n-queens

Algorithm NQueens ( k, n) //Prints all Solution to the n-queens problem { for i := 1 to n do { if Place (k, i) then { x[k] := i; if ( k = n) then write ( x [1 : n] else NQueens ( k+1, n); } } } Algorithm Place (k, i) { for j := 1 to k-1 do if (( x[ j ] = // in the same column or (Abs( x [ j ] - i) =Abs ( j – k ))) // or in the same diagonal then return false; return true; } The above code is for solving N Queens problem using backtracking.I think that it can place the first 2 queens of two rows in respective columns and then when it comes to 3rd row queen it can't be placed as no queen needs

I'm stuck on the extended exercise 28.2 of How to Design Programs . I used a vector of true or false values to represent the board instead of using a list. This is what I've got which doesn't work: #lang Scheme (define-struct posn (i j)) ;takes in a position in i, j form and a board and ; returns a natural number that represents the position in index form ;example for board xxx ; xxx ; xxx ;(0, 1) -> 1 ;(2, 1) -> 7 (define (board-ref a-posn a-board) (+ (* (sqrt (vector-length a-board)) (posn-i a-posn)) (posn-j a-posn))) ;reverse of the above function ;1 -> (0, 1) ;7 -> (2, 1) (define (get-posn

I have just solved the nqueen problem in python. The solution outputs the total number of solutions for placing n queens on an nXn chessboard but trying it with n=15 takes more than an hour to get an answer. Can anyone take a look at the code and give me tips on speeding up this program...... A novice python programmer. #!/usr/bin/env python2.7 ############################################################################## # a script to solve the n queen problem in which n queens are to be placed on # an nxn chess board in a way that none of the n queens is in check by any other #queen using

I am quite confused with idea of implementing 8-queen problem using dynamic programming. It seems it is not possible at one end as for DP " if the problem was broken up into a series of subproblems and the optimal solution for each subproblem was found, then the resulting solution would be realized through the solution to these subproblems. A problem that does not have this structure cannot be solved with dynamic programming" ( Reference ). By taking this in account, the optimal solution for 7x7 board might not optimal as well (even incorrect) for 8x8. So, the result of problem might not

In Art of Prolog of Sterling & Shapiro, exercise Section 14.1 (v): queens(N,Qs) :- length(Qs,N), place_queens(N,Qs,_,_). place_queens(0,_Qs,_Ups,_Downs). place_queens(I,Qs,Ups,[_|Downs]) :- I > 0, I1 is I-1, place_queens(I1,Qs,[_|Ups] ,Downs), place_queen(I,Qs,Ups,Downs). place_queen(Q,[Q|_],[Q|_],[Q|_]). place_queen(Q,[_|Qs],[_|Ups],[_|Downs] ):- place_queen(Q,Qs,Ups,Downs). It is a splendid program, in 11 lines, which quickly solves the problem of positioning queens on a chessboard. It's magical: there is only a counter, recursion, and lists that get longer and shorter. I, even with the help