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A permutation P = P1P2P3…Pn of n distinct marks may be written as
where Pi = ρ(i). A permutation is called cyclic if it contains only one cycle, i. e. ρn(i) = i. In this paper, an efficient algorithm for generating all cyclic permutations of length n is derived, and its correctness is proven. Its average time complexity for generating a cyclic permutation is θ(3), while its space complexity is θ(n). Some interesting results are also provided.
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