Backtracking results in same repeating course - backtracking

Question

I am trying to solve a puzzle, and it has been suggested that I use backtracking - I did not know the term so did some investigation, and found the following in Wikipedia:
In order to apply backtracking to a specific class of problems, one must provide the data P for the particular instance of the problem that is to be solved, and six procedural parameters, root, reject, accept, first, next, and output. These procedures should take the instance data P as a parameter and should do the following:
root(P): return the partial candidate at the root of the search tree.
reject(P,c): return true only if the partial candidate c is not worth completing.
accept(P,c): return true if c is a solution of P, and false otherwise.
first(P,c): generate the first extension of candidate c.
next(P,s): generate the next alternative extension of a candidate, after the extension s.
output(P,c): use the solution c of P, as appropriate to the application.
The backtracking algorithm reduces the problem to the call backtrack(root(P)), where backtrack is the following recursive procedure:
procedure backtrack(c) is
if reject(P, c) then return
if accept(P, c) then output(P, c)
s ← first(P, c)
while s ≠ NULL do
backtrack(s)
s ← next(P, s)
I have attempted to use this method for my solution, but after the method finds a rejected candidate it just starts again and finds the same route, rather than the next possible one.
I now don't think I have used the next(P,s) correctly, because I don't really understand the wording 'after the extension s'.
I've tried 2 methods:
(a) in the first() function, generating all possible extensions, storing them in a list, then using the first. The next() function then uses the other extensions from the list in turn. But this maybe can't work because of the calls to backtrack() in between the calls to next().
(b) adding a counter to the data (i.e. the class that includes all the grid info) and incrementing this for each call of next(). But can't work out where to reset this counter to zero.
Here's the relevant bit of code for method (a):
private PotentialSolution tryFirstTrack(PotentialSolution ps)
{
possibleTracks = new List<PotentialSolution>();
for (Track trytrack = Track.Empty + 1; trytrack < Track.MaxVal; trytrack++)
{
if (validMove(ps.nextSide, trytrack))
{
ps.SetCell(trytrack);
possibleTracks.Add(ps);
}
}
return tryNextTrack(ps);
}
private PotentialSolution tryNextTrack(PotentialSolution ps)
{
if (possibleTracks.Count == 0)
{
ps.SetCell(Track.Empty);
return null;
}
ps = possibleTracks.First();
// don't use same one again
possibleTracks.Remove(ps);
return ps;
}
private bool backtrackTracks(PotentialSolution ps)
{
if (canExit)
{
return true;
}
if (checkOccupiedCells(ps))
{
ps = tryFirstTrack(ps);
while (ps != null)
{
// 'testCells' is a copy of the grid for use with graphics - no need to include graphics in the backtrack stack
testCells[ps.h, ps.w].DrawTrack(g, ps.GetCell());
if (ps.TestForExit(endColumn, ref canExit) != Track.MaxVal)
{
drawRowColTotals(ps);
return true;
}
ps.nextSide = findNextSide(ps.nextSide, ps.GetCell(), ref ps.h, ref ps.w);
if (ps.h >= 0 && ps.h < cellsPerSide && ps.w >= 0 && ps.w < cellsPerSide)
{
backtrackTracks(ps);
ps = tryNextTrack(ps);
}
else
return false;
}
return false;
}
return false;
}
and here's some code using random choices. This works fine, so I conclude that the methods checkOccupiedCells() and findNextSide() are working correctly.
private bool backtrackTracks(PotentialSolution ps)
{
if (canExit)
{
return true;
}
if (checkOccupiedCells(ps))
{
Track track = createRandomTrack(ps);
if (canExit)
return true;
if (track == Track.MaxVal)
return false;
ps.SetCell(track);
ps.nextSide = findNextSide(ps.nextSide, track, ref ps.h, ref ps.w);
if (ps.h >= 0 && ps.h < cellsPerSide && ps.w >= 0 && ps.w < cellsPerSide)
backtrackTracks(ps);
else
return false;
}
}
If it helps, there's more background info in the puzzle itself here