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Very simple java library to generate permutations, combinations and other combinatorial sequences.

There is a newer version: 2.3





This package contains the integer partitions generator.


  In number theory, a partition of a positive integer n is a way of writing n
  as a sum of positive integers. Two sums that differ only in the order of
  their summands are considered to be the same partition; if order matters then
  the sum becomes a composition. A summand in a partition is also called a
  part.

  WARNING! Be careful because number of all partitions can be very high even
  for not great given N.

  The partitions of 5 are listed below:

  1 + 1 + 1 + 1 + 1
  
2 + 1 + 1 + 1
  
2 + 2 + 1
  
3 + 1 + 1
  
3 + 2
  
4 + 1
  
5


  The number of partitions of n is given by the partition function p(n). In
  number theory, the partition function p(n) represents the number of possible
  partitions of a natural number n, which is to say the number of distinct (and
  order independent) ways of representing n as a sum of natural numbers.

  Let's generate all possible partitions of 5:



// Create an instance of the partition generator to generate all
// possible partitions of 5
Generator<Integer> gen = CombinatoricsFactory.createPartitionGenerator(5);

// Print the partitions
for (ICombinatoricsVector<Integer> p : gen) {
	System.out.println(p);
}




  And the result of all 7 integer possible partitions


  CombinatoricsVector=([1, 1, 1, 1, 1], size=5)
  CombinatoricsVector=([2, 1, 1, 1], size=4)
  CombinatoricsVector=([2, 2, 1], size=3)
  CombinatoricsVector=([3, 1, 1], size=3)
  CombinatoricsVector=([3, 2], size=2)
  CombinatoricsVector=([4, 1], size=2)
  CombinatoricsVector=([5], size=1)