![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 1 at position [1, 1]
*Fulfil Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-11-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 1 at position [1, 2]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-12-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 1 at position [2, 2]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-13-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 2 at position [3, 2]
*Fulfil Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-14-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [1, 3]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-15-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [2, 3]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-16-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [3, 3]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-17-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [4, 3]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-18-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 2 at position [4, 2]
*Fulfil Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-20-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [1, 3]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-21-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [2, 3]
*Fulfil Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-22-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 4 at position [1, 4]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-23-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 4 at position [2, 4]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-24-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 4 at position [3, 4]](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-25-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 4 at position [4, 4]
No more valid Cells, so Backtrack it’s
immediate variable](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-26-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [3, 3]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-27-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [4, 3]
* Violating Constraints
No more valid Cells, so Backtrack it’s
immediate immediate variable](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-28-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 1 at position [2, 1]
* Fulfil Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-29-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 2 at position [1, 2]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-30-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 2 at position [2, 2]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-31-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 2 at position [3, 2]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-32-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 2 at position [4, 2]
*Fulfil Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-33-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 3 at position [1, 3]
*Fulfil Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-34-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 4 at position [1, 4]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-35-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 4 at position [2, 4]
* Violating Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-36-320.jpg)
![18.10.2017
4-Queens Using Backtracking
1 2 3 4
1
2
3
4
Place Queen 4 at position [3, 4]
*Fulfil Constraints](https://image.slidesharecdn.com/cspaibyjoy01733600472v1-190907161443/85/Constraint-Satisfaction-Problem-CSP-by-A-z-m-jalal-uddin-joy_v1-0-1-37-320.jpg)
Constraint Satisfaction Problem (CSP) by A z m jalal uddin joy_v1.0.1
- 1. 18.10.2017 Constraint Satisfaction Problem (CSP) Prepared By – ABU ZAHID MD JALAL UDDIN JOY Student, Department of Software Engineering Daffodil International University
- 2. 18.10.2017 CSP – What is it ? ➢ A kind of decision problem ➢ Making decisions without violating constraint
- 3. 18.10.2017 CSP – Consists of 3 Components ➢ A set of variables ➢ A set of values for each of the variables ➢ A set of constraints
- 4. 18.10.2017 Applications ➢ Time Tabling (class rooms, times) ➢ Configuration (hardware, cars…) ➢ Airplane Applications • (British airways uses Constraint Satisfaction to schedule aircraft) ➢ Image Processing • (Microsoft auto collage uses it to blend photos together) ➢ Spreadsheets ➢ Scheduling ➢ Floor Planning ➢ Sudoku etc.
- 5. 18.10.2017 Scientific Challenges ➢ Modelling • (Defining the decisions and constraint) ➢ Combinatorial Explosion • (How to decide, who to do which job and when?)
- 6. 18.10.2017 Finding Solution ➢ If each variable has d values and there are n variables, so we have 𝒅 𝒏 possible assignments
- 7. 18.10.2017 Solving N-Queens as a CSP ➢ The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other. For example, following is a solution for 4 Queen problem.
- 8. 18.10.2017 Solving N-Queens Using Backtracking ➢ N Queen as a example problem that can be solved using Backtracking.
- 9. 18.10.2017 Backtracking ➢ Backtracking is considered an important technique to solve constraint satisfaction issues and puzzles. ➢ Backtracking is one of the main methods for solving problems like N-Queens.
- 10. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 ➢ Variables: Q ➢ Domains: D = {1, 2, 3, 4} ➢ Constraints • Qi≠Qj (cannot be in same row) • |Qi - Qj| ≠ |i - j| (or same diagonal)
- 11. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 1 at position [1, 1] *Fulfil Constraints
- 12. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 1 at position [1, 2] * Violating Constraints
- 13. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 1 at position [2, 2] * Violating Constraints
- 14. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 2 at position [3, 2] *Fulfil Constraints
- 15. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [1, 3] * Violating Constraints
- 16. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [2, 3] * Violating Constraints
- 17. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [3, 3] * Violating Constraints
- 18. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [4, 3] * Violating Constraints
- 19. 18.10.2017 Backtrack ➢ No more valid Cells, so Backtrack it’s immediate stage (Variable)
- 20. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 2 at position [4, 2] *Fulfil Constraints
- 21. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [1, 3] * Violating Constraints
- 22. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [2, 3] *Fulfil Constraints
- 23. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 4 at position [1, 4] * Violating Constraints
- 24. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 4 at position [2, 4] * Violating Constraints
- 25. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 4 at position [3, 4]
- 26. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 4 at position [4, 4] No more valid Cells, so Backtrack it’s immediate variable
- 27. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [3, 3] * Violating Constraints
- 28. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [4, 3] * Violating Constraints No more valid Cells, so Backtrack it’s immediate immediate variable
- 29. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 1 at position [2, 1] * Fulfil Constraints
- 30. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 2 at position [1, 2] * Violating Constraints
- 31. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 2 at position [2, 2] * Violating Constraints
- 32. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 2 at position [3, 2] * Violating Constraints
- 33. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 2 at position [4, 2] *Fulfil Constraints
- 34. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 3 at position [1, 3] *Fulfil Constraints
- 35. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 4 at position [1, 4] * Violating Constraints
- 36. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 4 at position [2, 4] * Violating Constraints
- 37. 18.10.2017 4-Queens Using Backtracking 1 2 3 4 1 2 3 4 Place Queen 4 at position [3, 4] *Fulfil Constraints
- 38. 18.10.2017 This was the basic explanation ➢ Do you have any questions ?