public void SolveTenBlockPuzzle(out FiveBlocks bottomLayerOfSolution, out FiveBlocks topLayerOfSolution)
{
// get the blocks needed for the 10 piece wooden puzzle
BlockFactory blockFactory = new BlockFactory();
TenBlocks tenBlocks = blockFactory.GetPuzzleWithTenBlocks();
// get a collection of all 5 block variations including all possible flipped blocks.
// each of these FiveBlocks objects forms the bottom of a potential solution, until disproved
HashSet <FiveBlocks> listsOfFiveBlocks = CalculateAllFiveBlockVariationsIncludingReversals(tenBlocks);
CalculateLayerOfSolution(out bottomLayerOfSolution, out topLayerOfSolution, tenBlocks, listsOfFiveBlocks);
}
public TenBlocks GetPuzzleWithTenBlocks()
{
List <Block> blocks = new List <Block>();
// creating blocks from real blocks. turning the blocks so that the more "interesting" stuff is on the left, just to make recognising blocks easier.
blocks.Add(
CreateBlock(
1, CreateBlockSlotArray1()));
blocks.Add(
CreateBlock(
2, CreateBlockSlotArray2()));
blocks.Add(
CreateBlock(
3, CreateBlockSlotArray3()));
blocks.Add(
CreateBlock(
4, CreateBlockSlotArray4()));
blocks.Add(
CreateBlock(
5, CreateBlockSlotArray5()));
blocks.Add(
CreateBlock(
6, CreateBlockSlotArray6()));
blocks.Add(
CreateBlock(
7, CreateBlockSlotArray7()));
blocks.Add(
CreateBlock(
8, CreateBlockSlotArray8()));
blocks.Add(
CreateBlock(
9, CreateBlockSlotArray9()));
blocks.Add(
CreateBlock(
10, CreateBlockSlotArray10()));
TenBlocks tenBlocks = new TenBlocks(blocks);
return(tenBlocks);
}
private void CalculateLayerOfSolution(out FiveBlocks bottomLayerOfSolution, out FiveBlocks topLayerOfSolution, TenBlocks tenBlocks, HashSet <FiveBlocks> listsOfFiveBlocks)
{
bottomLayerOfSolution = null;
topLayerOfSolution = null;
foreach (var bottomFiveBlocks in listsOfFiveBlocks)
{
// now get the remaining five blocks
FiveBlocks topFiveBlocks = new FiveBlocks(tenBlocks.Where(b => !bottomFiveBlocks.Contains(b)).ToList());
Dictionary <Block, int> blockToIndexMaping = GetTopLayerBlockMappingToBottomLayerIndex(bottomFiveBlocks, topFiveBlocks);
if (blockToIndexMaping.Count == 5)
{
// this means we've matched all 5! we're done!
// assign the layers
bottomLayerOfSolution = bottomFiveBlocks;
topLayerOfSolution = new FiveBlocks(blockToIndexMaping.Keys.ToList());
break;
}
}
}
private HashSet <FiveBlocks> CalculateAllFiveBlockVariationsIncludingReversals(TenBlocks tenBlocks)
{
// all variations of true and false:
// - true = not reversed block
// - false = reversed block
Variations <bool> flagVariations = CalculateAndPrintFlagVariations();
var blockVariations = new Variations <Block>(tenBlocks, 5);
HashSet <FiveBlocks> listsOfFiveBlocks = new HashSet <FiveBlocks>();
foreach (var variation in blockVariations)
{
// now we have an ordered list of 5 blocks.
// for each permutation, there 2 ^ 5 = 32 ways to flip the pieces
foreach (List <bool> flagVariation in flagVariations)
{
List <Block> finalFixedList = new List <Block>();
for (int i = 0; i < flagVariation.Count; i++)
{
// use the flag to choose reversed block or not
// TODO: memoization can easily be used here to not keep reversing the blocks
finalFixedList.Add(flagVariation[i] ? variation[i] : new Block(variation[i]));
}
// final list for the bottom is built
listsOfFiveBlocks.Add(new FiveBlocks(finalFixedList));
}
}
return(listsOfFiveBlocks);
}
