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;; Copyright (c) Jeffrey Straszheim. All rights reserved. The use and
;; distribution terms for this software are covered by the Eclipse Public
;; License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) which can
;; be found in the file epl-v10.html at the root of this distribution. 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.
;;
;; graph
;;
;; Basic Graph Theory Algorithms
;;
;; straszheimjeffrey (gmail)
;; Created 23 June 2009
(ns clojure.contrib.graph
(use [clojure.contrib.macros :only (letfn)])
(use [clojure.contrib.seq-utils :only (flatten indexed)]))
(defstruct directed-graph
:count ; The count of nodes in the graph
:neighbors) ; A function that, given a node (0 .. count-1) returns
; a collection neighbor nodes.
(defn get-neighbors
"Get the neighbors of a node."
[g n]
((:neighbors g) n))
(defn reverse-graph
"Given a directed graph, return another directed graph with the
order of the edges reversed."
[g]
(let [op (fn [rna idx]
(let [ns (get-neighbors g idx)
am (fn [m val]
(assoc m val (conj (get m val []) idx)))]
(reduce am rna ns)))
rn (reduce op {} (range (:count g)))]
(struct directed-graph (:count g) rn)))
(comment
(def test-graph-1
(struct directed-graph 5
{0 [1 2]
1 [0 2]
2 [3 4]
3 [0 1]
4 [3]}))
test-graph-1
(reverse-graph test-graph-1)
(reverse-graph (reverse-graph test-graph-1))
(= test-graph-1 (reverse-graph (reverse-graph test-graph-1)))
)
(defn- post-ordered-visit
"Starting at node n, perform a post-ordered walk."
[g n [visited acc :as state]]
(if (visited n)
state
(let [[v2 acc2] (reduce (fn [st nd] (post-ordered-visit g nd st))
[(conj visited n) acc]
(get-neighbors g n))]
[v2 (conj acc2 n)])))
(defn post-ordered-nodes
"Return a sequence of indexes of a post-ordered walk of the graph."
[g]
(fnext (reduce #(post-ordered-visit g %2 %1)
[#{} []]
(range (:count g)))))
(defn scc
"Returns, as a sequence of sets, the strongly connected components
of g."
[g]
(let [po (reverse (post-ordered-nodes g))
rev (reverse-graph g)
step (fn [stack visited acc]
(if (empty? stack)
acc
(let [[nv comp] (post-ordered-visit rev
(first stack)
[visited #{}])
ns (remove nv stack)]
(recur ns nv (conj acc comp)))))]
(step po #{} [])))
(defn self-recursive-sets
"Returns, as a sequence of sets, the components of a graph that are
self-recursive."
[g]
(letfn [recursive? [n]
(or (> (count n) 1)
(some n (get-neighbors g (first n))))]
(filter recursive? (scc g))))
(comment
(def test-graph-2
(struct directed-graph 10
{0 [1 2]
1 [0 2]
2 [3 4]
3 [0 1]
4 [3]
5 [5]
6 [0 5]
7 []
8 [9]
9 [8]}))
(post-ordered-visit test-graph-2 0 [#{} []])
(post-ordered-nodes test-graph-2)
(scc test-graph-2)
(self-recursive-sets test-graph-2)
)
(defn fixed-point
"Repeatedly apply fun to data until (equal old-data new-data)
returns true. If max iterations occur, it will throw an
exception. Set max to nil for unlimited iterations."
[data fun max equal]
(let [step (fn step [data idx]
(when (and idx (= 0 idx))
(throw (Exception. "Fixed point overflow")))
(let [new-data (fun data)]
(if (equal data new-data)
new-data
(recur new-data (and idx (dec idx))))))]
(step data max)))
(defn- fold-into-sets
[priorities]
(let [step (fn [acc [idx dep]]
(assoc acc dep (conj (acc dep) idx)))]
(reduce step
(vec (replicate (inc (apply max 0 priorities)) #{}))
(indexed priorities))))
(defn dependency-list
"Similar to a topological sort, this returns a vector of sets, each
a set of nodes that depend on the earlier nodes in the vector.
Assume the input graph (which much be acyclic) has an edge a->b
when a depend on b."
[g]
(let [step (fn [d]
(let [update (fn [n]
(inc (apply max -1 (map d (get-neighbors g n)))))]
(vec (map update (range (:count g))))))
counts (fixed-point (vec (replicate (:count g) 0))
step
(inc (:count g))
=)]
(fold-into-sets counts)))
(defn stratification-list
"Similar to dependency-list (see doc), except two graphs are
provided. The first is as dependency-list. The second (which may
have cycles) provides a partial-dependency relation. If node a
depends on node b (meaning an edge a->b exists) in the second
graph, node a must be equal or later in the sequence."
[g1 g2]
(assert (= (:count g1) (:count g2)))
(let [step (fn [d]
(letfn [update [n]
(max (inc (apply max -1
(map d (get-neighbors g1 n))))
(apply max -1 (map d (get-neighbors g2 n))))]
(vec (map update (range (:count g1))))))
counts (fixed-point (vec (replicate (:count g1) 0))
step
(inc (:count g1))
=)]
(fold-into-sets counts)))
(comment
(dependency-list test-graph-2)
(def test-graph-3
(struct directed-graph 6
{0 [1]
1 [2]
2 [3]
3 [4]
4 [5]
5 []}))
(dependency-list test-graph-3)
(def test-graph-4
(struct directed-graph 8
{0 []
1 [0]
2 [0]
3 [0 1]
4 [3 2]
5 [4]
6 [3]
7 [5]}))
(dependency-list test-graph-4)
(def test-graph-5
(struct directed-graph 8
{0 []
1 []
2 [1]
3 []
4 []
5 []
6 [5]
7 []}))
(dependency-list test-graph-5)
(stratification-list test-graph-4 test-graph-5)
)
;; End of file
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