30:T762,function placeTiles(board, tiles, {maxSolutions=1}={}) { // Pack the board. const initialState = board.pack(new BigUint64Array(1), 0)[0]; console.log("board", initialState.toString(16)); // Initialize an array of packed tile placements. const moves = new BigUint64Array(tiles.length + 1); moves[moves.length - 1] = initialState; // Initialize an empty list of complete solutions. const solutions = [ ]; // Precompute all possible placements of each tile. const placements = tiles.map(tile => tilePlacements(tile, board.width, board.height)); console.log("placements", placements.map(p => p.length)); // Calculate the total number of permutations to try. const nperms = placements.map(p => p.length).reduce((a,b) => a * b, 1); const idxVector = new Array(tiles.length); // Define a function to iterate over all possible placements of one tile. function placeOne(state, turn) { // Calculate all possible placements of this tile. const places = placements[turn]; for(let idx=0; idx a*(b+1), 1) / nperms; solutions.push({ solution, progress }); if(solutions.length >= maxSolutions) throw new Error("maxSolutions reached"); } else { // Try to place the remaining tiles with this placement. placeOne(state | places[idx], turn + 1); } } } try { placeOne(initialState, 0); } catch(e) { console.log("Got maxSolutions"); } return solutions; }31:T412, function tilePermutations(tile) { const {height, width, at} = tile; const size = Math.max(height, width), s = size - 1; const perms = [ ]; for(const flip of [ ([i,j]) => [i,j], // normal ([i,j]) => [j,i] // flipped ]) { for(const rotate of [ ([i,j]) => [i,j], // normal ([i,j]) => [j,s-i], // rotate 90 ([i,j]) => [s-i,s-j], // rotate 180 ([i,j]) => [s-j,i] // rotate 270 ]) { let values = new Uint8Array(size * size); for(let i=0; i < height; ++i) { for(let j=0; j < width; ++j) { if(tile.at(i,j)) { //if(at(i,j)) { const [i2,j2] = flip(rotate([i,j])); values[i2*size + j2] = 1; } } } const perm = new PixelData(size, size, values.slice()).squeezed(); // Check that this permutation is new. let isNew = true; for(const old of perms) if(perm.isEqualTo(old)) { isNew = false; break; } if(isNew) perms.push(perm); } } return perms; }32:[] 2e:{"title":"Calendar Tile Puzzle","cells":[{"id":0,"value":"# Calendar Tile Puzzle\n\nTools to analyze the [A-Puzzle-A-Day](https://www.dragonfjord.com/product/a-puzzle-a-day/) daily puzzle game. If you just want to know how easy or hard today's puzzle is, go [here](https://observablehq.com/@dkirkby/a-puzzle-a-day).\n\nAll of the 8 tile designs fit within a 3x4 grid. Design your own tile by clicking on the pixels below to toggle them on/off:","pinned":false,"hidden":false,"mode":"md"},{"id":12,"value":"viewof tile = PixelView({width:3, height:4, size:32, values: [1,1,1,1,0,0,1,0,0,1,0,0], editable:true})","pinned":false,"hidden":false,"mode":"ojs"},{"id":161,"value":"tilePlacesDisplay = {\n const S = 5;\n const packed = tilePlacements(tile, S, S);\n const unpacked = PixelData.unpack(packed, {height:S, width:S});\n return html`\n

\n ${unpacked.map(d => {\n return html.fragment`${new PixelView({size:12, data:d, editable: false})} `;\n })}\n

\n `;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":174,"value":"Here is the board design on an 8x8 grid, showing the squares that are prefilled so cannot take a tile:","pinned":false,"hidden":false,"mode":"md"},{"id":176,"value":"viewof board = PixelView({\n width:8, height:8, size:24,\n values: [0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1],\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":217,"value":"Here are the tiles to place in this board:","pinned":false,"hidden":false,"mode":"md"},{"id":191,"value":"html`

\n ${tiles.map((d,i) => {\n return html.fragment`${new PixelView({\n size:24, data:d, editable: false, fill:d3.schemeCategory10[i%10]\n })} `;\n })}\n

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":319,"value":"Here are some generated solutions:","pinned":false,"hidden":false,"mode":"md"},{"id":221,"value":"{\n const start = new Date();\n const solns = placeTiles(board, tiles, {maxSolutions:16});\n const stop = new Date();\n const elapsed = d3.format(\".3f\")((stop - start) / 1000);\n return html`\n

Calculated ${solns.length} solutions in ${elapsed} seconds

\n ${solns.map((d,i) => {\n return html.fragment`${new PixelView({\n size:24, data:d.solution, editable: false, fillScheme:d3.schemeCategory10\n })} `;\n })}\n

`;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":315,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":188,"value":"tiles = [\n new PixelData(4, 2, [1,1,1,0,1,0,1,0]),\n new PixelData(4, 2, [1,0,1,1,1,0,1,0]),\n new PixelData(2, 3, [1,0,1,1,1,1]),\n new PixelData(3, 3, [0,0,1,1,1,1,1,0,0]),\n new PixelData(2, 3, [1,1,1,1,1,1]),\n new PixelData(3, 3, [1,0,0,1,0,0,1,1,1]),\n new PixelData(2, 4, [0,0,1,1,1,1,1,0]),\n new PixelData(2, 3, [1,1,1,0,1,1]),\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":219,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":153,"value":"function tilePlacements(tile, w, h) {\n // Get all flipped and rotated variations.\n const perms = tilePermutations(tile);\n const placements = new BigUint64Array(w * h * perms.length);\n let idx = 0;\n for(const perm of perms) {\n const {width, height} = perm;\n for(let dy=0; dy < h - height + 1; ++dy) {\n for(let dx=0; dx < w - width + 1; ++dx) {\n perm.pack(placements, {idx, dx, dy});\n idx++;\n }\n }\n }\n // Return a trimmed array of packed values.\n return placements.slice(0, idx);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":28,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"id":80,"value":"html = htl.html","pinned":false,"hidden":false,"mode":"ojs"},{"id":5,"value":"import {PixelView,PixelData} from \"@dkirkby/pixels\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W32","stdlib":"1","titling":"auto"}