2021-02-05

create and analyse set selections: permutations, combinations and similar

part of sph-lib

(sph selection)

procedure: divisions count ->

integer -> ((integer ...) ...)

returns the compositions.

return all integer selections that sum to count.

distinctness is defined by length, order and value.

example for count 3: ((1 1 1) (1 2) (2 1) (3))

algorithm:

collect all possible values and associate a rest value that following values have to sum to.

for each of those associations, reduce the rest value and the list of possible values while producing possible tails.

the rest values are removed after all combinations have been found

return all integer selections that sum to count.

distinctness is defined by length, order and value.

example for count 3: ((1 1 1) (1 2) (2 1) (3))

algorithm:

collect all possible values and associate a rest value that following values have to sum to.

for each of those associations, reduce the rest value and the list of possible values while producing possible tails.

the rest values are removed after all combinations have been found

procedure: number-divisions b count ->

number integer -> ((number ...) ...)

return all selections of multiples of b divided by count that sum to b.

distinctness is defined by length, order and value.

example

b: 60, count: 3

result: ((20 20 20) (20 40) (40 20) (60))

distinctness is defined by length, order and value.

example

b: 60, count: 3

result: ((20 20 20) (20 40) (40 20) (60))

variable: sph-selection-description

procedure: vector-distinct-count a [min-width max-width] ->

vector integer integer -> integer

count all distinct sub-vectors in a vector with lengths from min-width to max-width.

distinctness is defined by length, order and value.

how sub-vectors are counted:

#([1 2 3] 4)

#(1 [2 3 4])

#([1 2] 3 4)

#(1 [2 3] 4)

#(1 2 [3 4])

distinctness is defined by length, order and value.

how sub-vectors are counted:

#([1 2 3] 4)

#(1 [2 3 4])

#([1 2] 3 4)

#(1 [2 3] 4)

#(1 2 [3 4])

procedure: vector-distinct-maximum width [min-width] ->

integer integer -> integer

calculate the maximum number of possible distinct tuples in a tuple up to width, optionally ignoring widths smaller than min-width

procedure: vector-distinct-stream a [min-width max-width] ->

procedure: vector-numeric-increment-be a base ->

vector integer -> vector

treat integers in a vector as digits of a number to \"base\" and increment it.

the least significant digit is the last element of the vector.

returns false if the maximum value has been reached

the least significant digit is the last element of the vector.

returns false if the maximum value has been reached

procedure: vector-numeric-increment-be! a base ->

vector integer -> true/false

like \"vector-numeric-increment-be\" but modifies the input vector

procedure: vector-numeric-increment-le a base ->

vector integer -> vector

treat integers in a vector as digits of a number to \"base\" and increment it.

the least significant digit is the first element of the vector.

return false if the maximum value has been reached

the least significant digit is the first element of the vector.

return false if the maximum value has been reached

procedure: vector-numeric-increment-le! a base ->

vector integer -> true/false

like \"vector-numeric-increment-le\" but modifies the input vector

procedure: vector-selection set-indices set ->

vector:#(integer ...) vector -> vector

return a new vector of values at indices in set

procedure: vector-selection-maximum set-length [selection-width] ->

integer integer -> integer

calculate the maximum number of possible distinct selections from a set with length \"set-length\" and

optional \"selection-width\" which defaults to \"set-length\"

optional \"selection-width\" which defaults to \"set-length\"

procedure: vector-selections set [width] ->

vector integer -> (vector ...)

return a list of all distinct selections of values from \"set\" with duplicate elements allowed. set can contain any datatype.

the optional parameter \"width\" specifies the length of selections.

for example, a width of two creates all possible two element selections of set.

the default for \"width\" is the length of the set

the optional parameter \"width\" specifies the length of selections.

for example, a width of two creates all possible two element selections of set.

the default for \"width\" is the length of the set

procedure: vector-selections-stream selection [width] ->

vector width -> stream

like vector-selections but returns an srfi-41-stream and calculates next results on demand