Generate Exhaustive Permutations

Illustrates generation of exhaustive permutation of symbols given the symbolic bases.

Generate Exhaustive Permutations

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[1] main executing reference usage: usage_generateExhaustivePermutation

The objective is to illustrate generation of exhaustive permutation of symbols given the symbolic bases.

The method of generation is a kronecker-akin approach. The indexRepresentedPermutations may be mapped to any symbols provided.

Sample output:

ssssGiven bases = 'AB';

lengthOf1PatternSeq = 3;

< symbols >

AAA

AAB

ABA

ABB

BAA

BAB

BBA

BBB

< indexRepresentedPermutations >

1 1 1

1 1 2

1 2 1

1 2 2

2 1 1

2 1 2

2 2 1

2 2 2

ssssGiven bases = '01';

lengthOf1PatternSeq = 4;

< symbols >

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

1110

1111

< indexRepresentedPermutations >

1 1 1 1

1 1 1 2

1 1 2 1

1 1 2 2

1 2 1 1

1 2 1 2

1 2 2 1

1 2 2 2

2 1 1 1

2 1 1 2

2 1 2 1

2 1 2 2

2 2 1 1

2 2 1 2

2 2 2 1

2 2 2 2

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[2] main executing reference usage: usage_computePermutationSeqForSpecificIndex

Obtain a sequence of permutation by direct computation, instead of extracting from a pre-generated exhaustive sequence of prescribed order.

This accelerate the process and saves memory space.

Sample output:

The sequence is CGGGCAG.

The sequence indexed extracted from exhaustive list is CGGGCAG from index: 4044.

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The sequence is CCCTATC.

The sequence indexed extracted from exhaustive list is CCCTATC from index: 101.

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The sequence is CCTGGAC.

The sequence indexed extracted from exhaustive list is CCTGGAC from index: 505.

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The sequence is CCGGATA.

The sequence indexed extracted from exhaustive list is CCGGATA from index: 999.

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* Caveat : Illustrative Purposes

- may run out of memory when lengthOf1PatternSeq >= 10;

- note as well that lengthOf1PatternSeq has to be >= length(bases)

- uncomment variables for display, eg. indexRepresentedPermutations

If the demo has more elegant presentation, please do not hesitate to suggest and send feedback to author.

Thank you.

Regards,

Michael Chan JT