The document describes the backtracking algorithm and its application to solve the 8 queens problem. It provides an overview of backtracking as a general method for problems that search for solutions or require an optimal solution. It then gives a maze pathfinding problem as an example of a backtracking algorithm. The document outlines the recursive pseudo code for backtracking and applies it to the 8 queens problem, describing the problem and providing an algorithm to find all solutions by placing queens on an 8x8 chessboard without any attacking each other. It provides two examples of solutions to the 8 queens problem.

1. BACKTRACKING,GENERAL
METHOD , 8 QUEEN’S PROBLEM
S.Nandhini
II – Msc(CS&IT)
Nadar Saraswathi College Of Arts And Science
Theni.

2. BACKTRACKING
General method
 Problems searching for a set of solutions or Which
require an optimal solution can be solved using the
backtracking method.
 To apply the backtracking method, the solution must
be expressible as an n- tuple (x1…..xn).
 Where xi are chosen from finite set si.
 The solution vector must satisfy the criterion function
p(x1…….xn).

3. BACKTRACKING ALGORITHM
EXAMPLE:
Find path through maze
 Start at beginning of maze
 If at exit ,return true
Else for each step from current location
 Recursively Find path
 Return with first successfull step
 Return false if all steps fail

4. RECURSIVE BACKTRACKING
Pseudo code for recursive backtracking algorithms
If at a solution return success for(every possible choice from
current state/node)
 Make that choice and take one step along path
 Use recursive to solve the problem for the new node/state
 If the recursive call succeeds report the success to the next
high level
 Back out of the current choice to restore the state at the
beginning of the loop.
Report failure

5. BACKTRACKING ALGORITHM

6. 8 QUEEN’S PROBLEM
 The 8 queens problem puzzle is the problem of
placing eight chess queens an on 8.
 8 chessboard so that no two queens attack each
other.
 Thus a solution requires that no two queens
share the same row, column , diagonal.
 The eight queens puzzle is an example of the
more general n-queens problem of placing n
queens on an n n chessboard.

7.  Where solution exist for all natural numbers n
with the exception of 1,2 and 3
 The solution possibilities are discovered only up
to 23 queen.

8. 8 QUEEN’S ALGORITHM
All solutions to the n-queens problem
Algorithm NQueens (k,n)
{
For I :=1 to n do
{
If Place( k,i)then
{
X[k]:=I;
If(k=n)then write (x[1:n]);
Else NQueens9(k+1.n);
}
}
}

9. 8 QUEEN’S PROBLEM

10. FORMULATION:
Status
Any arrangement of 0 to 8 queens on the board
Initial state
0 queens on the board
Successor function
Add a queen in any square
Goal test
8 queens on the board ,none attacked

11. EXAMPLE 8 QUEENS
1
2
3
4
5
(8,5,4,3,2)=1649

12. 1
2
3
4
5
6
(8,5,3,1,2,1)=769

13. THANK YOU