private void Expand(Dir[,] choice, int r, int c, int from, int to, int totalScore, int stage, int mask)
{
if (r == n_)
{
from *= 3;
to *= 3;
int fromStart = 0, fromEnd = 2;
if ((stage & 0x1) > 0)
{
// can only accept states with no start or end
fromEnd = 0;
}
else if (stage == 0x2)
{
// has end in the column but no start, can only accept states with start (only)
fromStart = 1;
fromEnd = 1;
}
int toAdd = 0;
if ((stage & 0x2) > 0) toAdd = 2;
else if (stage == 0x1) toAdd = 1;
for (int fromAdd = fromStart; fromAdd <= fromEnd; fromAdd++)
{
List<Entry> parents = prev_[from + fromAdd];
for (int i = 0; i < parents.Count; i++)
{
int currentScore = parents[i].score + totalScore;
DisjointSet groups = new DisjointSet(n_);
bool invalid = false;
for (int j = 0; j < n_; j++)
{
if (choice[j, 0] == Dir.Down || choice[j, 1] == Dir.Up)
{
groups.Union(j, j - 1);
}
if (choice[j, 0] == Dir.Left || choice[j, 1] == Dir.Right)
{
// find out whether the rhs has connected to anything above it
int rhs = (parents[i].groups >> j * 2) & 0x3;
int connected = -1;
for (int k = j - 1; k >= 0; k--)
{
if (choice[k, 0] == Dir.Left || choice[k, 1] == Dir.Right)
{
if (((parents[i].groups >> k * 2) & 0x3) == rhs)
{
connected = k;
break;
}
}
}
if (connected != -1)
{
invalid |= !groups.Union(connected, j);
// this forms a closed loop, which is an invalid formation
if (invalid) break;
}
// else rhs does not connect to anything above it
}
}
if (invalid) continue;
toAdd = Math.Max(toAdd, fromAdd);
List<Entry> current = next_[to + toAdd];
int toGroups = groups.Normalize(mask);
bool fnd = false;
var currentSolution = parents[i].solution.Select(s => s).ToList();
currentSolution.Add((Dir[,])choice.Clone());
for (int j = 0; j < current.Count; j++)
{
if (current[j].groups == toGroups)
{
if (currentScore > current[j].score)
{
current[j].score = currentScore;
current[j].solution = currentSolution;
}
fnd = true;
break;
}
}
if (!fnd)
{
current.Add(new Entry(toGroups, currentScore, currentSolution));
}
}
}
return;
}
for (int k = 0; k < Dirs.Values.GetLength(0); k++)
{
if (grid_[r, c] == 0 && k > 0) break;
if (stage == 1 && Dirs.Values[k, 0] == Dir.None && k > 0) break;
if ((stage & 0x2) > 0 && Dirs.Values[k, 1] == Dir.None && k > 0) break;
if (r > 0 &&
(choice[r - 1, 0] == Dir.Up && Dirs.Values[k, 1] != Dir.Up || choice[r - 1, 1] == Dir.Down && Dirs.Values[k, 0] != Dir.Down))
continue;
if (Dirs.Values[k, 0] == Dir.Down && (r == 0 || choice[r - 1, 1] != Dir.Down)) continue;
if (Dirs.Values[k, 1] == Dir.Up && (r == 0 || choice[r - 1, 0] != Dir.Up)) continue;
if (Dirs.Values[k, 1] == Dir.Down && r == n_ - 1) continue;
if (Dirs.Values[k, 0] == Dir.Up && r == n_ - 1) continue;
choice[r, 0] = Dirs.Values[k, 0];
choice[r, 1] = Dirs.Values[k, 1];
int fromBit = 0;
int toBit = 0;
if (choice[r, 0] == Dir.Left)
{
fromBit = 1;
}
else if (choice[r, 1] == Dir.Right)
{
fromBit = 2;
}
if (choice[r, 0] == Dir.Right)
{
toBit = 2;
}
else if (choice[r, 1] == Dir.Left)
{
toBit = 1;
}
int nextStage = stage;
if (Dirs.Values[k, 0] == Dir.None && k > 0) nextStage |= 0x1;
else if (Dirs.Values[k, 1] == Dir.None && k > 0) nextStage |= 0x2;
int nextMask = mask;
if (choice[r, 1] == Dir.Left || choice[r, 0] == Dir.Right)
{
nextMask |= 1 << r;
}
Expand(choice, r + 1, c, from * 3 + fromBit, to * 3 + toBit, k == 0 ? totalScore : totalScore + grid_[r, c], nextStage, nextMask);
}
}
