#103
Generating k-combinations
 

Difficulty:Medium
Topics:seqs combinatorics


Given a sequence S consisting of n elements generate all k-combinations of S, i. e. generate all possible sets consisting of k distinct elements taken from S. The number of k-combinations for a sequence is equal to the binomial coefficient.
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(= (__ 1 #{4 5 6}) #{#{4} #{5} #{6}})
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(= (__ 10 #{4 5 6}) #{})
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(= (__ 2 #{0 1 2}) #{#{0 1} #{0 2} #{1 2}})
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(= (__ 3 #{0 1 2 3 4}) #{#{0 1 2} #{0 1 3} #{0 1 4} #{0 2 3} #{0 2 4}
                         #{0 3 4} #{1 2 3} #{1 2 4} #{1 3 4} #{2 3 4}})
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(= (__ 4 #{[1 2 3] :a "abc" "efg"}) #{#{[1 2 3] :a "abc" "efg"}})
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(= (__ 2 #{[1 2 3] :a "abc" "efg"}) #{#{[1 2 3] :a} #{[1 2 3] "abc"} #{[1 2 3] "efg"}
                                    #{:a "abc"} #{:a "efg"} #{"abc" "efg"}})


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