How can you use backtracking to solve problems?

1 What is backtracking?

Backtracking is a recursive method that tries different choices or paths until it finds a solution or exhausts all options. It is based on the idea of depth-first search, which explores one branch of a tree or graph until it reaches a dead end or a goal, and then backtracks to the previous choice point and tries another branch. Backtracking can be seen as a systematic way of generating and testing all possible candidates for a problem.

2 How does backtracking work?

Backtracking is a method of problem-solving that involves defining the problem as a set of constraints or conditions that must be satisfied by a solution, then choosing a variable or element to assign a value or make a decision. Generating a set of possible values or decisions for that variable or element, based on the problem definition and the current state of the solution, is then necessary. For each value or decision, it must be determined if it is consistent with the constraints or conditions; if yes, it should be added to the solution and recursively backtrack on the next variable or element. If no, discard it and try another value or decision. If all variables or elements have been assigned or decided, and the solution satisfies the problem, return the solution. If no solution is found, return failure.

3 When to use backtracking?

Backtracking is a powerful tool for finding solutions to problems that involve combinations, permutations, sequences, subsets, or arrangements of elements that satisfy some criteria or optimize some objective. Additionally, it can be used to find all possible solutions or the best solution when a problem has multiple solutions. As an example, backtracking can be used to solve problems such as Sudoku, N-queens, subset sum, and Hamiltonian cycle. Specifically, it can be used to fill a 9x9 grid with digits from 1 to 9 such that each row, column, and 3x3 subgrid contains each digit exactly once; place N queens on an NxN chessboard such that no two queens attack each other; find a subset of a given set of integers that sums up to a given target value; and find a cycle in a graph that visits each vertex exactly once.

4 What are the advantages of backtracking?

Backtracking is a useful algorithm design technique, offering simplicity and intuitiveness in implementation, as it follows a trial-and-error approach. It is also capable of handling problems with complex and dynamic constraints or conditions, as it checks the validity of each choice at each step. Furthermore, backtracking can find all possible solutions or the optimal solution, as it explores the entire search space.

5 What are the challenges of backtracking?

Backtracking can be an inefficient and time-consuming process, as it often generates and tests a large number of candidates that may not be feasible or optimal. Additionally, it can consume a lot of memory, as it requires storing the state of the solution and the choices at each recursive call. Furthermore, it can be challenging to determine the order and range of choices, as this may influence the performance and quality of the solution.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?