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Last active November 18, 2020 03:08
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Implementing Tarjan in Clojure, step by step
;; Relaize that only the stack size matters, env now maps nodes to "low" or nil.
(defn tarjan
"Returns the strongly connected components of a graph specified by its nodes
and a successor function succs from node to nodes.
The used algorithm is Tarjan's one."
[nodes succs]
(letfn [(sc [env node]
; env is a map from nodes to stack length or nil, nil means the node is known to belong to another SCC
; there are two special keys: ::stack for the current stack and ::sccs for the current set of SCCs
#_{:post [(contains? % node)]}
(if (contains? env node)
(let [stack (::stack env)
n (count stack)
env (assoc env node n ::stack (conj stack node))
env (reduce (fn [env succ]
(let [env (sc env succ)]
(assoc env node (min (or (env succ) n) (env node)))))
env (succs node))]
(if (= n (env node)) ; no link below us in the stack, call it a SCC
(loop [scc #{} nodes (::stack env) env env]
(let [curr (peek nodes)
scc (conj scc curr)
env (assoc env curr nil)] ; clear all stack lengths for this SCC's nodes since this SCC is done
(if (= curr node)
(assoc env ::stack stack ::sccs (conj (::sccs env) scc))
(recur scc (pop nodes) env))))
(::sccs (reduce sc {::stack () ::sccs #{}} nodes))))
=> (def g {:c #{:d} :a #{:b :c} :b #{:a :c}})
=> (tarjan (keys g) g)
#{#{:c} #{:d} #{:a :b}}
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xsc commented Nov 4, 2016

@cgrand Thank you for this! Would you consider adding a license (maybe MIT?) to this gist?
I'd like to use your implementation in a library but without a license that's not possible.

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