Editing Backtracking (section)

===Usage considerations===
The ''reject'' procedure should be a [[Boolean-valued function]] that returns ''true'' only if it is certain that no possible extension of ''c'' is a valid solution for ''P''.  If the procedure cannot reach a definite conclusion, it should return ''false''. An incorrect ''true'' result may  cause the ''backtrack'' procedure to miss some valid solutions.  The procedure may assume that ''reject''(''P'',''t'') returned ''false'' for every ancestor ''t'' of ''c'' in the search tree.

On the other hand, the efficiency of the backtracking algorithm depends on ''reject'' returning ''true'' for candidates that are as close to the root as possible.  If ''reject'' always returns ''false'', the algorithm will still find all solutions, but it will be equivalent to a brute-force search.

The ''accept'' procedure should return ''true'' if ''c'' is a complete and valid solution for the problem instance ''P'', and ''false'' otherwise.  It may assume that the partial candidate ''c'' and all its ancestors in the tree have passed the ''reject'' test.

The general pseudo-code above does not assume that the valid solutions are always leaves of the potential search tree.  In other words, it admits the possibility that a valid solution for ''P'' can be further extended to yield other valid solutions.

The ''first'' and ''next'' procedures are used by the backtracking algorithm to enumerate the children of a node ''c'' of the tree, that is, the candidates that differ from ''c'' by a single  extension step.  The call ''first''(''P'',''c'') should yield the first child of ''c'', in some order; and the call ''next''(''P'',''s'') should return the next sibling of node ''s'', in that order.  Both functions should return a distinctive "NULL" candidate, if the requested child does not exist.

Together, the ''root'', ''first'', and ''next'' functions define the set of partial candidates and the potential search tree.  They should be chosen so that every  solution of ''P'' occurs somewhere in the tree, and no partial candidate occurs more than once.  Moreover, they should admit an efficient and effective ''reject'' predicate.