nextOrderedPartition -- iterates over ordered partitions of a number

Synopsis

Usage:

P = nextOrderedPartition(n,Lists)

P' = nextOrderedPartition(P,n,Lists)
Inputs:
- n, an integer,
- Lists, a list,
- P, a list, an initial partition (optional)
Outputs:
- P', a list, the next ordered partition, if any

Description

Given an integer $n$ and lists $L_1,\ldots,L_k$ of distinct nonnegative integers, this method iterates over all tuples $(l_1,\ldots,l_k)$ such that $\sum_i l_i = n$ and $l_i\in L_i$. The tuples are produced one at a time.

Returns "null" if none.

i1 : L = {{0,1},{0,1,2},{2,3}};

i2 : P = nextOrderedPartition (5,L)

o2 = {0, 2, 3}

o2 : List

i3 : P = nextOrderedPartition (P,5,L)

o3 = {1, 1, 3}

o3 : List

i4 : P = nextOrderedPartition (P,5,L)

o4 = {1, 2, 2}

o4 : List

i5 : assert(nextOrderedPartition (P,5,L) === null)

Ways to use nextOrderedPartition :

nextOrderedPartition(List,ZZ,List)
nextOrderedPartition(ZZ,List)

For the programmer

The object nextOrderedPartition is a method function.