Introduction To Backtracking Algorithm

Backtracking is a generic algorithmic strategy that takes into account searching through each and every possibility in order to resolve a computational issue.

Backtracking algorithm is used in Data structures and algorithms to solve problems using various techniques. In this article, we will discuss the backtracking algorithm, its types, and multiple problems that are solved using it. 

Backtracking Algorithm

Backtracking is an algorithmic strategy for solving problems recursively by attempting to slowly construct a solution, one piece at a time, and discarding those solutions that fail to satisfy the constraints of the issue at any point in the given time. (Time refers to the elapsed time for reaching a specific level in a search tree).

You can also explore: BFS vs DFS: Understanding the Difference

Optimizing problems do not involve backtracking. When we need all of the possible solutions and have many ones, we backtrack.

Backtracking implies that we are moving back and forward; if the condition is satisfied, we return with success; otherwise, we go back. It is designed to resolve a problem where a sequence of items must be selected from a given set in order for the sequence to meet certain requirements.

You can also explore: Breadth-First Search Algorithm

The backtracking algorithm is stated below:

Backtrack(a)     if a isn’t a solution         return 0     if a is a solution         add to solutions     backtrack(expand a)

Backtracking Algorithm Types

There are three different problems present in backtracking:

• Decision-making: In this type, we look for a workable answer.
• Optimization: The best solution is searched for this problem.
• Enumeration: In this problem, one finds all the solvable options.

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State Space Tree

A space state tree is a tree that depicts all of the potential states of the issue, starting at the root and ending at the leaf.

You can also explore: Introduction to Greedy Algorithm

Using Backtracking Algorithm

When faced with a variety of options, we choose based on those options. The backtracking algorithm must be used in the following circumstances:

• When there isn’t enough information at hand to make the optimal decision, we employ the backtracking approach to explore every option.
• New choices are shown by each choice. On the other hand, we go back and make fresh choices. We must apply the backtracking approach in this situation.

You can also explore: Preorder Traversal – All That You Need To Know

Take the SudoKo game as an example to understand the use of Backtracking. we try filling in the digits one at a time. We erase the current digit (backtrack) and try the next one whenever we discover that it is unable to lead to a solution. This is preferable to the naive approach because it never loses a set of permutations. The naive strategy would generate all possible digit combinations and then attempt each combination one at a time.

You can also explore: Introduction to Bellman Ford Algorithm

How does Algorithm work?

1. Backtracking is a methodical way of trying out requires different sequences until you find one that works. Let’s use an illustration to clarify.With a start node, we begin.
   
   We start by going to node A. As a result of it being an impractical option, we move on to node B. We turn back to node A from node B because it is not a workable solution and is a dead end.

2. Assume a different route connects nodes A and C. As a result, we switch from A to C. Additionally, it leads to nothing, so go backward from C toA. From node A, we move to the initial node .
   
   

2. We will now determine if there is another path leading from the beginning node. We now move to node D from the start node. We go over to E from D as it is not a workable solution. Additionally, the E-node is not a workable solution. Since it leads nowhere, we turn around and go from  E to D.
   
   

4. Assume a different route connects the D to F node. We then go from the D node to the F node. We search for another way from node F because it is a dead end and not a workable option.
   
   

5. Assume there is a different route that can be taken to get from F node to G. A success node is node G.
   
   

Common terms related to Backtracking problems:

• Live node: Nodes that can be produced further are referred to as live nodes.
• E node: In this, Nodes whose offspring are produced and develop into success nodes.
• Success node: If a node offers a workable solution, it is referred to be a successful node.
• Dead node: A dead node is a node that cannot be generated further and does not offer a workable solution

Conclusion

In this article, we have discussed backtracking and the problem of Sudoku related to it. Backtracking is an algorithmic strategy for solving problems recursively by attempting to slowly construct a solution, one piece at a time, and discarding those solutions that fail to satisfy the constraints of the issue at any point in the given time. We have also understood the illustration of the algorithm along with its uses and working. 

Author: Megha Chadha