A Quick Guide to Backtracking Algorithm

Introduction

A backtracking algorithm solves some computational problems, especially constraint satisfaction problems. In the algorithm, candidates progress incrementally toward the solution, and when a backtrack is no longer possible, the algorithm abandons the candidate.

Introduction to Backtracking Algorithm

A backtracking algorithm uses brute force to discover all possible solutions for a given problem. During this process, all possible solutions are gradually compiled. Whenever an issue has constraints, solutions that don't meet those constraints will be removed.

Backtracking Algorithm

 Backtrack(a)if a is not a solutionreturn falseif a is a new solutionadd to list of solutionsbacktrack(expand a)

The algorithm finds a solution by building a solution step by step, using recursive calls to increase levels over time. These solutions are found by using a search tree known as a state-space tree.

The branches of a state-space tree represent variables, and the levels represent solutions. A backtracking algorithm uses a depth-first search approach. When exploring the possible solutions, the algorithm applies the abounding function to determine whether it meets the constraints.

The search will continue if it finds one. Without such a result, the algorithm returns to its previous level by removing the branch.

How Does a Backtracking Algorithm Work?

Using backtracking, you try out a series of decisions until you find out which works best. Here's an example to help you understand.

A start node is the first step. Our first step is to move to node A since it isn't a feasible solution, so we proceed to node B. There is no feasible solution at node B, so we backtrack to node A.

There is another path between nodes A and C. Unfortunately, that path is also dead-end, so we backtrack from node C to node A.

As we move from the starting node to node D, we will check if any other paths exist from the starting node. As we cannot find a feasible solution, we move from node D to node E. There is no feasible solution at node E either. We have reached a dead end, so we go back to node D from node E.

It is possible to move from node D to node F in another way. As a result, we move from node D to node F. However, the path from node F is not feasible and dead-end, so we try another route.

Let's say another path exists from node F to node G, so connect node F to node G, which is the node of success.

Backtracking terms include:

• Live node: A live node is a node that is capable of being further generated.
• E node: A node whose children become success nodes.
• Success node: Success nodes provide feasible solutions.
• Dead node: Nodes that cannot be generated further and do not provide a feasible solution are known as dead nodes.

Application of Backtracking Algorithm

There are many applications for the backtracking algorithm, including

• N-queen problem.
• The knight tour problem.
• Maze solving problems.
• The search for all Hamilton paths in a graph.

When to Use a Backtracking Algorithm

There are some specific problems for which the backtracking algorithm is applicable.

• For example, we can use it to determine a feasible solution to a decision problem.
• Also, it proved very effective for solving optimization problems.
• Backtracking algorithms have helped to find feasible solutions for the enumeration problem in some instances.
• The backtracking technique, however, is not considered an optimized technique.
• When a problem has no time limit, you can use it to find a solution.