An Efficient Algorithm for Permutation Iteration Using a Singly Linked List

TL;DR

This paper introduces an efficient permutation iteration algorithm using a singly linked list that minimizes memory allocation and maintains smooth transitions between permutations.

Contribution

It presents a novel permutation generation method leveraging elementary operations on recursive lists, with a proof of concept and a polynomial-time permutation index algorithm.

Findings

No new nodes allocated during permutation generation

Permutations generated in an unusual but smooth order

Polynomial-time algorithm for permutation indexing

Abstract

We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are rearranged within the original nodes of the singly linked list throughout the process. While permutations are generated in an unusual order, the transitions between consecutive permutations remain smooth. A proof of concept written in the Lisp programming language is referenced and discussed. We also present a polynomial-time algorithm for computing an arbitrary permutation given its index.