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A purely functional implementation of levenshtein distance in clojure
(ns levenshtein
^{:doc "A purely functional implementation of the levenshtien distance in clojure"})
(defn- compute-next-row
"computes the next row using the prev-row current-element and the other seq"
[prev-row current-element other-seq pred]
(reduce
(fn [row [diagonal above other-element]]
(let [update-val
(if (pred other-element current-element)
;; if the elements are deemed equivalent according to the predicate
;; pred, then no change has taken place to the string, so we are
;; going to set it the same value as diagonal (which is the previous edit-distance)
diagonal
;; in the case where the elements are not considered equivalent, then we are going
;; to figure out if its a substitution (then there is a change of 1 from the previous
;; edit distance) thus the value is diagonal + 1 or if its a deletion, then the value
;; is present in the columns, but not in the rows, the edit distance is the edit-distance
;; of last of row + 1 (since we will be using vectors, peek is more efficient)
;; or it could be a case of insertion, then the value is above+1, and we chose
;; the minimum of the three
(inc (min diagonal above (peek row)))
)]
(conj row update-val)))
;; we need to initialize the reduce function with the value of a row, since we are
;; constructing this row from the previous one, the row is a vector of 1 element which
;; consists of 1 + the first element in the previous row (edit distance between the prefix so far
;; and an empty string)
[(inc (first prev-row))]
;; for the reduction to go over, we need to provide it with three values, the diagonal
;; which is the same as prev-row because it starts from 0, the above, which is the next element
;; from the list and finally the element from the other sequence itself.
(map vector prev-row (next prev-row) other-seq)))
(defn levenshtein-distance
"Levenshtein Distance - http://en.wikipedia.org/wiki/Levenshtein_distance
In information theory and computer science, the Levenshtein distance is a metric for measuring the amount of difference between two sequences. This is a functional implementation of the levenshtein edit
distance with as little mutability as possible.
Still maintains the O(n*m) guarantee.
"
[a b & {p :predicate :or {p =}}]
(peek
(reduce
;; we use a simple reduction to convert the previous row into the next-row using the
;; compute-next-row which takes a current element, the previous-row computed so far
;; and the predicate to compare for equality.
(fn [prev-row current-element]
(compute-next-row prev-row current-element b p))
;; we need to initialize the prev-row with the edit distance between the various prefixes of
;; b and the empty string.
(map #(identity %2) (cons nil b) (range))
a)))
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