Backtracking algorithms

Backtracking algorithms

Backtracking algorithms are like problem-solving strategies which help in exploring different options to find the best solution possible. They work by trying out different paths and if one doesn’t work, it backtracks together with tries another until they find the right one. It is to solve a puzzle by testing various pieces until they fit in together perfectly.

What is a Backtracking Algorithm?

Backtracking is a problem-solving algorithmic technique which involves finding a solution incrementally by trying different options and also undoing them if they lead to a dead end.

It is very common to use in this situation where one needs to explore quite a few possibilities to solve problems, like searching for paths in a maze or solving puzzles like Sudoku. When a dead end is about to be reached, the algorithm backtracks to the previous decision point and tours a different path until a solution is found and all possibilities have been exhausted.

How Does a Backtracking Algorithm Work?

A backtracking algorithm works by recursively exploring all possible solutions to the problem. It starts by choosing an early solution, and then it finds all possible extensions of the solution. If an extension drives to a solution, the algorithm gets back that solution. If an extension does not lead the way to a solution, the algorithm backtracks to the forgoing solution and tries a different extension.

The following are the general outline of how a backtracking algorithm works:

• First choose an initial solution.
• Then, look for all the possible extensions of the current solution.
• If there is an extension leading to a solution,then return that solution.
• If an extension does not lead to a solution,then backtrack to the forgoing  solution and try a dissimilar extension.
• Then, repeat these steps 2-4 until all the possible solutions have been looked at.
• Let's take a example of a Backtracking Algorithm
• Let's try to find the shortest path through a maze
• Input: A maze represented as the 2D array, where 0 speaks for an open space and 1 appears for a wall.

Algorithm:

• Start at the starting point.
• For each of the 4 possible directions (down,up,right, left), try moving in that direction.
• Moving in the direction leads to the end point, returning the path taken.
• If moving in that direction does not lead to the ending point, backtrack to the previous position and try a different direction.
• Repeat these steps 2-4 until the end point is reached or all possible paths have been explored.

When to Use a Backtracking Algorithm?

Backtracking algorithms are one of the best used to solve problems that have the following characteristics:

1. There are multiple possible solutions to all the problems.
2. These problems can be broken down into the smaller subproblems.
3. The subproblems are to be solved independently.

Applications of Backtracking Algorithm

• Backtracking algorithms are used in a wide range of applications, including:

1. Solving puzzles like Sudoku, crossword puzzles.
2. Finds the shortest path through a maze.
3. Scheduling the problems.
4. Resourcing allocation problems.
5. Networking optimization problems.

When to use a Backtracking algorithm?

When one has multiple choices, then one can make the decisions from the available choices. In the backing cases, one needs to use the backtracking algorithm: A piece of enough information is not available to make the best choice, so one uses the backtracking strategy to try out all the possible solutions available.

Each decision guides a new set of choices. Then again, one backtracks to make a new decision. In these cases, one needs to use the backtracking strategy.

These terms are related to the backtracking are:

1. Live node: The nodes that can be further made are known as live nodes.
2. E node: The nodes whose children are being made and become a success node.
3. Success node: The nodes are said to be a success node if it provide a practical solution.
4. Dead node: The nodes which cannot be further generated and also do not provide a feasible solution is known as a dead node.

• Many problems get solved by the backtracking strategy, and all the problems satisfy a complex set of the constraints, and these constraints are of two types: 1 Implicit constraint and 2 Explicit constraint.

1. Implicit constraint: It is the rule in which each of the elements in a tuple is related.
2. Explicit constraint: The rules are restricted to each element to be chosen from the specified set.

Applications of the Backtracking

1. N-queens problem
2. Sum of the subset problem
3. Graphic coloring
4. Hamilton cycles