data structures- back tracking

data structures- back tracking

• 1.
  BACKTRACKING,GENERAL METHOD , 8QUEEN’S PROBLEM S.Nandhini II – Msc(CS&IT) Nadar Saraswathi College Of Arts And Science Theni.
• 2.
  BACKTRACKING General method  Problemssearching 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 paththrough 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
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  RECURSIVE BACKTRACKING Pseudo codefor 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
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  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.
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   Where solutionexist 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 Allsolutions 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); } } }
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  8 QUEEN’S PROBLEM
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  FORMULATION: Status Any arrangement of0 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
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  EXAMPLE 8 QUEENS 1 2 3 4 5 (8,5,4,3,2)=1649
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  1 2 3 4 5 6 (8,5,3,1,2,1)=769
• 13.
  THANK YOU