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General method
of
backtracking
seminar

Introductionof
backtracking
 Backtracking can be defined as a general algorithmic technique
that considers searching every possible combination in order to
solve a computational problem.

Introductionof
backtracking
algorithm
 Backtracking is an algorithmic technique for solving
problems recursively by trying to build a solution
incrementally, one piece at a time, removing those
solutions that fail to satisfy the constraints of the
problem at any point of time (by time, here, is referred
to the time elapsed till reaching any level of the search
tree).

Basic
terminologies
 Candidate: A candidate is a potential choice or element that can
be added to the current solution.
 Solution: The solution is a valid and complete configuration that
satisfies all problem constraints.
 Partial Solution: A partial solution is an intermediate or
incomplete configuration being constructed during the
backtracking process.
 Decision Space: The decision space is the set of all possible
candidates or choices at each decision point.
 Decision Point: A decision point is a specific step in the algorithm
where a candidate is chosen and added to the partial solution.

 Feasible Solution: A feasible solution is a partial or complete solution that adheres to all
constraints.
 Dead End: A dead end occurs when a partial solution cannot be extended without violating
constraints.
 Backtrack: Backtracking involves undoing previous decisions and returning to a prior
decision point.
 Search Space: The search space includes all possible combinations of candidates and
choices.
 Optimal Solution: In optimization problems, the optimal solution is the best possible
solution.

Typesofbacktracking
problems
Problems associated with backtracking can be
categorized into 3
categories:
 Decision Problems: Here, we search for a feasible
solution.
 Optimization Problems: For this type, we search for
the best solution.
 Enumeration Problems: We find set of all possible
feasible solutions to the problems of this type.

Applicationsof
backtracking
 Creating smart bots to play Board Games such as
Chess.
 Solving mazes and puzzles such as N-Queen problem.
 Network Routing and Congestion Control.
 Decryption
 Text Justification

EXAMPLE
We start with a start node. First, we move to node A. Since it
is not a feasible solution so we move to the next node, i.e., B is
also not a feasible solution, and it is a dead-end so we backtrack
from node B to node A.
Suppose another path exists from node A to node C. So, we
move from node A to node C. It is also a dead-end, so again
backtrack from node C to node A. We move from node A to the
starting node.

Now we will check any other path exists from the starting node. So, we move
from start node to the node D. Since it is not a feasible solution so we move
from node D to node E. The node E is also not a feasible solution. It is a dead
end so we backtrack from node E to node D.
Suppose another path exists from node D to node F. So, we move from node
D to node F. Since it is not a feasible solution and it's a dead-end, we check
for another path from node F.

 Suppose there is another path exists from the node F to
node G so move from node F to node G. The node G is a
success node.

Thetermsrelatedto
thebacktrackingare
•Live node: The nodes that can be further generated are known
as live nodes.
•E node: The nodes whose children are being generated and
become a success node.
•Success node: The node is said to be a success node if it provides
a feasible solution.
•Dead node: The node which cannot be further generated and
also does not provide a feasible solution is known as a dead node.
Many problems can be solved by backtracking strategy, and that
problems satisfy complex set of constraints, and these
constraints are of two types:
•Implicit constraint: It is a rule in which how each element in a
tuple is related.
•Explicit constraint: The rules that restrict each element to be
chosen from the given set.

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