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Permutations by swapping: Difference between revisions
→Recursive version
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=={{header|Clojure}}==
===Recursive version===
<lang clojure>
(defn
"List of swap indexes to generate all permutations of n elements"
[n]
(if (= n 2) `((0 1))
(let [old-swaps
swaps-> (partition 2 1 (range n))
swaps<- (reverse swaps->)]
(mapcat (fn [old-swap side]
(case side
:first swaps<-
:right (conj swaps<- old-swap)
:left (conj swaps-> (map inc old-swap))))
(conj old-swaps nil)
(cons :first (cycle '(:left :right)))))))
(defn swap [v [i j]]
(-> v
(assoc i (nth v j))
(assoc j (nth v i))))
(let [permutations (reduce
(fn [all-perms new-swap]
(conj all-perms (swap (last all-perms)
new-swap)))
(vector (vec (range n)))
(permutation-swaps n))
output (map vector
permutations
(cycle '(1 -1)))]
output))
(doseq [n [2 3 4]]
(dorun (map println (permutations n))))
</lang>
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<pre>
[[0 1] 1]
▲user=> (permutations [1 2 3])
[[1 0] -1]
[[0 1 2] 1]
[[0 2 1] -1]
[[2 0 1] 1]
[[2 1 0] -1]
[[1 2 0] 1]
[[1 0 2] -1]
[[0 1 2 3] 1]
[[0 1 3 2] -1]
[[0 3 1 2] 1]
[[3 0 1 2] -1]
[[3 0 2 1] 1]
[[0 3 2 1] -1]
[[0 2 3 1] 1]
[[0 2 1 3] -1]
[[2 0 1 3] 1]
[[2 0 3 1] -1]
[[2 3 0 1] 1]
[[3 2 0 1] -1]
[[3 2 1 0] 1]
[[2 3 1 0] -1]
[[2 1 3 0] 1]
[[2 1 0 3] -1]
[[1 2 0 3] 1]
[[1 2 3 0] -1]
[[1 3 2 0] 1]
[[3 1 2 0] -1]
[[3 1 0 2] 1]
[[1 3 0 2] -1]
[[1 0 3 2] 1]
[[1 0 2 3] -1]
</pre>
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