What are the best use cases for backtracking algorithms?

1 Solving puzzles

One of the most common and intuitive use cases for backtracking algorithms is solving puzzles, such as sudoku, crossword, or word search. These puzzles require finding a configuration of elements that meet certain rules and conditions. A backtracking algorithm can solve these puzzles by trying different options for each element, checking if they are valid, and moving on to the next element. If an option leads to a contradiction or a dead end, the algorithm can backtrack to the previous element and try another option, until it finds a solution or exhausts all possibilities.

4 Optimizing resources and costs

Another use case for backtracking algorithms is optimizing the allocation of resources or the minimization of costs in various scenarios, such as scheduling, assignment, or packing problems. These problems involve assigning tasks, workers, or objects to slots, locations, or containers, such that some objective function is maximized or minimized. A backtracking algorithm can solve these problems by trying different assignments for each slot, location, or container, and calculating the value of the objective function. If the assignment is feasible and improves the current best value, the algorithm can update it and move on to the next slot, location, or container. If the assignment is infeasible or worse than the current best value, the algorithm can backtrack to the previous slot, location, or container and try another assignment, until it finds the optimal solution or reaches a limit.

5 Searching for patterns and matches

Backtracking algorithms can also be used to search for patterns and matches in strings, which are sequences of characters. For example, regular expressions are a way of describing patterns that can match certain strings, such as email addresses, phone numbers, or dates. A backtracking algorithm can search for these patterns by matching one character at a time, and following the rules and symbols of the regular expression. If the character matches, the algorithm can advance to the next character in the string and the pattern. If the character does not match, the algorithm can backtrack to the previous character and try another option, such as a wildcard, an alternative, or a repetition, until it finds a match or reaches the end of the string or the pattern.

6 Designing experiments and simulations

Backtracking algorithms can also be used to design experiments and simulations that involve testing different hypotheses, scenarios, or parameters. For example, in scientific research, backtracking algorithms can help design experiments that test the effects of different variables or factors on an outcome or a response. A backtracking algorithm can design these experiments by choosing one variable or factor at a time, and setting its value or level. Then, it can recursively choose and set the remaining variables or factors, and measure the outcome or the response. If the outcome or the response meets some criteria or expectations, the algorithm can output or store the current experiment. Otherwise, the algorithm can reset the last variable or factor and try another value or level, until it tests all the possible combinations or reaches a limit.

7 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?