Write short notes on: (b) Backtracking

Backtracking

Backtracking is a general algorithm for finding solutions to some computational problems, notably finding all (or some) solutions to a constraint satisfaction problem. Backtracking involves incrementally building candidate solutions and abandoning each partial candidate ("backtracking") as soon as it is determined not to lead to a valid solution.

In general, the backtracking algorithm proceeds as follows:

1. Start with an initial empty solution.
2. Recursively explore the search space by extending the current partial solution with a valid extension.
3. If the extended partial solution is complete and satisfies the problem constraints, then the solution is reported.
4. Otherwise, remove the extension from the partial solution and backtrack to explore other extensions.

The efficiency of backtracking can be improved by using heuristics to guide the search and by pruning the search space early when it is clear that a partial solution will not lead to a valid solution.

Examples of Backtracking

The following are some examples of problems that can be solved using backtracking:

• The N-queens problem: Given an NxN chessboard, find a placement of N queens on the board such that no two queens attack each other.
• The knapsack problem: Given a set of items with weights and values, find the subset of items that has the maximum total value and whose total weight does not exceed a given capacity.
• The traveling salesman problem: Given a set of cities and the distances between them, find the shortest tour that visits each city exactly once and returns to the starting city.

Advantages of Backtracking

• Backtracking is a systematic approach to solving problems that can be decomposed into a series of smaller subproblems.
• Backtracking can be used to find all solutions to a problem, or to find the first solution that satisfies a given criterion.
• Backtracking is relatively easy to implement.

Disadvantages of Backtracking

• Backtracking can be inefficient for problems with a large search space.
• Backtracking can be difficult to apply to problems that have complex constraints.
• Backtracking can be difficult to parallelize.

Conclusion

Backtracking is a powerful algorithm for solving constraint satisfaction problems. It is easy to implement and can be used to find all solutions to a problem or to find the first solution that satisfies a given criterion. However, backtracking can be inefficient for problems with a large search space or complex constraints.