Iteratively Construct Trie from a Tree - clojure

Question

Introduction
The following function iteratively traverses a tree structure made of nested vectors. It tests each leaf against a predicate. The paths to all leaves which pass that truth-test are returned in a Trie structure. The later describes all found paths in a non-redundant way.
(defn get-trie-of-matches [is? tree]
(loop [[tree i path fk] [tree 0 [] nil]
accum {}]
(cond
(>= i (count tree)) ;; end of level / go up
(if (nil? fk) accum (recur fk accum))
(vector? (tree i)) ;; level down
(recur [(tree i) 0 (conj path i) [tree (inc i) path fk]] accum)
(is? (tree i)) ;; match
(let [new-accum (assoc-in accum (conj path i) {})]
(recur [tree (inc i) path fk] new-accum))
:else ;; next on same level
(recur [tree (inc i) path fk] accum))))
For further explanations see this post.
Example
Consider the following tree
(def tree [7 9 [7 5 3 [4 6 9] 9 3] 1 [2 7 9 9]])
Applied to the function, using even? as a predicate:
(get-trie-of-matches even? tree)
=> {2 {3 {0 {}, 1 {}}}, 4 {0 {}}}
The result describes the three paths to even numbers in tree. Namely 2-3-0, 2-3-1 and 4-0.
Problem
Even though the above function works, there might be better ways to construct the Trie while traversing the tree. At the moment a hash-map is flooded. On each match via assoc-in. The algorithm traverses the tree structure relatively from level to level but attaches each path in a global fashion to accum, which is not necessary. Also this method is only possible since a hashmap is used. It might anyways be better to use a sequential data-structure for the Trie in order to facilitate further iterations over it. This could not be adopted to the above method.
Question
How could a Trie be created from within the above function get-trie-of-matches without relying on hash-map specific 'global' 'write' functions?

Answer 1

I would propose to take a look at clojure's walk api.
It allows you to recursively apply some function to nested collections.
In this case you could use postwalk:
user> (require '[clojure.walk :as w])
user> (w/postwalk-demo [1 3 [4 [6] 7] [[8]]])
Walked: 1
Walked: 3
Walked: 4
Walked: 6
Walked: [6]
Walked: 7
Walked: [4 [6] 7]
Walked: 8
Walked: [8]
Walked: [[8]]
Walked: [1 3 [4 [6] 7] [[8]]]
[1 3 [4 [6] 7] [[8]]]
The key thing is you can replace any item at every step:
user> (w/postwalk #(if (coll? %) (reverse %) (inc %))
[1 3 [4 [6] 7] [[8]]])
(((9)) (8 (7) 5) 4 2)
Here we increment all the numbers, and reverse all the collections, keeping the nested structure.
Now applying to your task:
You could walk through your tree, keeping just even number's indices and not empty collections (e.g. collections containing even numbers, and not empty collections):
;; helper function
(defn empty-coll? [item]
(and (coll? item) (not (seq item))))
(defn make-trie [pred tree]
(w/postwalk
#(if (coll? %)
(keep-indexed (fn [idx item]
(cond (empty-coll? item) nil
(coll? item) (list idx item)
item idx
:else nil))
%)
(pred %))
tree))
in repl:
user> (def tree [7 9 [7 5 3 [4 6 9] 9 3] 1 [2 7 9 9]])
#'user/tree
user> (make-trie even? tree)
((2 ((3 (0 1)))) (4 (0)))
user> (make-trie #(> % 7) tree)
(1 (2 ((3 (2)) 4)) (4 (2 3)))
The structure is similar to your map. In fact you can produce any structure you want with minor changes to the function, for example your map structure:
(defn make-trie-map [pred tree]
(w/postwalk
#(if (coll? %)
(into {}
(keep-indexed (fn [idx item]
(cond (empty-coll? item) nil
(coll? item) {idx item}
item {idx {}}
:else nil))
%))
(pred %))
tree))
user> (make-trie-map even? tree)
{2 {3 {0 {}, 1 {}}}, 4 {0 {}}}