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Railway circuit (view source)

Revision as of 23:51, 9 July 2022

12,234 bytes added ,  1 year ago
Added vector reversal to equivalence logic, graphic display
(→‎{{header|Python}}: Reorganized code to be faster and to handle angles other than 30 degrees)
(Added vector reversal to equivalence logic, graphic display)
Line 607:
 
=={{header|Julia}}==
<pre>
<lang julia>import Main.≈, Main.+
Exhaustive search for complete railway (railroad track) circuits. A valid circuit begins and ends at the
same point facing in the same direction. Track are either right handed or left handed 30 degree
curves or are straight track that can be placed at -90, 0, or 90 degree angles from starting points.
 
Turns are defined by 1 for left turn, -1 for right turn, 0 for no turn (0 only with straight track)
 
Equivalent circuits are all in the same equivalence group, as follows:
 
The equivalence group of rotational (circular) permutations of the turns vector in product with the
complementation (scalar multiplication by -1) of those turns determines the equivalence group
for a turns vector.
 
So, the equivalence group is composed: (rotational permutations) X (scalar multiplication by -1)
 
There is another factor in equivalence groups not mentioned in the task as of June 2022: __vector reversal__.
If __vector reversal__ is included, (-1 1 -1 1 1 1 -1) is considered to group with (-1 1 1 1 -1 1 -1).
 
Furthermore, if chosen, reversal of the turns vector (not mentioned as a source of symmetry in the task)
is also multiplied in for a larger equivalence group:
 
(rotational permutations) X (scalar multiplication by -1) X (vector reversal)
 
Each unique and valid turn vector is chosen to be the maximum vector in its
equivalence group. All turns vectors must represent a closed path ending in a direction
identical to (mod 2π radians from) its initial vector direction on the plane.
 
Time required for an N turns solution is O(2^N) for curved track and O(3^N) for straight track.
 
Graphic displays of solutions are via a Gtk app and Cairo graphics.
</pre>
<lang ruby>
""" Rosetta Code task rosettacode.org/wiki/Railway_circuit. """
 
using Gtk, Cairo
 
""" Point is a 2D point in the plane: type T can be Float64 for this usage """
struct Point{T}
x::T
y::T
end
+(p::Point, q) = Point(p.x + q.x, p.y + q.y)
≈(p::Point, q) = isapprox(p.x, q.x, atol=0.0001) && isapprox(p.y, q.y, atol=0.0001)
 
""" add Points as vectors on plane """
const twelvesteps = [Point(sinpi(a/6), cospi(a/6)) for a in 1:12]
Base.:+(p::Point, q::Point) = Point(p.x + q.x, p.y + q.y)
const foursteps = [Point(sinpi(a/2), cospi(a/2)) for a in 1:4]
 
""" Tracks align if within absolute tolerance of 1 in 100 (with radius of curvature 1) """
function addsymmetries!(infound, turns)
Base.:≈(p::Point, q::Point) =
circularsymmetries(c) = [circshift(c, i) for i in 0:length(c)-1]
isapprox(p.x, q.x, atol = 0.01) && isapprox(p.y, q.y, atol = 0.01)
allsym = [circularsymmetries(turns); circularsymmetries([-x for x in turns])]
 
for c in allsym
""" a curve section 30 degrees is 1/12 of a circle angle or π/6 radians """
infound[c] = 1
const twelvesteps = [Point(sinpi(a / 6), cospi(a / 6)) for a = 1:12]
 
""" a straight section 90 degree angle is 1/4 of a circle angle or π/2 radians """
const foursteps = [Point(sinpi(a / 2), cospi(a / 2)) for a = 1:4]
 
""" Determine if vector `turns` is in an equivalence group with the vector `groupmember` """
function isinequivalencegroup(turns, groupmember)
for i in eachindex(turns)
groupmember == circshift(turns, i - 1) && return true
end
invturns = -1 .* turns
for i in eachindex(invturns)
groupmember == circshift(invturns, i - 1) && return true
end
return false
end
 
""" get the maximum member of the equivalence group containing vector turns """
function maximumofsymmetries(turns, groupsfound, reversals = false)
maxofgroup = turns
for i in eachindex(turns)
t = circshift(turns, i - 1)
push!(groupsfound, t)
if t > maxofgroup
maxofgroup = t
end
end
invturns = -1 .* turns
for i in eachindex(invturns)
t = circshift(invturns, i - 1)
push!(groupsfound, t)
if t > maxofgroup
maxofgroup = t
end
end
if reversals # [1 -1 1 1] => [1 1 -1 1]
revturns = reverse(turns)
for i in eachindex(revturns)
t = circshift(revturns, i - 1)
push!(groupsfound, t)
if t > maxofgroup
maxofgroup = t
end
end
revinvturns = -1 .* revturns
for i in eachindex(revinvturns)
t = circshift(revinvturns, i - 1)
push!(groupsfound, t)
if t > maxofgroup
maxofgroup = t
end
end
end
return maximum(allsym)maxofgroup
end
 
""" Returns true if the path of turns returns to starting point, and on that return is
function isclosedpath(turns, straight, start=Point(0.0, 0.0))
moving in a direction opposite to the starting direction.
if sum(turns) % (straight ? 4 : 12) != 0
"""
function isclosedpath(turns, straight, start = Point(0.0, 0.0))
if sum(turns) % (straight ? 4 : 12) != 0 # turns angle sum must be a multiple of 2π
return false
end
Line 647 ⟶ 735:
end
 
""" Draw the curves found, display on a Gtk canvas. """
function allvalidcircuits(N, doprint, straight=false)
function RailroadLayoutApp(turnsarray, savefilename; straight = false, reversals = false)
win = GtkWindow("Showing $(length(turnsarray)) circuits with $(length(turnsarray[1])) turns ($(reversals ? "excl" : "incl")uding reversed curves)",
720, 1000) |> (can = GtkCanvas())
set_gtk_property!(can, :expand, true)
 
@guarded draw(can) do widget
ctx = getgc(can)
h, w = height(can), width(can)
r = (w + h) / 96
nsquares = length(turnsarray[1])
gridx = isqrt(nsquares)
gridy = (nsquares + gridx - 1) ÷ gridx
x0, y0, = 6r, 6r
for (i, turns) in enumerate(turnsarray)
x, y = x0 + 6 * r * (i % gridx), y0 + 6 * r * ((i - 1) ÷ gridx)
angle = 0
if straight
for turn in turns
# black dot at layout track segment start point
set_source_rgb(ctx, 0, 0, 0)
arc(ctx, x, y, 2, 0, 2π)
fill(ctx)
# red line segment for track
set_source_rgb(ctx, 255, 0, 0)
angle += turn * π/2
newx, newy = x + r * cos(angle), y + r * sin(angle)
move_to(ctx, x, y)
line_to(ctx, newx, newy)
x, y = newx, newy
stroke(ctx)
end
else
for turn in turns
# black dot at layout track segment start point
set_source_rgb(ctx, 0, 0, 0)
arc(ctx, x, y, 2, 0, 2π)
fill(ctx)
# bluegreen dot at center of radius of curvature
set_source_rgb(ctx, 0, 120, 180)
centerangle = (-angle - turn * π/2) % 2π
centerx, centery = x - r * cos(centerangle), y - r * sin(centerangle)
arc(ctx, centerx, centery, 2, 0, 2π)
fill(ctx)
# red curve for track
set_source_rgb(ctx, 255, 0, 0)
centerangle2 = (centerangle + turn * π/6) % 2π
a1, a2 = min(centerangle, centerangle2), max(centerangle, centerangle2)
if a2 - a1 > π
a1, a2 = a2, a1
end
arc(ctx, centerx, centery, r, a1, a2)
stroke(ctx)
# compute x and y of next start point (endppoint of curve just drawn)
x, y = centerx + r * cos(centerangle2), centery + r * sin(centerangle2)
# compute next starting angle
angle -= turn * π/6
end
end
end
end
showall(win)
end
 
"""
function allvalidcircuits(N; verbose = false, straight = false, reversals = true, graphic = true)
"""
function allvalidcircuits(N; verbose = false, straight = false, reversals = false, graphic = false)
found = Vector{Vector{Int}}()
infoundgroupmembersfound = DictSet{Vector{Int},Int}()
println("\nFor N of $N and ", straight ? "straight" : "curved", " track, $(reversals ? "excl" : "incl")uding reversed curves: ")
for i in (straight ? (0:3^N-1) : (0:2^N-1))
turns = straight ?
straight ?
[d == 0 ? 0 : (d == 1 ? -1 : 1) for d in digits(i, base=3, pad=N)] :
[d == 0 ? -0 : (d == 1 ? 1 : -1) for d in digits(i, base =2 3, pad = N)] :
[d == 0 ? 1 : -1 for d in digits(i, base = 2, pad = N)]
if isclosedpath(turns, straight) && !haskey(infound, turns)
if isclosedpath(turns, straight) && !(turns in groupmembersfound)
canon = addsymmetries!(infound, turns)
if length(found) == 0 || all(t -> !isinequivalencegroup(turns, t), found)
doprint && println(canon)
canon = maximumofsymmetries(turns, groupmembersfound, reversals)
push!(found, canon)
verbose && println(canon)
push!(found, canon)
end
end
end
println("There are ",Found $(length(found), ") unique valid circuits.")
graphic && @async begin RailroadLayoutApp(deepcopy(found), "N$N.png"; reversals = reversals) end
return found
end
 
for i in= 12:4:3632, rev in false:true, str in false:true
str && i > 16 && continue
allvalidcircuits(i, i < 28)
allvalidcircuits(i; verbose = !str && i < 28, reversals = rev, straight = str, graphic = i == 24)
end
 
for i in 4:2:16
allvalidcircuits(i, i < 12, true)
end
</lang>{{out}}
<pre>
For N of 12 and curved track, including reversed curves:
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
There areFound 1 unique valid circuits.
 
For N of 1612 and curvedstraight track, including reversed curves:
Found 141 unique valid circuits.
 
For N of 12 and curved track, excluding reversed curves:
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
Found 1 unique valid circuits.
 
For N of 12 and straight track, excluding reversed curves:
Found 95 unique valid circuits.
 
For N of 16 and curved track, including reversed curves:
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1]
There areFound 1 unique valid circuits.
 
For N of 16 and straight track, including reversed curves:
Found 6045 unique valid circuits.
 
For N of 16 and curved track, excluding reversed curves:
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1]
Found 1 unique valid circuits.
 
For N of 16 and straight track, excluding reversed curves:
Found 3217 unique valid circuits.
 
For N of 20 and curved track, including reversed curves:
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1]
Line 689 ⟶ 865:
[1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1]
[1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1]
There areFound 6 unique valid circuits.
 
For N of 2420 and curved track, excluding reversed curves:
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1]
There are 40 unique valid circuits.
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1]
 
[1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1]
For N of 28 and curved track:
[1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1]
There are 293 unique valid circuits.
[1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1]
 
[1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1]
For N of 32 and curved track:
ThereFound are 27936 unique valid circuits.
 
For N of 36 and curved track:
There are 30117 unique valid circuits.
 
For N of 4 and straight track:
[1, 1, 1, 1]
There are 1 unique valid circuits.
 
For N of 624 and straightcurved track, including reversed curves:
[1, 1, 01, 1, 1, 01, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]
There are 1 unique valid circuits.
[1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1]
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1]
[1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1]
[1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1]
[1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1]
[1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1]
[1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1]
[1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1]
[1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1]
[1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1]
[1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1]
Found 40 unique valid circuits.
 
For N of 824 and straightcurved track, excluding reversed curves:
[1, 1, 01, 01, 1, 1, 01, 01, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 01, 1, 01, 1, 01, 1, 01, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]
[1, 1, 01, 1, 01, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1]
[1, 1, 1, 01, 1, 1, 1, 1, -1, 1, -1, -1, 01, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1]
There are 7 unique valid circuits.
[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1]
[1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1]
[1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1]
[1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1]
[1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1]
Found 27 unique valid circuits.
 
For N of 1028 and straightcurved track, including reversed curves:
Found 293 unique valid circuits.
[1, 1, 0, 0, 0, 1, 1, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 1, 0, 0]
[1, 1, -1, 1, 0, 1, 0, 1, 0, 0]
[1, 1, 0, 1, 0, 0, 1, 1, 0, -1]
[1, 1, 1, 0, -1, 0, -1, -1, 0, 0]
[1, 1, 0, 0, 1, 0, 1, 1, -1, 0]
[1, 1, 1, 0, 0, -1, -1, 0, -1, 0]
[1, 1, 1, 0, 0, -1, -1, -1, 1, -1]
[1, 1, 1, 0, 0, 1, 1, 1, -1, -1]
[1, 1, 0, 0, 1, 0, 1, 0, 1, -1]
[1, 1, 0, 0, 1, 1, -1, 1, 1, -1]
[1, 1, 1, 1, 1, 1, 0, 1, 1, 0]
[1, 1, 1, 1, -1, -1, 0, -1, -1, 0]
[1, 1, 1, -1, 1, 0, 1, 1, 0, -1]
[1, 1, 1, 1, -1, 0, -1, -1, 0, -1]
[1, 1, 1, -1, 0, 1, 1, 0, 1, -1]
[1, 1, 1, 1, 0, -1, -1, 0, -1, -1]
[1, 1, 1, 0, -1, 1, 1, 1, 0, -1]
[1, 1, 1, 0, 1, -1, -1, -1, 0, -1]
[1, 1, 0, 1, -1, 1, 1, 0, 1, -1]
[1, 1, -1, 1, 0, 1, 1, -1, 1, 0]
[1, 1, 1, -1, 0, 1, 1, 1, -1, 0]
[1, 1, 1, -1, 0, -1, -1, -1, 1, 0]
There are 23 unique valid circuits.
 
For N of 1228 and straightcurved track, excluding reversed curves:
ThereFound are 141174 unique valid circuits.
 
For N of 1432 and straightcurved track, including reversed curves:
ThereFound are 8712793 unique valid circuits.
 
For N of 1632 and straightcurved track, excluding reversed curves:
ThereFound are 60451485 unique valid circuits.
</pre>
 
Wherrera
4,103

edits

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