IJAM: Volume 37, No. 4 (2024)

DOI: 10.12732/ijam.v37i4.7

AN ALGORITHM FOR LISTING ALL

PERMUTATIONS OF N ELEMENTS

USING MODULO ARITHMETIC

Dubravko Sabolic

University of Zagreb, FER

Unska 3

10000 Zagreb, CROATIA

Abstract. This article presents a novel algorithm that can list all of the N-element permutations in a straightforward and easily automated manner. If N is fed as input, the algorithm will find all the permutations of N elements using modulo arithmetic, which makes it different from earlier algorithms. We do not present rigorous mathematical proofs for the algorithm or its time comple-xity. Instead, relying on the elementary rules of modulo arithmetic, we provide intuitive justification of the rather obvious algorithm and numerical examples to show that it has the time complexity of the order O(N! x N!) or simply O(N!), as expected based on the elementary analysis of the computational procedure.

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How to cite this paper?
DOI: 10.12732/ijam.v37i4.7
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 4

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