General methodin Data Structure for UG.pptx
- 2. Introductionof backtracking Backtracking can be defined as a general algorithmic technique that considers searching every possible combination in order to solve a computational problem.
- 3. Introductionof backtracking algorithm Backtracking is an algorithmic technique for solving problems recursively by trying to build a solution incrementally, one piece at a time, removing those solutions that fail to satisfy the constraints of the problem at any point of time (by time, here, is referred to the time elapsed till reaching any level of the search tree).
- 4. Basic terminologies Candidate: A candidate is a potential choice or element that can be added to the current solution. Solution: The solution is a valid and complete configuration that satisfies all problem constraints. Partial Solution: A partial solution is an intermediate or incomplete configuration being constructed during the backtracking process. Decision Space: The decision space is the set of all possible candidates or choices at each decision point. Decision Point: A decision point is a specific step in the algorithm where a candidate is chosen and added to the partial solution.
- 5. Feasible Solution: A feasible solution is a partial or complete solution that adheres to all constraints. Dead End: A dead end occurs when a partial solution cannot be extended without violating constraints. Backtrack: Backtracking involves undoing previous decisions and returning to a prior decision point. Search Space: The search space includes all possible combinations of candidates and choices. Optimal Solution: In optimization problems, the optimal solution is the best possible solution.
- 6. Typesofbacktracking problems Problems associated with backtracking can be categorized into 3 categories: Decision Problems: Here, we search for a feasible solution. Optimization Problems: For this type, we search for the best solution. Enumeration Problems: We find set of all possible feasible solutions to the problems of this type.
- 7. Applicationsof backtracking Creating smart bots to play Board Games such as Chess. Solving mazes and puzzles such as N-Queen problem. Network Routing and Congestion Control. Decryption Text Justification
- 8. EXAMPLE We start with a start node. First, we move to node A. Since it is not a feasible solution so we move to the next node, i.e., B is also not a feasible solution, and it is a dead-end so we backtrack from node B to node A. Suppose another path exists from node A to node C. So, we move from node A to node C. It is also a dead-end, so again backtrack from node C to node A. We move from node A to the starting node.
- 9. Now we will check any other path exists from the starting node. So, we move from start node to the node D. Since it is not a feasible solution so we move from node D to node E. The node E is also not a feasible solution. It is a dead end so we backtrack from node E to node D. Suppose another path exists from node D to node F. So, we move from node D to node F. Since it is not a feasible solution and it's a dead-end, we check for another path from node F.
- 10. Suppose there is another path exists from the node F to node G so move from node F to node G. The node G is a success node.
- 11. Thetermsrelatedto thebacktrackingare •Live node: The nodes that can be further generated are known as live nodes. •E node: The nodes whose children are being generated and become a success node. •Success node: The node is said to be a success node if it provides a feasible solution. •Dead node: The node which cannot be further generated and also does not provide a feasible solution is known as a dead node. Many problems can be solved by backtracking strategy, and that problems satisfy complex set of constraints, and these constraints are of two types: •Implicit constraint: It is a rule in which how each element in a tuple is related. •Explicit constraint: The rules that restrict each element to be chosen from the given set.