...

julia/CubeShapeCounting.jl

@@ -1,6 +1,117 @@
+include("Shape.jl")
 include("ImmutableOrientedShape.jl")
+include("Powerset.jl")
+include("TupleMisc.jl")
+include("plot.jl")
+using XXhash
+using Serialization
+using DataStructures
+using ArgParse
 
-function main(i::Int64)
+function main()
-    D = Dict{ImmutableOrientedShape}()
+    s = ArgParseSettings()
-    S = Stack{Int64}();
+    @add_arg_table s begin
+        "-g"
+            help = "generator"
+            arg_type = Int
+        "-l"
+            help = "list"
+            action = :store_true
+        "-p"
+            help = "plot n_cubes i_shape"
+            nargs = '+'
+            arg_type = Int
     end
+
+    parsed_args = parse_args(s)
+
+    generate = get(parsed_args, "g", nothing)
+    if generate !== nothing && generate > 0
+        scanForShapes(generate)
+    end
+    if get(parsed_args, "l", false)
+        listShapes()
+    end
+    plot = get(parsed_args, "p", nothing)
+    if length(plot) == 1
+        plotShapes(plot)
+    elseif length(plot) == 2
+        plotShape(plot)
+    end
+end
+
+function scanForShapes(MaxSize::Int64)
+    D = Dict{UInt, ImmutableOrientedShape}()
+    S = Stack{Shape}();
+    cube = getCube()
+    immutableCube = getImmutableOrientedShape(cube)
+    D[immutableCube.hash] = immutableCube
+    push!(S, cube)
+
+    while !isempty(S)
+        cube = pop!(S)
+        growableSpaces = collect(getPossibleNeighbors(cube))
+        acceptable_growth = MaxSize - length(cube.cubes)
+        for i ∈ 1:acceptable_growth
+            possibleGrowth = Powerset.getPowerSubSet(length(growableSpaces), i)
+            for j ∈ axes(possibleGrowth, 1)
+                cubesToAdd = growableSpaces[possibleGrowth[j, :]]
+                newShape = deepcopy(cube)
+                for c ∈ cubesToAdd
+                    push!(newShape, c)
+                end
+                collision = checkForCollision(newShape, D)
+                if !collision
+                    push!(S, newShape)
+                    immutableNewShape = getImmutableOrientedShape(newShape)
+                    D[immutableNewShape.hash] = immutableNewShape
+                end
+            end
+        end
+    end
+    sanitizedData = sanitize(D, MaxSize)
+    serialize("results.bin", sanitizedData)
+end
+
+function listShapes()
+    T = deserialize("results.bin")
+    print("size: ")
+    println(T[1])
+    for V ∈ T[2]
+        for v ∈ V
+            println(v)
+        end
+    end
+end
+
+function checkForCollision(S::Shape, D::Dict{UInt, ImmutableOrientedShape})
+    for i ∈ 1:24
+        hash = hashList(S.orderedLists[i])
+        value = get(D, hash, nothing)
+        if value !== nothing && hash == value.hash
+            return true
+        end
+    end
+    return false
+end
+
+function hashList(L::Vector{Tuple{Int64, Int64, Int64}})
+    diffList = Vector{Tuple{Int64, Int64, Int64}}(undef, length(L)-1)
+    for i ∈ eachindex(diffList)
+        diffList[i] = L[i+1] - L[i]
+    end
+    return xxh3_64(diffList)
+end
+
+function sanitize(D::Dict{UInt, ImmutableOrientedShape}, size::Int64)
+    data = Vector{Vector{Vector{Tuple{Int64, Int64, Int64}}}}(undef, size)
+    for i ∈ eachindex(data)
+        data[i] = Vector{Vector{Tuple{Int64, Int64, Int64}}}(undef, 0)
+    end
+    for (K, V) ∈ D
+        push!(data[length(V.cubes)], V.cubes)
+    end
+    return (size, data)
+end
+
+main()

julia/ImmutableOrientedShape.jl

@@ -1,11 +1,10 @@
-include("Shape.jl")
 using XXhash
 
 struct ImmutableOrientedShape
-    cubes::Vector{Tuple{Int8, Int8, Int8}}
+    cubes::Vector{Tuple{Int64, Int64, Int64}}
     hash::UInt
 end
 
 function getImmutableOrientedShape(S::Shape)
-    shape = ImmutableOrientedShape(S.orderedLists[1], xxh3_64(S.orderedLists[1]))
+    shape = ImmutableOrientedShape(S.orderedLists[1], hashList(S.orderedLists[1]))
 end

julia/Plot.jl

@@ -0,0 +1,134 @@
+using PyCall
+using Serialization
+
+py"""
+import numpy as np
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.pyplot as plt
+
+def plotShapePY(v):
+    fig = plt.figure()
+    ax = fig.add_subplot(111, projection='3d')
+    plotSingleShape(ax, v)
+    
+    plt.show()
+
+def plotShapesPY(vs):
+    n = len(vs)
+    if n == 1:
+        plotShapePY(vs[0])
+    else:
+        fig = plt.figure()
+        print(n)
+        n_rows = int(np.ceil(0.6*n))
+        n_cols = int(np.ceil(n/n_rows))
+        print(n_rows)
+        print(n_cols)
+        for i in range(len(vs)):
+            v = vs[i]
+            ax = fig.add_subplot(n_cols, n_rows, i+1, projection='3d')
+            plotSingleShape(ax, v)
+        plt.show()
+
+def plotSingleShape(ax, v):
+    l = len(v)
+
+    for i in range(l):
+        X1, Y1, Z1 = horizontalPlane(v[i][0]  , v[i][1]  , v[i][2]  )
+        X2, Y2, Z2 = horizontalPlane(v[i][0]  , v[i][1]  , v[i][2]+1)
+        X3, Y3, Z3 = verticalPlaneX( v[i][0]  , v[i][1]  , v[i][2]  )
+        X4, Y4, Z4 = verticalPlaneX( v[i][0]  , v[i][1]+1, v[i][2]  )
+        X5, Y5, Z5 = verticalPlaneY( v[i][0]  , v[i][1]  , v[i][2]  )
+        X6, Y6, Z6 = verticalPlaneY( v[i][0]+1, v[i][1]  , v[i][2]  )
+
+        ax.plot_surface(X1, Y1, Z1, alpha=0.8, color='orange')
+        ax.plot_surface(X2, Y2, Z2, alpha=0.8, color='orange')
+        ax.plot_surface(X3, Y3, Z3, alpha=0.8, color='green' )
+        ax.plot_surface(X4, Y4, Z4, alpha=0.8, color='green' )
+        ax.plot_surface(X5, Y5, Z5, alpha=0.8, color='cyan'  )
+        ax.plot_surface(X6, Y6, Z6, alpha=0.8, color='cyan'  )
+
+    x_min = np.inf
+    x_max = -np.inf
+    y_min = np.inf
+    y_max = -np.inf
+    z_min = np.inf
+    z_max = -np.inf
+    for i in range(l):
+        x_min = np.min([x_min, v[i][0]])
+        x_max = np.max([x_max, v[i][0]])
+        y_min = np.min([y_min, v[i][1]])
+        y_max = np.max([y_max, v[i][1]])
+        z_min = np.min([z_min, v[i][2]])
+        z_max = np.max([z_max, v[i][2]])
+    
+    biggest_length = max([x_max-x_min, y_max-y_min, z_max-z_min])
+    x_diff = (biggest_length - (x_max - x_min)) / 2
+    x_lim_min = x_min - x_diff
+    x_lim_max = x_max + x_diff
+    
+    y_diff = (biggest_length - (y_max - y_min)) / 2
+    y_lim_min = y_min - y_diff
+    y_lim_max = y_max + y_diff
+    
+    z_diff = (biggest_length - (z_max - z_min)) / 2
+    z_lim_min = z_min - z_diff
+    z_lim_max = z_max + z_diff
+    
+    ax.scatter([x_lim_min, x_lim_max+1], [y_lim_min, y_lim_max+1], [z_lim_min, z_lim_max+1], alpha=0)
+
+def getPoints(a):
+    x = a[0]
+    y = a[1]
+    z = a[2]
+    p = [
+        [x,   y,   z  ],
+        [x+1, y,   z  ],
+        [x+1, y+1, z  ],
+        [x,   y+1, z  ],
+        [x,   y,   z+1],
+        [x+1, y,   z+1],
+        [x+1, y+1, z+1],
+        [x,   y+1, z+1]
+    ]
+    return p
+
+def horizontalPlane(x, y, z):
+    one = np.ones(4).reshape(2, 2)
+    r1 = [x, x + 1]
+    r2 = [y, y + 1]
+    X, Y = np.meshgrid(r1, r2)
+    Z = one*z
+    return X, Y, Z
+
+def verticalPlaneX(x, y, z):
+    one = np.ones(4).reshape(2, 2)
+    r1 = [x, x + 1]
+    r2 = [z, z + 1]
+    X, Z = np.meshgrid(r1, r2)
+    Y = one*y
+    return X, Y, Z
+    
+
+def verticalPlaneY(x, y, z):
+    one = np.ones(4).reshape(2, 2)
+    r1 = [y, y + 1]
+    r2 = [z, z + 1]
+    Y, Z = np.meshgrid(r1, r2)
+    X = one*x
+    return X, Y, Z
+"""
+
+function plotShape(t::Vector{Int64})
+    T = deserialize("results.bin")
+    v = T[2][t[1]][t[2]]
+
+    py"plotShapePY"(v)
+end
+
+function plotShapes(t::Vector{Int64})
+    T = deserialize("results.bin")
+    v = T[2][t[1]]
+
+    py"plotShapesPY"(v)
+end

julia/Powerset.jl

@@ -4,6 +4,8 @@ global _calculatedPowerSets = Matrix{Int64}(undef, 1, 0)
 global _grownUntil = 0
 
 function getPowerSet(setSize::Integer)
+    global _calculatedPowerSets
+    global _grownUntil
     wantedPowerSetSize = 2^setSize
     if setSize <= _grownUntil
         return _calculatedPowerSets[1:wantedPowerSetSize, 1:setSize]
@@ -29,13 +31,19 @@ end
 
 function getPowerSubSet(setSize::Integer, subSetSize::Integer)
     PowerSet = getPowerSet(setSize)
-    setSizes = dropdim(sum(Powerset, dims = 2), dims = 2)
+    setSizes = dropdims(sum(PowerSet, dims = 2), dims = 2)
     powerSubSetSize = binomial(setSize, subSetSize)
-    powerSubSets = Matrix{Int64}(undef, powerSubSetSize, setSize)
+    powerSubSets = Matrix{Int64}(undef, powerSubSetSize, subSetSize)
     j = 1
-    for i ∈ 1:setSize
+    for i ∈ axes(PowerSet, 1)
         if setSizes[i] == subSetSize
-            powerSubSets[j, :] = PowerSet[i, :]
+            l = 1
+            for k ∈ axes(PowerSet, 2)
+                if PowerSet[i, k] == 1
+                    powerSubSets[j, l] = k
+                    l += 1
+                end
+            end
             j += 1
         end
     end

julia/Rotations.jl

@@ -0,0 +1,59 @@
+
+const global _rot01(x) = (x[1], x[2], x[3])
+const global _rot02(x) = (x[2], x[3], x[1])
+const global _rot03(x) = (x[3], x[1], x[2])
+
+const global _rot04(x) = (x[1], x[2], -x[3])
+const global _rot05(x) = (x[2], x[3], -x[1])
+const global _rot06(x) = (x[3], x[1], -x[2])
+
+const global _rot07(x) = (x[1], -x[2], x[3])
+const global _rot08(x) = (x[2], -x[3], x[1])
+const global _rot09(x) = (x[3], -x[1], x[2])
+
+const global _rot10(x) = (x[1], -x[2], -x[3])
+const global _rot11(x) = (x[2], -x[3], -x[1])
+const global _rot12(x) = (x[3], -x[1], -x[2])
+
+const global _rot13(x) = (-x[1], x[2], x[3])
+const global _rot14(x) = (-x[2], x[3], x[1])
+const global _rot15(x) = (-x[3], x[1], x[2])
+
+const global _rot16(x) = (-x[1], x[2], -x[3])
+const global _rot17(x) = (-x[2], x[3], -x[1])
+const global _rot18(x) = (-x[3], x[1], -x[2])
+
+const global _rot19(x) = (-x[1], -x[2], x[3])
+const global _rot20(x) = (-x[2], -x[3], x[1])
+const global _rot21(x) = (-x[3], -x[1], x[2])
+
+const global _rot22(x) = (-x[1], -x[2], -x[3])
+const global _rot23(x) = (-x[2], -x[3], -x[1])
+const global _rot24(x) = (-x[3], -x[1], -x[2])
+
+const global Rotations = [
+    _rot01,
+    _rot02,
+    _rot03,
+    _rot04,
+    _rot05,
+    _rot06,
+    _rot07,
+    _rot08,
+    _rot09,
+    _rot10,
+    _rot11,
+    _rot12,
+    _rot13,
+    _rot14,
+    _rot15,
+    _rot16,
+    _rot17,
+    _rot18,
+    _rot19,
+    _rot20,
+    _rot21,
+    _rot22,
+    _rot23,
+    _rot24
+]

julia/Shape.jl

@@ -1,28 +1,40 @@
-include("SortingModifiers.jl")
+include("Rotations.jl")
 
 struct Shape
-    cubes::Set{Tuple{Int8, Int8, Int8}}
+    cubes::Set{Tuple{Int64, Int64, Int64}}
-    recentCubes::Set{Tuple{Int8, Int8, Int8}}
+    recentCubes::Set{Tuple{Int64, Int64, Int64}}
-    orderedLists::Vector{Vector{Tuple{Int8, Int8, Int8}}}
+    orderedLists::Vector{Vector{Tuple{Int64, Int64, Int64}}}
 end
 
-function trypush!(S::Shape, t::Tuple{Int8, Int8, Int8})
+function Base.:push!(S::Shape, t::Tuple{Int64, Int64, Int64})
-    if t ∈ S.cubes
-        return false
-    else
     push!(S.cubes, t)
     for i ∈ 1:24
-            index = searchsortedfirst(S.orderedLists[i], t, by=SortingModifiers[i])
+        t_rot = Rotations[i](t)
-            insert!(S.orderedLists, index, t)
+        index = searchsortedfirst(S.orderedLists[i], t_rot)
+        insert!(S.orderedLists[i], index, t_rot)
     end
-        return true
 end
+
+function getPossibleNeighbors(S::Shape)
+    possibleSpots = Set{Tuple{Int64, Int64, Int64}}()
+    for p ∈ S.cubes
+        push!(possibleSpots,
+            p + (1, 0, 0),
+            p + (0, 1, 0),
+            p + (0, 0, 1),
+            p - (1, 0, 0),
+            p - (0, 1, 0),
+            p - (0, 0, 1)
+        )
+    end
+    spots = setdiff(possibleSpots, S.cubes)
+    return spots
 end
 
 function getCube()
     return Shape(
-        {(0, 0, 0)},
+        Set([(0, 0, 0)]),
-        {(0, 0, 0)},
+        Set([(0, 0, 0)]),
         [
             [(0, 0, 0)],
             [(0, 0, 0)],

julia/SortingModifiers.jl

@@ -1,59 +0,0 @@
-
-const global _comp01(x) = (x[1], x[2], x[3])
-const global _comp02(x) = (x[2], x[3], x[1])
-const global _comp03(x) = (x[3], x[1], x[2])
-
-const global _comp04(x) = (x[1], x[2], -x[3])
-const global _comp05(x) = (x[2], x[3], -x[1])
-const global _comp06(x) = (x[3], x[1], -x[2])
-
-const global _comp07(x) = (x[1], -x[2], x[3])
-const global _comp08(x) = (x[2], -x[3], x[1])
-const global _comp09(x) = (x[3], -x[1], x[2])
-
-const global _comp10(x) = (x[1], -x[2], -x[3])
-const global _comp11(x) = (x[2], -x[3], -x[1])
-const global _comp12(x) = (x[3], -x[1], -x[2])
-
-const global _comp13(x) = (-x[1], x[2], x[3])
-const global _comp14(x) = (-x[2], x[3], x[1])
-const global _comp15(x) = (-x[3], x[1], x[2])
-
-const global _comp16(x) = (-x[1], x[2], -x[3])
-const global _comp17(x) = (-x[2], x[3], -x[1])
-const global _comp18(x) = (-x[3], x[1], -x[2])
-
-const global _comp19(x) = (-x[1], -x[2], x[3])
-const global _comp20(x) = (-x[2], -x[3], x[1])
-const global _comp21(x) = (-x[3], -x[1], x[2])
-
-const global _comp22(x) = (-x[1], -x[2], -x[3])
-const global _comp23(x) = (-x[2], -x[3], -x[1])
-const global _comp24(x) = (-x[3], -x[1], -x[2])
-
-const global SortingModifiers = [
-    _comp01,
-    _comp02,
-    _comp03,
-    _comp04,
-    _comp05,
-    _comp06,
-    _comp07,
-    _comp08,
-    _comp09,
-    _comp10,
-    _comp11,
-    _comp12,
-    _comp13,
-    _comp14,
-    _comp15,
-    _comp16,
-    _comp17,
-    _comp18,
-    _comp19,
-    _comp20,
-    _comp21,
-    _comp22,
-    _comp23,
-    _comp24
-]

julia/TupleMisc.jl

@@ -0,0 +1,3 @@
+
+Base.:+(X::Tuple{Integer, Integer, Integer}, Y::Tuple{Integer, Integer, Integer}) = (X[1]+Y[1], X[2]+Y[2], X[3]+Y[3])
+Base.:-(X::Tuple{Integer, Integer, Integer}, Y::Tuple{Integer, Integer, Integer}) = (X[1]-Y[1], X[2]-Y[2], X[3]-Y[3])