Partition (number theory)

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.

For example, 4 can be partitioned in five distinct ways:

4

3 + 1

2 + 2

2 + 1 + 1

1 + 1 + 1 + 1

import org.paukov.combinatorics.Factory;
import org.paukov.combinatorics.Generator;
import org.paukov.combinatorics.ICombinatoricsVector;

public class PartitionEx {

    public static void main(String args[]) {
        // Create an instance of the partition generator to generate all
        // possible partitions of 4
        Generator<Integer> gen = Factory.createPartitionGenerator(4);

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

Output

[1, 1, 1, 1]
[2, 1, 1]
[2, 2]
[3, 1]
[4]

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