P332: Enumeration of all partitions of an integer $n$

P332: Enumeration of all partitions of an integer $n$

Input:

Two integers $n$ and $k$.

Output:

All partitions $D(n, k)$ of $n$ into distinct parts of size at most $k$.

Complexity:

$O(N)$ total time. E.g., $D(10, 5) = \{\{5, 4, 1\}, \{5, 3, 2\}, \{4, 3, 2, 1\}\}$ and $D(11, 4) = \emptyset$.

Comment:

$N$ is the number of partitions.

Reference:

[Rasmussen1995] (Bibtex)