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Kahn's topological sort in Clojure
;; Copyright (c) Alan Dipert. All rights reserved.
;; The use and distribution terms for this software are covered by the
;; Eclipse Public License 1.0 (
;; By using this software in any fashion, you are agreeing to be bound by
;; the terms of this license.
;; You must not remove this notice, or any other, from this software.
(ns alandipert.kahn
(:require [clojure.set :refer [difference union intersection]]))
(defn without
"Returns set s with x removed."
[s x] (difference s #{x}))
(defn take-1
"Returns the pair [element, s'] where s' is set s with element removed."
[s] {:pre [(not (empty? s))]}
(let [item (first s)]
[item (without s item)]))
(defn no-incoming
"Returns the set of nodes in graph g for which there are no incoming
edges, where g is a map of nodes to sets of nodes."
(let [nodes (set (keys g))
have-incoming (apply union (vals g))]
(difference nodes have-incoming)))
(defn normalize
"Returns g with empty outgoing edges added for nodes with incoming
edges only. Example: {:a #{:b}} => {:a #{:b}, :b #{}}"
(let [have-incoming (apply union (vals g))]
(reduce #(if (get % %2) % (assoc % %2 #{})) g have-incoming)))
(defn kahn-sort
"Proposes a topological sort for directed graph g using Kahn's
algorithm, where g is a map of nodes to sets of nodes. If g is
cyclic, returns nil."
(kahn-sort (normalize g) [] (no-incoming g)))
([g l s]
(if (empty? s)
(when (every? empty? (vals g)) l)
(let [[n s'] (take-1 s)
m (g n)
g' (reduce #(update-in % [n] without %2) g m)]
(recur g' (conj l n) (union s' (intersection (no-incoming g') m)))))))
(def acyclic-g
{7 #{11 8}
5 #{11}
3 #{8 10}
11 #{2 9}
8 #{9}})
(def cyclic-g
{7 #{11 8}
5 #{11}
3 #{8 10}
11 #{2 9}
8 #{9}
2 #{11}}) ;oops, a cycle!
(kahn-sort acyclic-g) ;=> [3 5 7 8 10 11 2 9]
(kahn-sort cyclic-g) ;=> nil

narkisr commented Mar 30, 2013

Could you please add a license?


jjcomer commented May 10, 2013

+1 for a license.
Also you can remove items from a set without performing a difference:

(disj s x)

alandipert commented Aug 6, 2013

@narkisr @jjcomer updated w/ license. Stuck with difference so that it works on values that aren't sets.

Awesome, thanks. Needed this and I was able to use it without a single modification to my original code. Now, try that on Java!

spieden commented Jun 17, 2016

Also used to good effect! I'm not sure what you mean by working on non-set values by using difference, though, @alandipert, as "difference" only works on sets as much as "disj" does.

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