/// <summary> Creates an empty queen set with bitboards initialized. </summary>
public static QueenSet Empty()
{
var bbCount = Board.BitboardCount;
var dim = Board.Dimension;
var tFilesInv = ~BitBase.TrailingBitFiles;
var tRanksInv = ~BitBase.TrailingBitRanks;
var emptySet = new QueenSet(new ulong[bbCount], new ulong[bbCount]);
// Exclude all files beyond N:
for (var i = dim - 1; i < bbCount; i += dim)
{
emptySet.Fill[i] = tFilesInv;
}
// Exclude all ranks beyond N:
for (var i = bbCount - dim; i < bbCount; i++)
{
emptySet.Fill[i] |= tRanksInv;
}
return(emptySet);
}
protected override void Solve()
{
/* We don't need to check every position in the first rank.
* In fact, we only need to check half of them (+1 if N is odd).
* This is because placing the first queen on the other half
* of the rank will produce the same fundamental results - only
* mirrored horizontally. */
var halfWay = Master.N / 2 + Master.N % 2;
/* The main search stage begins after all root nodes are collected.
* A root node is basically a description of an incomplete set
* containing the first 2 queens placed on the first 2 ranks. The
* reason for the whole concept is parallelism. Each thread will
* handle one path starting from some root node. Why 2 queens and
* not just the first one? Well, that way there are more starting
* points meaning more iterations, and therefore the parallel loop
* will work more efficiently. */
var nodes = new ConcurrentBag <Node>();
/* Also we need some original fill mask that takes redundant utmost
* bits into consideration. Those are bits that need to be excluded
* from the leftmost and topmost bitboards in case N is not a power of 8.
* By doing that right away, we don't need to worry about it anymore.
* The Empty() function handles the redundant bits. */
var fillMask = QueenSet.Empty().Fill;
// Gather the root nodes:
Parallel.For(0, halfWay, Master.ThreadingOptions, i =>
{
// The index of the bitboard containing the examined square:
var bbIdx = i / 8;
// The first queen's bit-position:
var bitPos = 1UL << (i % 8);
// The first queen's attack mask:
var attacks = BitBase.Attacks[bbIdx][bitPos];
// The root fill mask will combine the attack mask and the original fill mask:
var rootFill = new ulong[Board.BitboardCount];
for (var j = 0; j < Board.BitboardCount; j++)
{
rootFill[j] = attacks[j] | fillMask[j];
}
// Now go through the 2nd rank and get all the ways of placing
// the 2nd queen, effectively collecting a set of root nodes:
for (var j = 0; j < Board.Dimension; j++)
{
AddNode(nodes, rootFill, j, bbIdx, bitPos, 0xFF00);
}
});
// Perform the search per each root node:
Parallel.ForEach(nodes, Master.ThreadingOptions, node =>
{
Search(node, 0, 2, 0xFF0000);
// Notify the user that something is going on (helpful in case of big N):
Events.OnProgress();
});
// All solutions should be found at this point.
Events.OnAllSolutionsFound();
}