clojure.set/intersection med-pairs (set pairs)))))

@ericnormand
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Author

ericnormand commented Jun 3, 2020

@KingCode

(set (for [m1 meds
           m2 meds
           :when (not= m1 m2)]
         [m1 m2]))

This is quadratic because it builds a set of m * m pairs.

@KingCode
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KingCode commented Jun 3, 2020

@ericnormand, Thanks for your comment! Indeed, I was assuming that meds being small that would be acceptable - but indeed, quadratic times makes for fast growth even on relatively small meds.

What do you think of the following? This won't exactly cut the linearity down, but could be a good speedup on large contraindications lists:

(defn step [rxs pair]
  (when (every? rxs pair) 
    pair))

(defn contraindications [meds pairs]
  (let [rxs (set (map :rxNorm meds))]
    (clojure.core.reducers/fold  
     (clojure.core.reducers/monoid #(concat %1 %2) (constantly nil)) 
     (fn [acc p] (if-let [contra? (step rxs p)]
                   (conj acc contra?)
                   acc))
     pairs)))

@KingCode
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KingCode commented Jun 3, 2020

In case it helps, here are some fixtures and tests for (most?) corner cases and additionally some using generated inputs - I am learning how to use test.check generators (please bear with my hacking). This is far away from properties based testing, but it can be used for benchmarking.

Below are tests using generated fixtures with up to a thousand meds, 10k contraindications and 500 conflicts, but you can create your own by changing the numbers.

Please let me know if I missed corner cases and I will add them...Thanks!

  (ns my-namespace-test 
   (:require [my-namespace :as sut]
            [clojure.spec.alpha :as s]
            [clojure.spec.gen.alpha :as gen]
            [clojure.test :refer [deftest testing is are]]))

(let [alias-str "sut"
      sym (symbol (str alias-str "/contraindications"))]
  (def ci (resolve sym)))

(def fixtures [[[{:name "Blythenal"   ;; input meds 
                   :rxNorm "blyth"}
                  {:name "Masbutol"
                   :rxNorm "masbut"}
                  {:name "Welbutril"
                   :rxNorm "welb"}],
)
                [["nr913ng" "blyth"]     ;; input contra-indications
                 ["masbut"  "87f2h139049f"]
                 ["nr913ng" "j1j81f0"]
                 ["blyth" "welb"]
                 ["masbut"  "welb"]],
                
                [["blyth", "welb"],   ;; expected output, can be any seqable (including sets in 
                 ["masbut" "welb"]]], ;; any order, and the same for inner pairs


              [[{:name "Maalox"
                 :rxNorm "yuck"}
                {:name "Cola"
                 :rxNorm "cola"}],
               [["drumpfspeak" "any"]
                ["clorox" "any"]]
               nil],

               [[{:name "Niceone"
                  :rxNorm "yum"}]
                []
                nil],

               [[]
               [["drumpfspeak" "any"]
                ["clorox" "any"]]
                nil]

               [[] [] nil]])

(s/def ::string+ (s/with-gen string? 
                   #(gen/such-that (complement empty?) 
                                  (gen/string-alphanumeric))))
(s/def ::name ::string+) 
(s/def ::rxNorm ::string+)
(s/def ::med (s/keys :req-un [::name ::rxNorm]))
(s/def ::contra (s/coll-of ::rxNorm :count 2 :distinct true))
;; (s/def ::contras (s/coll-of ::contra :into []))
(s/def ::meds (s/coll-of ::med))

(defn insert-med-pfx [med pfx]
  (update med :rxNorm #(str pfx %)))

(defn distinct-rand-int [n limit]
  (let [gen (fn [] (repeatedly n #(rand-int limit)))]
    (if (<= limit n)
      (range limit)
      (loop [acc (set (gen))] 
        (if (<= n (count acc))
          (take n acc)
          (recur (into acc (gen))))))))

(defn pairs+conflicts [pairs conflicts-siz pfx]
  (let [idxs (distinct-rand-int conflicts-siz (count pairs))] 
    (reduce (fn [[pairs conflicts] i]
              (let [p (mapv (partial str pfx) (pairs i))]
                [(assoc pairs i p),
                 (conj conflicts p)]))
            [(vec pairs) []]
            idxs)))

(defn make-large-fixture [meds-siz contras-siz conflicts-siz]
  (assert (and (<= conflicts-siz contras-siz)
               (<= (* 2 conflicts-siz) meds-siz)) 
          (str "violation of: 2 x conflicts-siz <= meds-siz "
               "AND conflicts-siz <= contras-siz"))
  (let [[pairs conflicts] (pairs+conflicts 
                           (gen/sample (s/gen ::contra) contras-siz)
                           conflicts-siz "conflict_")  
        ;; conflicts (repeatedly conflicts-siz #(rand-nth pairs))
        conflict-meds (mapcat (fn [pair] 
                                (->> pair
                                     (map (fn [rx]
                                            {:name (gen/generate (s/gen ::name))
                                             :rxNorm rx}))))
                              conflicts)
        meds (->> conflict-meds
                  (into (gen/sample 
                         (gen/fmap #(insert-med-pfx % "no-conflict_") 
                                   (s/gen ::med)) 
                         (- meds-siz (* 2 conflicts-siz))))
                  shuffle)]
    [meds, pairs, conflicts]))

#_(deftest make-large-fixture-test
  (are [m c x] (let [[meds contras xfl] (make-large-fixture m c x)
                     meds-rx (set (map :rxNorm meds))]
                 (and 
                  (= m (count meds))
                  (= c (count contras))
                  (= x (count xfl))
                  (every? meds-rx (set (flatten xfl)))
                  (every? (set contras) (set xfl))))
    10 10 2
    10 100 1
    10 10000 3
    100 10000 50
    1000 20000 450))

;; make-large-fixture debugging
#_(defn find-failed [gen-f]
  (->>
   (repeatedly #(let [[meds contras exp :as fixt] (gen-f)
                      out (apply ci (take 2 fixt))]
                  [out exp [meds contras]]))
   (drop-while (fn [[out exp _]]
                 (= (set exp) (set out))))
   first))

(defn passing? [[meds contras exp]]
  (is (= (set (map set exp)) (set (map set (ci meds contras))))))

(defn passing?-strict [[meds contras exp]]
  (is (let [out (ci meds contras)] 
        (and (= (set (map set exp)) (set (map set out)))
             (if (empty? out)
               (nil? out)
               true)))))

(deftest contraindications-test
  (testing "correctness and corner cases on small inputs"
    (doall (map passing?-strict fixtures)))
  (testing  ;; no corner cases
      "correctness and linear performance on large contraindications"
    (are [m c k] (passing? (make-large-fixture m c k))
      4 1 1
      4 10 1
      10 10000 2   ;; large contras
      10 10000 3
      100 10000 50 ;; + large conflicts
      1000 10000 500  ;; + large meds
      30 10000 8  ;; worth iterating over quadratically generated meds' pairs?
      30 10000 15 ;; same, maximum conflicts 
)))

@duzunov
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duzunov commented Jun 4, 2020

Looks like my solution is quadratic, any recommendations for something to read on time complexity?

@burnall
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burnall commented Jun 4, 2020

I noticed several similar solutions with every, I preferred to use the fact of pairs explicitly

(defn contraindications [meds pairs]
   (let [rx-norms (->> meds
                  (map :rxNorm)
                  (set))]
     (->> pairs
          (filter (fn [[a b]] (and (rx-norms a) (rx-norms b))))
          (seq))))

@ndonolli
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ndonolli commented Jun 4, 2020

@KingCode I think your first solution is linear in that it fulfills the bonus requirement :

linear in the number of the patient medications and the number of the contraindication pairs.

A set is a constant time lookup, you only traverse the pairs list once, and the pairs will always have a fixed length of two. There are probably ways to solve it in fewer operations, but given that both the meds and pairs are vectors I have a hard time imagining a solution where you don't have to traverse each at minimum once.

@KingCode
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KingCode commented Jun 5, 2020

@ndonolli, that's an interesting comment - traversing two structures is still linear time indeed. The use of quadratic times pair generation of meds' rxNorm values might also be worthwhile when the meds list is much shorter than the contra pairs, if the inner pairs were sets instead of vectors.

Suppose meds is a 10 rxNorm list, and pairs is 10,000 long. As you say, if set membership is a constant time lookup, then quadratic-time generation of 10x10 = 100 meds combo duples to be checked for membership in 10000 pairs set looks good. However, the 10,000 pairs needing to be converted to sets with something like (set (map set pairs)) prior, that is probably still slower than straight linear operation over the pairs.
EDIT. Actually, we wouldn't need to make every contra pair a set, just put the 10K pairs in a set: (set pairs) since the 100 med pairs have all orderings. I don't know how much does the conversion from vector to set cost, but it's at most linear then probably worth it:

(defn contraindications [meds pairs]  ;; size(meds) ^2 < size(pairs)
  (seq
   (let [meds (map :rxNorm meds)
         pairs (set pairs)]
     (for [rx1 meds
           rx2 meds
           :when (not= rx1 rx2)
           :when (pairs [rx1 rx2])]
        [rx1 rx2]))))

@ndonolli
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ndonolli commented Jun 5, 2020

@KingCode I see what you’re saying. When solving the problem I hadn’t considered the case of a much longer pairs list and the algorithmic tradeoffs to make. Interestingly this probably is a more real world case so production level code would have to take this requirement into account.

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