Backtracking Method

Introduction

• It is one of the very important types of algorithms.

Definition

• Backtracking is a general algorithmic technique that is used to solve a wide range of problems, including combinatorial optimization problems, constraint satisfaction problems, and other problems that involve finding a solution among a large set of possible solutions.

Characteristics

• The backtracking algorithm can be implemented using recursion or iteration, depending on the problem and the programming language.
• In general, backtracking is a powerful technique that can solve many complex problems, but it can be inefficient for problems with a large solution space.

Working Principle

• The basic idea of backtracking is to explore all possible solutions by incrementally building up a potential solution and checking if it satisfies the constraints. If the current solution violates any constraint, the algorithm backtracks to the previous step and tries another solution.
• In other words, backtracking builds a solution incrementally, one step at a time, while simultaneously checking if the partial solution can be extended to a complete solution. If at any point it is discovered that the current partial solution cannot be extended to a complete solution, then the algorithm “backtracks” to the previous step, and tries a different path.
• There are the following general steps involved in the backtracking algorithm:-
  • Define the problem: First, identify the constraints and the goal of the problem that we want to solve.
  • Choose a starting point: Start with an initial configuration of the problem, which can be an empty solution or a partial solution.
  • Construct a candidate solution: Generate the next possible solution based on the current state.
  • Check if the solution satisfies the constraints: Evaluate the candidate solution to see if it satisfies the problem’s constraints. If it does not, discard it and backtrack to the previous step.
  • If the solution satisfies the constraints, check if it is the goal: If the solution satisfies all the constraints and is also the goal of the problem, then accept it as the solution and stop. Otherwise, move to the next step.
  • Repeat the process: If the solution is not the goal, repeat the process from step 3 by generating the next candidate solution.
  • Backtrack: If there are no more candidate solutions to explore, backtrack to the previous step and try another candidate solution.
  • Stop: If all candidate solutions have been explored and none of them satisfy the constraints or the goal, then stop and report that there is no solution to the problem.