Backtracking#
This library contains a generic tool for constructing large sets whose elements can be enumerated by exploring a search space with a (lazy) tree or graph structure.
GenericBacktracker
: Depth first search through a tree described by achildren
function, with branch pruning, etc.
This module has mostly been superseded by RecursivelyEnumeratedSet
.
- class sage.combinat.backtrack.GenericBacktracker(initial_data, initial_state)#
Bases:
object
A generic backtrack tool for exploring a search space organized as a tree, with branch pruning, etc.
See also
RecursivelyEnumeratedSet_forest
for handling simple special cases.
- class sage.combinat.backtrack.PositiveIntegerSemigroup#
Bases:
UniqueRepresentation
,RecursivelyEnumeratedSet_forest
The commutative additive semigroup of positive integers.
This class provides an example of algebraic structure which inherits from
RecursivelyEnumeratedSet_forest
. It builds the positive integers a la Peano, and endows it with its natural commutative additive semigroup structure.EXAMPLES:
sage: from sage.combinat.backtrack import PositiveIntegerSemigroup sage: PP = PositiveIntegerSemigroup() sage: PP.category() Join of Category of monoids and Category of commutative additive semigroups and Category of infinite enumerated sets and Category of facade sets sage: PP.cardinality() +Infinity sage: PP.one() 1 sage: PP.an_element() 1 sage: some_elements = list(PP.some_elements()); some_elements [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]
- children(x)#
Return the single child
x+1
of the integerx
EXAMPLES:
sage: from sage.combinat.backtrack import PositiveIntegerSemigroup sage: PP = PositiveIntegerSemigroup() sage: list(PP.children(1)) [2] sage: list(PP.children(42)) [43]
- one()#
Return the unit of
self
.EXAMPLES:
sage: from sage.combinat.backtrack import PositiveIntegerSemigroup sage: PP = PositiveIntegerSemigroup() sage: PP.one() 1
- roots()#
Return the single root of
self
.EXAMPLES:
sage: from sage.combinat.backtrack import PositiveIntegerSemigroup sage: PP = PositiveIntegerSemigroup() sage: list(PP.roots()) [1]