Which of the following is an application of the backtracking technique?

The correct answer is Finding the shortest path in a graph.

Key Points

• Backtracking is a general algorithmic technique that involves exploring all possible solutions to a problem by incrementally building candidates and abandoning a candidate as soon as it is determined that it cannot lead to a valid solution.
• It is commonly used in problems that can be solved by generating all possible configurations and selecting the best or valid one.
• Finding the shortest path in a graph is a classic application of backtracking, as it involves exploring multiple paths and backtracking whenever a path does not lead to the desired result.
• Backtracking is particularly useful in problems like:
  • N-Queens problem
  • Solving mazes
  • Subset sum problems
  • Sudoku solvers

Additional Information

• Backtracking systematically tries all possibilities for a solution by going deeper into the decision tree.
• It utilizes recursion to explore different possibilities and prune branches that do not yield valid solutions.
• In the case of finding the shortest path in a graph, backtracking can be used to traverse all paths and find the optimal one by comparing their lengths.
• While backtracking is effective, it can be time-consuming for large datasets. Hence, optimizations like branch-and-bound and heuristic methods are often used in conjunction with backtracking.