# tigertv/superpermutation

Generator of superpermutations
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.
.gitignore
Makefile
egan.c
greg.js
original-5.txt
original-6-872.txt
original-6-873.txt
original-7-5908.txt
original-8-46205.txt
superp.cpp

# Superpermutation

In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring.

It has been shown that for 1 ≤ n ≤ 5, the smallest superpermutation on n symbols has length 1! + 2! + … + n! (sequence A180632 in the OEIS). The first five superpermutations have respective lengths 1, 3, 9, 33, and 153, forming the strings 1, 121, 123121321, 123412314231243121342132413214321, and the 8 strings for n=5.

The following program produces permutations and the string using greedy algorithm.

Example output for n=4:

Command line

./superp 4

Output:

1234
2341
3412
4123
===========
2314
3142
1423
4231
===========
3124
1243
2431
4312
===========
===========
2134
1342
3421
4213
===========
1324
3241
2413
4132
===========
3214
2143
1432
4321
==============================================
len=33

In superperm-4.txt the string

123412314231243121342132413214321

https://rosettacode.org/wiki/Superpermutation_minimisation

http://mathsci.wikia.com/wiki/The_Haruhi_Problem

http://www.njohnston.ca/publications/non-uniqueness-of-minimal-superpermutations/

http://www.gregegan.net/SCIENCE/Superpermutations/Superpermutations.html

https://bosker.wordpress.com/2014/08/22/tackling-the-minimal-superpermutation-problem/

https://bosker.wordpress.com/2018/10/20/superpermutations-lower-bound/

https://stackoverflow.com/questions/2253232/generate-sequence-with-all-permutations/2274978

https://math.stackexchange.com/questions/15510/what-is-the-shortest-string-that-contains-all-permutations-of-an-alphabet

http://oeis.org/A180632

Inspired by https://habr.com/post/431528/

You can’t perform that action at this time.