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Résolution du diabolicube en julia
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snake_cube_julia.ipynb
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"# Résolution du casse-tête diabolicube"
]
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"Le diabolicube est un serpentin de bois, qui peut se replier sous forme de grand cube.\n",
"Il est composé de 64 petit cubes traversés par un grand élastique.\n",
"L'élastique traverse certains petits cubes sur toute leur longueur, entrant par une face et sortant par la face opposée.\n",
"Pour d'autres petits cubes, l'élastique forme un coude à l'intérieur, laissant un degré de liberté qui permet de changer la forme du serpentin. \n",
"\n",
"![diabolicube](http://www.ledelirant.fr/shop/img/p/34-243-thickbox.jpg)\n",
"\n",
"La solution présentée ici est une fonction julia qui prend en entrée la forme du serpentin (sous forme de vecteur de booléens) et qui sort un vecteur qui contient tous les pliages possibles en cube."
]
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"solve (generic function with 1 method)"
]
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"source": [
"function solve(turns)\n",
" axes = [CartesianIndex(1,0,0), CartesianIndex(0,1,0), CartesianIndex(0,0,1)]\n",
"\n",
" function recurse(cube, pos, axis, direction, n)\n",
" if !checkbounds(Bool, cube, pos) || cube[pos] != 0\n",
" return []\n",
" end\n",
"\n",
" cube[pos] = n\n",
"\n",
" if n == length(turns)\n",
" return [cube]\n",
" end\n",
"\n",
" new_pos = pos + axes[axis] * direction\n",
"\n",
" next = if turns[n+1]\n",
" [(a,d) for a = 1:3 if a != axis for d = [-1 1]]\n",
" else\n",
" [(axis, direction)]\n",
" end\n",
"\n",
" return [solution for (a,d) in next for solution in recurse(copy(cube), new_pos, a, d, n+1)]\n",
" end\n",
"\n",
" side = round(UInt8, cbrt(length(turns))) # Number of small cubes on a side\n",
" cube = zeros(Int8, side, side, side)\n",
" start_positions = [CartesianIndex(i,j,1) for i=1:side for j=1:side÷2]\n",
" return [solution for start_pos = start_positions for solution = recurse(copy(cube), start_pos, 1, 1, 1)]\n",
"end"
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"data": {
"text/plain": [
"64-element Array{Bool,1}:\n",
" false\n",
" false\n",
" true\n",
" false\n",
" false\n",
" true\n",
" false\n",
" false\n",
" true\n",
" false\n",
" false\n",
" true\n",
" true\n",
" ⋮\n",
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" true\n",
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" true\n",
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"source": [
"# false : cube traversé de part en part\n",
"# true : l'élastique forme un coude à l'intérieur du cube\n",
"turns = [\n",
" false, false, true,\n",
" false, false, true,\n",
" false, false, true,\n",
" false, false, true,\n",
" true,\n",
" false, false, true,\n",
" true,\n",
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" true,\n",
" true,\n",
" false, true,\n",
" true,\n",
" false, false, true,\n",
" false, true,\n",
" false, true,\n",
" true,\n",
" false, false, true, \n",
" true,\n",
" false, true,\n",
" true,\n",
" true,\n",
" true,\n",
" true,\n",
" true,\n",
" false, true,\n",
" true,\n",
" true,\n",
" true,\n",
" true,\n",
" false, false, true,\n",
" true,\n",
" false, false, false]"
]
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{
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{
"name": "stdout",
"output_type": "stream",
"text": [
" 8.995280 seconds (217.19 M allocations: 12.732 GiB, 16.49% gc time)\n"
]
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"data": {
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"source": [
"@time solutions = solve(turns)\n",
"length(solutions)"
]
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"data": {
"text/plain": [
"4×4×4 Array{Int8,3}:\n",
"[:, :, 1] =\n",
" 12 11 10 9\n",
" 1 24 25 8\n",
" 2 27 26 7\n",
" 3 4 5 6\n",
"\n",
"[:, :, 2] =\n",
" 13 22 31 32\n",
" 14 23 30 33\n",
" 15 28 29 34\n",
" 16 37 36 35\n",
"\n",
"[:, :, 3] =\n",
" 20 21 50 61\n",
" 19 48 49 62\n",
" 18 47 54 63\n",
" 17 38 55 64\n",
"\n",
"[:, :, 4] =\n",
" 43 44 51 60\n",
" 42 45 52 59\n",
" 41 46 53 58\n",
" 40 39 56 57"
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"execution_count": 4,
"metadata": {},
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"source": [
"solutions[2]"
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"using Plots\n",
"\n",
"for solution=solutions\n",
" coords = sort([CartesianIndex(x,y,z) for x=1:4 for y=1:4 for z=1:4], by=i->solution[i])\n",
" xs,ys,zs = [[x[i] for x=coords] for i=1:3]\n",
"\n",
" plt3d=Plots.plot(xs,ys,zs, zcolor=(1:64), marker=(2, 0.4, :inferno), legend=false)\n",
" display(plt3d)\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
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],
"source": [
"coords = sort([CartesianIndex(x,y,z) for x=1:4 for y=1:4 for z=1:4], by=i->solutions[1][i])\n",
"steps = copy(turns)\n",
"steps[[1,end]] = [true, true]\n",
"xyz = [x[i] for x=coords[steps], i=1:3]\n",
"\n",
"for i=2:size(xyz,1)\n",
" x,y,z = [xyz[1:i-1,j] for j=1:3]\n",
" plt = plot(x,y,z, color=:blue, legend=false, lims=(0,4), grid=false, dpi=60, axiscolor = invisible())\n",
" x,y,z = [xyz[i-1:i,j] for j=1:3]\n",
" plot!(plt, x,y,z, color=:red)\n",
" display(plt)\n",
"end"
]
},
{
"cell_type": "code",
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"metadata": {},
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}
],
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