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flat assembler > Examples and Tutorials > Calculation of all N! permutations

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SergeASM



Joined: 13 Nov 2015
Posts: 21
Calculation of all N! permutations
I just port to FASM my function to calculate a "next" permutation. The algorithm is called a "ladder". I saw it in the book

Martin Gardner
Time Travel and Other Mathematical Bewilderments
W.H. Freeman and Company New York 1988

Let we have all permutations of 1 element (number 0):

0

To get all permutations of N+1 elements we repeat N+1 times each permutation of N elements:

0
0

Now we use the algorithm "ladder" and insert an element number N+1:

Code:

0 1
1 0




and get all permutations of N+1 elements.

Another example:

Code:

0 1
0 1
0 1
1 0
1 0
1 0





Code:

   0   1 2
   0 2 1
2  0   1
2  1   0
   1 2 0
   1   0 2




Now we get all the permutations of 4 elements:


Code:

   0   1   2 3
   0   1 3 2
   0 3 1   2
3  0   1   2
3  0   2   1
   0 3 2   1
   0   2 3 1
   0   2   1 3
   2   0   1 3
   2   0 3 1
   2 3 0   1
3  2   0   1
3  2   1   0
   2 3 1   0
   2   1 3 0
   2   1   0 3
   1   2   0 3
   1   2 3 0
   1 3 2   0
3  1   2   0
3  1   0   2
   1 3 0   2
   1   0 3 2
   1   0   2 3




But this algorithm is recursive, it's not good. I wrote a function Next_permutation that takes any permutation and calculates the next permutation by this algorithm!

This list of N! permutations has two great features:

1. All permutations can be arranged on a circle and each one differs from two neighbor by 1 transposition neighboring elements.
2. Calculation of first N!/2 permutations is enough, because list of the next N!/2 permutations is mirror-symmetric to the list of first N!/2 permutations! We simply reverse each of first N!/2 permutations to get other N!/2!

I've attached simple console test app. While the function is not optimized and not combed. I hope it can be used in combinatorial mathematic.

Sorry for my English

Serge


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Post 20 Nov 2015, 09:46
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