RcppAlgos (version 2.5.0)

partitionsIter: Partition Iterator

Description

• Returns an iterator for iterating over partitions of a numbers.

• Supports random access via the [[ method.

• GMP support allows for exploration of cases where the number of partitions is large.

• Use the next methods to obtain results in lexicographical order.

Usage

partitionsIter(v, m = NULL, repetition = FALSE,
               freqs = NULL, target = NULL, 
               nThreads = NULL, tolerance = NULL)

Arguments

v

Source vector. If v is a positive integer, it will be converted to the sequence 1:v. If v is a negative integer, it will be converted to the sequence v:-1. Only integer and numeric vectors are accepted.

m

Width of the partition. If m = NULL, the length will be determined by the partitioning case (e.g. When we are generating distinct partitions of \(n\), the width will be equal to the smallest \(m\) such that sum(1:m) >= n).

repetition

Logical value indicating whether partitions should be with or without repetition. The default is FALSE.

freqs

A vector of frequencies used for producing all partitions of a multiset of v. Each element of freqs represents how many times each element of the source vector, v, is repeated. It is analogous to the times argument in rep. The default value is NULL.

target

Number to be partitioned.

nThreads

Specific number of threads to be used. The default is NULL.

tolerance

A numeric value greater than or equal to zero. This parameter is utilized when a constraint is applied on a numeric vector. The default value is 0 when it can be determined that whole values are being utilized, otherwise it is sqrt(.Machine$double.eps) which is approximately \(1.5e-8\). N.B. If the input vector is of type integer, this parameter will be ignored and strict equality will be enforced.

Value

• If nextIter or prevIter is called, a vector is returned

• Otherwise, a matrix with \(m\) columns

Details

Once you initialize a new iterator, the following methods are available:

nextIter

Retrieve the next lexicographical result

nextNIter

Pass an integer n to retrieve the next n lexicographical results

nextRemaining

Retrieve all remaining lexicographical results

currIter

Returns the current iteration

startOver

Resets the iterator

sourceVector

View the source vector

summary

Returns a list of summary information about the iterator

front

Retrieve the first lexicographical result

back

Retrieve the last lexicographical result

[[

Random access method. Pass a single value or a vector of valid indices. If a single value is passed, the internal index of the iterator will be updated, however if a vector is passed the internal state will not change. GMP support allows for flexible indexing.

References

• Lexicographical Order

• Subset Sum Problem

• Partition (Number Theory)

See Also

partitionsGeneral

Examples

# NOT RUN {
a = partitionsIter(0:10, repetition = TRUE)
a@nextIter()
a@nextNIter(3)
a@front()
a@nextRemaining()
a@summary()
a@back()
a[[5]]
a@summary()
a[[c(1, 17, 3)]]
a@summary()

## Multisets... no random access
b = partitionsIter(40, 5, freqs = rep(1:4, 10), target = 80)
b@nextIter()
b@nextNIter(10)
b@summary()
b@nextIter()
b@currIter()
# }