<algorithm> A scheme for solving a series of sub-problems each
of which may have multiple possible solutions and where the
solution chosen for one sub-problem may affect the possible
solutions of later sub-problems.
To solve the overall problem, we find a solution to the first
sub-problem and then attempt to recursively solve the other
sub-problems based on this first solution. If we cannot, or
we want all possible solutions, we backtrack and try the next
possible solution to the first sub-problem and so on.
Backtracking terminates when there are no more solutions to
the first sub-problem.
This is the algorithm used by logic programming languages
such as Prolog to find all possible ways of proving a
goal. An optimisation known as "intelligent backtracking"
keeps track of the dependencies between sub-problems and only
re-solves those which depend on an earlier solution which has
changed.
Backtracking is one algorithm which can be used to implement
nondeterminism. It is effectively a depth-first search of
a problem space.
