Counting occurences

One asked me how to count occurrences of each value in a collection. I answered (reduce #(assoc %1 %2 (inc (%1 %2 0))) {} coll). Since it can take some time to get accustomed to the functional way of thought, here is how one can work such an expression out:

How to count all occurrences of 42?

(count (filter #{42} coll))

How to express count using reduce?

(defn my-count [coll] (reduce (fn [n _] (inc n)) 0 coll))

How to count all occurrences of 42 using reduce?

(reduce (fn [n _] (inc n)) 0 (filter #{42} coll))

Can you get rid of the filter?

(reduce (fn [n x] (if (= 42 x) (inc n) n)) 0 coll)

I'd like the result to be {42 occurences-count}.

(reduce (fn [m x] (if (= 42 x) (assoc m 42 (inc (m 42))) m)) {42 0} coll)

42 is hardcoded in four places, it's bad!

(reduce (fn [m x] (if (= 42 x) (assoc m x (inc (m x))) m)) {42 0} coll)

Can't you replace {42 0} with {}?

No (inc (m x)) would fail because (m x) would return nil.

How does one provide a default value when the key is not found ?

(a-map a-key default-value)

Can't you replace {42 0} with {}?

(reduce (fn [m x] (if (= 42 x) (assoc m x (inc (m x 0))) m)) {} coll)

I changed my mind I'd like you to count occurrences of each value.

Easy! (reduce (fn [m x] (assoc m x (inc (m x 0)))) {} coll) or, terser, (reduce #(assoc %1 %2 (inc (%1 %2 0))) {} coll)

Exercise:

What does (merge-with + {:a 12} {:b 4} {:a 3 :b 7}) return?

Can you count occurrences of each value in a collection using merge-with?