Just for the fun of writing it:
(defn topological-sort [x]
(mapcat
#(for [[k v] % :when (empty? v)] k)
(take-while seq
(iterate #(into {} (for [[k v] % :when (seq v)] [k (mapcat % v)])) x))))
user=> (topological-sort {1 [2 3] 2 [3] 3 []})
(3 2 1)
Note that it's not the same algorithm as Jon's and it doesn't detect cycles.
Christophe
On Thu, Nov 12, 2009 at 7:06 AM, John Harrop <[email protected]> wrote:
> On Wed, Nov 11, 2009 at 2:04 PM, Nick Day <[email protected]> wrote:
>>
>> Hi,
>>
>> I've been trying to implement a topological sort and have been
>> struggling a bit. I have a map of symbol vs collection of symbols
>> like:
>>
>> {a [b c], b [c], c [nil]}
>>
>> which can be read as 'a' depends on 'b' and 'c', 'b' depends on 'c'
>> and 'c' doesn't depend on anything. I've been trying to write
>> something that returns a collection of the dependencies in order (c,
>> b, a) but so far I've only been able to do it using a ref to store
>> intermediate output of the sorting. I was wondering if anyone has
>> already done something similar?
>
> You mean pure functionally?
> First, I'd represent no dependencies as an empty vector rather than a vector
> with a single nil in it.
> Then, consider how you get the first few entries: you find all the nodes
> with no dependencies.
> How do you get the next few? The nodes whose only dependencies are nodes you
> already have.
> This suggests the algorithm:
> (defn find-a-node [deps already-have-nodes]
> (some (fn [[k v]] (if (empty? (remove already-have-nodes v)) k)) deps))
> This will return a key from deps whose corresponding value contains no
> objects not in the set already-have-nodes.
> Next, we just need to apply it repeatedly until it comes up empty:
> (defn order-nodes [deps]
> (loop [deps deps already-have-nodes #{} output []]
> (if (empty? deps)
> output
> (if-let [item (find-a-node deps already-have-nodes)]
> (recur
> (dissoc deps item)
> (conj already-have-nodes item)
> (conj output item))
> (throw (Exception. "Circular dependency."))))))
> This seems to work:
> user=> (order-nodes {1 [2 3] 2 [3] 3 []})
> [3 2 1]
> user=> (order-nodes {1 [2 3] 2 [3] 3 [2]})
> #<CompilerException java.lang.Exception: Circular dependency.
> (NO_SOURCE_FILE:0)>
> No refs, atoms, or other mutable state, or cheating using Java mutable
> objects or set-var-root!, etc.; rewriting the above with iterate, reduce, or
> similar instead of loop/recur is left as an exercise for the reader. :)
>
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