8 -Queen_Puzzle_Problem_Presentation.ppt
- 2. Basic Rules The board: a matrix of size N X N. In standard chess: N = 8.
- 3. Basic Rules The queen - moves horizontally, vertically, or diagonally.
- 4. The queen - moves horizontally, vertically, or diagonally. Can attack any piece on its way. Basic Rules
- 5. The queen - moves horizontally, vertically, or diagonally. Can attack any piece on its way. Basic Rules
- 6. Basic Rules Two queens threaten each other if they are on the same vertical, horizontal, or diagonal line.
- 7. Basic Rules Two queens threaten each other if they are on the same vertical, horizontal, or diagonal line.
- 8. 8-Queens puzzle Place 8 queens on the board such that no two queens are threatening each other.
- 9. Step-by-step Algorithm 1 . Initialize the board: Create an 8x8 chessboard and initialze all positions to 0(empty) . 2 . Recursive function : Base case- If the current row is 8(all queens have been placed), return true (solution found) . Iterative loop – For each column in the next row ; Check validity : i. If the current position is safe (no queen attack),place a queen there . ii. Recursively call the function for the next row . iii. If the recursive call returns true (solution found),return true . iv. Remove the queen from the current position(backtracking) . If no valid position is found in the current row, return false(no solution) .
- 11. 8-Queens puzzle Place 8 queens on the board such that no two queens are threatening each other.
- 12. Place a queen at a non-threatened cell.
- 13. Place a queen at a non-threatened cell.
- 14. Place a queen at a non-threatened cell.
- 15. Place a queen at a non-threatened cell.
- 16. Place a queen at a non-threatened cell.
- 17. Place a queen at a non-threatened cell.
- 18. Place a queen at a non-threatened cell.
- 19. Place a queen at a non-threatened cell.
- 20. Backtrack.
- 21. Backtrack.
- 22. Place a queen at a non-threatened cell.
- 23. Place a queen at a non-threatened cell.
- 24. Place a queen at a non-threatened cell. Backtrack…
- 25. • Each queen is an autonomous agent! Main ideas • Queens are added to the board from left to right. • A queen tries to find a safe position in its column. • If no safe position is found, then the queen asks its neighbors to advance to the next legal position. (In which no two neighbors threaten each other.) • Each queen has its own fixed column.
- 26. A queen places itself at a safe position in its column.
- 27. A queen places itself at a safe position in its column.
- 28. A queen places itself at a safe position in its column.
- 29. A queen places itself at a safe position in its column.
- 30. A queen places itself at a safe position in its column.
- 31. No safe position for queen 6 at column 6. Asks neighbor (queen 5) to change position.
- 32. No safe position for queen 6 at column 6. Asks neighbor (queen 5) to change position.
- 33. Queen 5 is at the last row. Asks neighbor (queen 4) to change position.
- 35. A queen places itself at a safe position in its column.
- 36. A queen places itself at a safe position in its column.
- 37. A queen places itself at a safe position in its column.
- 38. A queen places itself at a safe position in its column.
- 39. No safe position for queen 8 at column 8. Proceed the search in a similar way…