1. Sit-In Lab 1 Ob-CHESS-ion

2. N-Queens Puzzle Checker
Famous N-Queens puzzle
You want to check if the input solution is correct
No 2 queens can be on the same row, column or diagonal
Write a piece of code to verify the solution
Input:
N – Number of rows ( Number of queens on chessboard )
Followed by N rows of N numbers
0 – Empty space
1 – Queen
Output whether the puzzle is a valid solution

3. Example – Valid?
Output :

4. Example – Incorrect solution
Output : INVALID

5. Example – Valid Solution
Output : VALID

6. No other queen in same row, column and diagonal

7. Algorithm Loop through each square of the array:
Start from the top left, iterate row by row
For each queen found
Starting from the square on its right, check if there exists another queen in the same row
Starting from the square right below it, check if there exists another queen in the same column
Starting from the square on its bottom right, check if there exists another queen in the same right diagonal
Starting from the square on its bottom left, check if there exists another queen in the same left diagonal
Return false if there exists another queen

8. Visualisation – Start from top left

9. Visualisation – Queen is found, check rows and diagonals

10. Visualisation – Queen is found, check rows and diagonals
Valid

11. Visualisation – Iterate row by row
- No queen in this space

12. Visualisation – Another Queen is found

13. Visualisation – Queen is found, check rows and diagonals
Valid

14. Visualisation – Iterate row by row

15. Visualisation – Another Queen is found

16. Visualisation – Queen is found, check rows and diagonals
Invalid

17. Visualisation – Break from loop and return false
Invalid

18. Main method: Helper methods: Read in the inputs
Call helper methods and print the output
Helper methods:
Check rows, columns and diagonals ( 4 directions ), returning false if another queen is found
Check if given coordinates are out of array bounds ( >= N )

19. How to check diagonals?

20. 1 2
[1][3] 3 4 5 6 7

21. 1 2
[2][4] 3 4 5 6 7

22. 1 2 3 4 5 6 7
[3][5]

23. 1 2 3 4 5 6 7
[3][5]
Row++
Col++

24. 1 2
[1][3] 3 4 5 6 7

25. 1 2
[2][2] 3 4 5 6 7

26. 1 2 3 4 5 6 7
[3][1]

27. 1 2 3 4 5 6 7
[3][1]
Row++
Col--

28. Questions?