Searching with backtracking¶
Searching with backtracking is a fundamental approach in computer science for solving problems through trial-and-error. The idea is to try all possible solutions to a problem until the right solution is found.
In search algorithms with backtracking, we can distinguish the following features:
- Recursion: the most important aspect of backtracking algorithms is recursion. These algorithms usually rely on recursion to test all possible solutions.
- Choice and backtracking: in this approach, the algorithm makes a decision (choice) and then continues searching until it encounters an obstacle. At this point, the algorithm reverses to the previous state and tries another solution.
- Pruning: not all paths in a search tree need to be explored. Knowing certain features of the problem, it is possible to pruning some paths that will definitely not lead to a solution.
Applications¶
Search algorithms with backtracking have wide applications, including in:
- Solving puzzles, such as sudoku.
- Optimization problems, such as the travelling salesman problem.
- Decision problems, such as the graph coloring problem.
- Combinatorial problems, such as generating all possible permutations of elements.
Summary¶
Backtracking is a powerful tool for solving problems that seem too complicated to solve directly. Although these algorithms can be time-consuming (especially for large data sets), their ability to explore all possible solutions and dynamically adapt to problems makes them extremely useful in many situations. However, the key to using backtracking effectively is the ability to recognize moments when a search can be pruned to save time and computing power.