Lexicographic Permutations Tree

Author: Giannis Loizou
Description: Generates all permutations of the set {1, 2, ..., n} using a tree-based approach.

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Overview

This project implements an original approach to generating permutations in lexicographic order using a linked tree structure.

• Each node represents an element of the set.
• Children represent subsequent elements in the permutation.
• The mixer function recursively swaps root elements to generate all permutations.

This implementation demonstrates:

• Custom tree data structures
• Breadth-first traversal
• Lexicographic permutation generation without using Python's built-in itertools.permutations

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Features

• Construct a tree with all possible permutation paths
• Print each permutation in lexicographic order
• Interactive command-line program
• Modular, object-oriented design (abstract Tree class and concrete LinkedTree class)

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Usage

1. Clone the repository: git clone https://github.com/Hydrocast/Lexicographic-Permutations-Tree.git

2. cd LexicographicPermutationsTree

3. Run the program: python3 permutations_tree.py

4. Enter a positive integer n when prompted. The program will display all permutations of {1, 2, ..., n} in lexicographic order.

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Example:

Enter a positive integer n: 3

{ 1, 2, 3 }
{ 1, 3, 2 }
{ 2, 1, 3 }
{ 2, 3, 1 }
{ 3, 1, 2 }
{ 3, 2, 1 }