/// <summary>
/// Eliminate will remove the value from the tile and propagate changes via calls to Assign
/// if there is only a single value remaining
/// NOTE: This method mutates the CPBoard cpb parameter
/// </summary>
/// <param name="cpb"></param>
/// <param name="tile"></param>
/// <param name="value"></param>
/// <returns></returns>
static public bool Eliminate(CPBoard cpb, int tileIndex, string value)
{
var values = cpb.Get(tileIndex);
CDebug.Assert(values.Length > 0, "values.Length > 0");
if (values.Length == 1)
{
// Reached a contradiction, eliminating this value will leave the tile EMPTY!
if (values == value)
{
return(false);
}
// Value has already been eliminated from this tile
return(true);
}
var newValues = values.Replace(value, "");
cpb.Set(tileIndex, newValues);
// If there is only one possible value after the change
// Call assign to propagate changes
if (newValues.Length == 1)
{
return(Assign(cpb, tileIndex, newValues));
}
return(true);
}
/// <summary>
/// Function that initializes the internal representation of the constraint propagotion board
/// by relating all the tiles to each other via their units
/// Each tile will have 20 peers comprised of the row, column and square peers
/// </summary>
static private void populatePeers()
{
var indices = Enumerable.Range(0, Const.N);
// Helper function to reduce code duplication
// The index is for determining the offset in the array,
// basically row units are first 9, columns are second 9, squares are third 9
Action <HashSet <int>, int> relatePeers = (peers, unitIndex) => {
foreach (var peerIndex in peers)
{
// Except statement is to exclude self from the relation
Peers[peerIndex] = Peers[peerIndex].Union(peers).Except(new int[] { peerIndex }).ToHashSet();
Units[unitIndex] = peers;
}
};
foreach (var i in indices)
{
var rowPeers = (from c in indices select Utils.CalculateTileIndex(i, c)).ToHashSet();
relatePeers(rowPeers, i);
var columnPeers = (from r in indices select Utils.CalculateTileIndex(r, i)).ToHashSet();
relatePeers(columnPeers, i + Const.N);
int rs = i / Const.W;
int cs = i % Const.W;
var subRows = Enumerable.Range(0, Const.W).Select(j => rs * Const.W + j);
var subColumns = Enumerable.Range(0, Const.W).Select(j => cs * Const.W + j);
var squarePeers = (from r in subRows from c in subColumns select Utils.CalculateTileIndex(r, c)).ToHashSet();
relatePeers(squarePeers, i + Const.N * 2);
CDebug.Assert(Peers[i].Count == 20, $"Should be 20 peers each tile- {string.Join(',', Peers[i])}");
}
}
/// <summary>
/// Exhaustively try all possible values for the tiles, using constraints to
/// reduce the search space
/// </summary>
/// <param name="cpb"></param>
/// <param name="depth"></param> Parameter debugging and curiousity
/// <returns></returns>
static private SearchResult search(CPBoard cpb, int depth)
{
var freeTile = cpb.GetFreeTile();
// No free tile available
if (freeTile.Value == null)
{
return(new SearchResult(cpb, IsSolved(cpb)));
}
var possibleValues = freeTile.Value;
foreach (var c in possibleValues)
{
// Make a copy in case we reach contradiction and need to revert back
var copy = cpb.Copy();
bool didAssign = Assign(copy, freeTile.Key, c.ToString());
CDebug.Assert(copy.Get(freeTile.Key) != cpb.Get(freeTile.Key), "Original CPB mutated!");
if (didAssign)
{
SearchResult sr = search(copy, depth + 1);
if (sr.DidSolve)
{
return(sr);
}
}
}
return(new SearchResult(cpb, false));
}
public CPBoard(string board)
{
var indices = Enumerable.Range(0, Const.N);
CDebug.Assert(board.Length == Const.N2, "board.Length == Const.N2");
for (int i = 0; i < board.Length; i++)
{
int n = Utils.parseChar(board[i]);
if (n != 0)
{
Tiles[i] = n.ToString();
}
else
{
Tiles[i] = string.Join("", indices.Select((num) => num + 1));
}
}
}
/// <summary>
/// Assign a single value to the tile, propagate the changes via calls to Eliminate
/// NOTE: Method mutates the CPBoard cpb parameter
/// </summary>
/// <param name="cpb"></param>
/// <param name="tileIndex"></param>
/// <param name="value"></param>
/// <returns></returns>
static public bool Assign(CPBoard cpb, int tileIndex, string value)
{
CDebug.Assert(value.Length == 1, "Cannot assign multiple values");
var values = cpb.Get(tileIndex);
// Cannot assign a value that is a not possible value of the tile
if (!values.Contains(value))
{
return(false);
}
// Attempt to eliminate values from peers
cpb.Set(tileIndex, value);
foreach (var peer in Peers[tileIndex])
{
if (!Eliminate(cpb, peer, value))
{
return(false);
}
}
return(true);
}
