Backtracking Algorithm | Introduction To Backtracking | Data Structures

2. Agenda

3. Agenda What is Backtracking? N Queens Problem Implementation Conclusion

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5. What is Backtracking?

6. What is Backtracking? Backtracking is an algorithmic approach to solving a problem in a different way. To illustrate the issues, it use a recursive method. To solve an optimization problem, we might state that backtracking is required.

7. N Queens Problem

8. N Queens Problem We will start with the left most column

9. N Queens Problem We will check if all the queens have been placed or not.

10. N Queens Problem Now we will try every row in this column.

11. N Queens Problem Now we will try every row in this column. If the queen can be safely placed in this row, then we will mark it as part of the solution.

12. N Queens Problem Now we will try every row in this column. If the queen can be safely placed in this row, then we will mark it as part of the solution. Then we will recursively check if placing queen there will lead to the complete solution. If yes, then return true.

13. N Queens Problem Now we will try every row in this column. If the queen can be safely placed in this row, then we will mark it as part of the solution. Then we will recursively check if placing queen there will lead to the complete solution. If yes, then return true. If False, then we will backtrack and try different row, and repeat these steps back.

14. N Queens Problem In case if all the rows have been tried and nothing worked then return false to trigger backtracking

15. Implementation

16. Conclusion

17. Conclusion It is very easy to implement and contains less LOC . Most of the back tracking codes are generally few lines of recursive function code.

18. Conclusion It has a large space complexity because we are using recursion, so function information is stored on stack.

19. Conclusion It is very time inefficient in lot of cases when branching factor is large

20. Conclusion We can solve many problems like the knight’s tour, N queens, Rat in the maze, subset sum problem and so on