queens

Joe Riel — Sun, 07 Mar 2010 06:31:36 Z

There are several problems with this

L is reassigned to an empty array in place
L is local to queens, so even if the above were corrected there is an issue.
The inner while loop in queens should negate the result of place.

Here is a modified version. I made L a parameter to place.

place := proc(k,L)
local i;
    for i to k-1 do
        if L(i)=L(k) # two in the same column
        or abs(L(i)-L(k)) = abs(i-k) # in the same diagonal
        then
            return false;
        fi:
    end do;
    return true;
end proc:

queens := proc(n)
local k,L;
    L := Array(1..n);
    k := 1; # k is the current row
    while k > 0 do
        L(k) := L(k)+1; # move to the next column
        while L(k) <= n and not place(k,L) do # can this queen be placed
            L(k) := L(k) + 1;
        end do;
        if L(k)<=n # a position is found
        then if k = n # the solution has been found
             then print(L);
             else
                 k := k+1;
                 L(k) := 0;
             fi:
        else
            k := k-1; # backtrack
        end if;
    end do;
    return NULL;
end proc:

MaplePrimes - answers and comments on Question, queen problem by backtracking

queens