Faces from a mesh
You are encouraged to solve this task according to the task description, using any language you may know.
A mesh defining a surface has uniquely numbered vertices, and named, simple-polygonal faces described usually by an ordered list of edge numbers going around the face,
For example:
External image of two faces
Rough textual version without edges:
1
17
7 A
B
11
23
- A is the triangle (1, 11, 7), or equally (7, 11, 1), going anti-clockwise, or
any of all the rotations of those ordered vertices.
1
7 A
11
- B is the four-sided face (1, 17, 23, 11), or equally (23, 17, 1, 11) or any
of their rotations.
1
17
B
11
23
Let's call the above the perimeter format as it traces around the perimeter.
- A second format
A separate algorithm returns polygonal faces consisting of a face name and an unordered set of edge definitions for each face.
- A single edge is described by the vertex numbers at its two ends, always in
ascending order.
- All edges for the face are given, but in an undefined order.
For example face A could be described by the edges (1, 11), (7, 11), and (1, 7) (The order of each vertex number in an edge is ascending, but the order in which the edges are stated is arbitrary).
Similarly face B could be described by the edges (11, 23), (1, 17), (17, 23), and (1, 11) in arbitrary order of the edges.
Let's call this second format the edge format.
- Task
1. Write a routine to check if two perimeter formatted faces have the same perimeter. Use it to check if the following pairs of perimeters are the same:
Q: (8, 1, 3) R: (1, 3, 8) U: (18, 8, 14, 10, 12, 17, 19) V: (8, 14, 10, 12, 17, 19, 18)
2. Write a routine and use it to transform the following faces from edge to perimeter format.
E: {(1, 11), (7, 11), (1, 7)}
F: {(11, 23), (1, 17), (17, 23), (1, 11)}
G: {(8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)}
H: {(1, 3), (9, 11), (3, 11), (1, 11)}
Show your output here.
11l
<lang 11l>F perim_equal(p1, =p2)
I p1.len != p2.len | Set(p1) != Set(p2)
R 0B
I any((0 .< p1.len).map(n -> @p2 == (@p1[n ..] [+] @p1[0 .< n])))
R 1B
p2 = reversed(p2)
R any((0 .< p1.len).map(n -> @p2 == (@p1[n ..] [+] @p1[0 .< n])))
F edge_to_periphery(e)
V edges = sorted(e)
[Int] p
I !edges.empty
p = [edges[0][0], edges[0][1]]
edges.pop(0)
V last = I !p.empty {p.last} E -1
L !edges.empty
L(ij) edges
V (i, j) = ij
I i == last
p.append(j)
last = j
edges.pop(L.index)
L.break
E I j == last
p.append(i)
last = i
edges.pop(L.index)
L.break
L.was_no_break
R ‘>>>Error! Invalid edge format<<<’
R String(p[0 .< (len)-1])
print(‘Perimeter format equality checks:’) L(eq_check) [(‘Q’, [8, 1, 3],
‘R’, [1, 3, 8]),
(‘U’, [18, 8, 14, 10, 12, 17, 19],
‘V’, [8, 14, 10, 12, 17, 19, 18])]
V (n1, p1, n2, p2) = eq_check
V eq = I perim_equal(p1, p2) {‘==’} E ‘!=’
print(‘ ’n1‘ ’eq‘ ’n2)
print("\nEdge to perimeter format translations:") V edge_d = [‘E’ = [(1, 11), (7, 11), (1, 7)],
‘F’ = [(11, 23), (1, 17), (17, 23), (1, 11)],
‘G’ = [(8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)],
‘H’ = [(1, 3), (9, 11), (3, 11), (1, 11)]]
L(name, edges) edge_d
print(‘ ’name‘: ’edges"\n -> "edge_to_periphery(edges))</lang>
- Output:
Perimeter format equality checks:
Q == R
U == V
Edge to perimeter format translations:
E: [(1, 11), (7, 11), (1, 7)]
-> [1, 7, 11]
F: [(11, 23), (1, 17), (17, 23), (1, 11)]
-> [1, 11, 23, 17]
G: [(8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)]
-> [8, 14, 10, 12, 17, 19, 18]
H: [(1, 3), (9, 11), (3, 11), (1, 11)]
-> >>>Error! Invalid edge format<<<
Go
<lang go>package main
import (
"fmt" "sort"
)
// Check a slice contains a value. func contains(s []int, f int) bool {
for _, e := range s {
if e == f {
return true
}
}
return false
}
// Assumes s1, s2 are of same length. func sliceEqual(s1, s2 []int) bool {
for i := 0; i < len(s1); i++ {
if s1[i] != s2[i] {
return false
}
}
return true
}
// Reverses slice in place. func reverse(s []int) {
for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
s[i], s[j] = s[j], s[i]
}
}
// Check two perimeters are equal. func perimEqual(p1, p2 []int) bool {
le := len(p1)
if le != len(p2) {
return false
}
for _, p := range p1 {
if !contains(p2, p) {
return false
}
}
// use copy to avoid mutating 'p1'
c := make([]int, le)
copy(c, p1)
for r := 0; r < 2; r++ {
for i := 0; i < le; i++ {
if sliceEqual(c, p2) {
return true
}
// do circular shift to right
t := c[le-1]
copy(c[1:], c[0:le-1])
c[0] = t
}
// now process in opposite direction
reverse(c)
}
return false
}
type edge [2]int
// Translates a face to perimeter format. func faceToPerim(face []edge) []int {
// use copy to avoid mutating 'face'
le := len(face)
if le == 0 {
return nil
}
edges := make([]edge, le)
for i := 0; i < le; i++ {
// check edge pairs are in correct order
if face[i][1] <= face[i][0] {
return nil
}
edges[i] = face[i]
}
// sort edges in ascending order
sort.Slice(edges, func(i, j int) bool {
if edges[i][0] != edges[j][0] {
return edges[i][0] < edges[j][0]
}
return edges[i][1] < edges[j][1]
})
var perim []int
first, last := edges[0][0], edges[0][1]
perim = append(perim, first, last)
// remove first edge
copy(edges, edges[1:])
edges = edges[0 : le-1]
le--
outer:
for le > 0 {
for i, e := range edges {
found := false
if e[0] == last {
perim = append(perim, e[1])
last, found = e[1], true
} else if e[1] == last {
perim = append(perim, e[0])
last, found = e[0], true
}
if found {
// remove i'th edge
copy(edges[i:], edges[i+1:])
edges = edges[0 : le-1]
le--
if last == first {
if le == 0 {
break outer
} else {
return nil
}
}
continue outer
}
}
}
return perim[0 : len(perim)-1]
}
func main() {
fmt.Println("Perimeter format equality checks:")
areEqual := perimEqual([]int{8, 1, 3}, []int{1, 3, 8})
fmt.Printf(" Q == R is %t\n", areEqual)
areEqual = perimEqual([]int{18, 8, 14, 10, 12, 17, 19}, []int{8, 14, 10, 12, 17, 19, 18})
fmt.Printf(" U == V is %t\n", areEqual)
e := []edge{{7, 11}, {1, 11}, {1, 7}}
f := []edge{{11, 23}, {1, 17}, {17, 23}, {1, 11}}
g := []edge{{8, 14}, {17, 19}, {10, 12}, {10, 14}, {12, 17}, {8, 18}, {18, 19}}
h := []edge{{1, 3}, {9, 11}, {3, 11}, {1, 11}}
fmt.Println("\nEdge to perimeter format translations:")
for i, face := range [][]edge{e, f, g, h} {
perim := faceToPerim(face)
if perim == nil {
fmt.Printf(" %c => Invalid edge format\n", i + 'E')
} else {
fmt.Printf(" %c => %v\n", i + 'E', perim)
}
}
}</lang>
- Output:
Perimeter format equality checks: Q == R is true U == V is true Edge to perimeter format translations: E => [1 7 11] F => [1 11 23 17] G => [8 14 10 12 17 19 18] H => Invalid edge format
Haskell
<lang haskell>import Data.List (find, delete, (\\)) import Control.Applicative ((<|>))
newtype Perimeter a = Perimeter [a]
deriving Show
instance Eq a => Eq (Perimeter a) where
Perimeter p1 == Perimeter p2 =
null (p1 \\ p2)
&& ((p1 `elem` zipWith const (iterate rotate p2) p1)
|| Perimeter p1 == Perimeter (reverse p2))
rotate lst = zipWith const (tail (cycle lst)) lst
toEdges :: Ord a => Perimeter a -> Maybe (Edges a) toEdges (Perimeter ps)
| allDifferent ps = Just . Edges $ zipWith ord ps (tail (cycle ps)) | otherwise = Nothing where ord a b = if a < b then (a, b) else (b, a)
allDifferent [] = True allDifferent (x:xs) = all (x /=) xs && allDifferent xs
newtype Edges a = Edges [(a, a)]
deriving Show
instance Eq a => Eq (Edges a) where
e1 == e2 = toPerimeter e1 == toPerimeter e2
toPerimeter :: Eq a => Edges a -> Maybe (Perimeter a) toPerimeter (Edges ((a, b):es)) = Perimeter . (a :) <$> go b es
where
go x rs
| x == a = return []
| otherwise = do
p <- find ((x ==) . fst) rs <|> find ((x ==) . snd) rs
let next = if fst p == x then snd p else fst p
(x :) <$> go next (delete p rs)</lang>
First task.
λ> Perimeter [8,1,3] == Perimeter [1,3,8] True λ> Perimeter [8,1,3] == Perimeter [1,8,3] True λ> Perimeter [18,8,14,10,12,17,19] == Perimeter [8,14,10,12,17,19,18] True λ> Perimeter [18,8,14,10,12,17,19] == Perimeter [8,14,10,12,17,19] False λ> Perimeter [18,8,14,10,12,17,19] == Perimeter [8,14,10,12,17,18,19] False
Second task
λ> toPerimeter (Edges [(1,11),(7,11),(1,7)]) Just (Perimeter [1,11,7]) λ> toPerimeter (Edges [(11,23),(1,17),(17,23),(1,11)]) Just (Perimeter [11,23,17,1]) λ> toPerimeter (Edges [(8,14),(17,19),(10,12),(10,14),(12,17),(8,18),(18,19)]) Just (Perimeter [8,14,10,12,17,19,18]) λ> toPerimeter (Edges [(1,3),(9,11),(3,11),(1,11)]) Nothing
J
First task:
NB. construct a list of all rotations of one of the faces NB. including all rotations of the reversed list. NB. Find out if the other face is a member of this list. NB. ,&:rotations -> append, but first enlist the rotations. rotations=. |."0 1~ i.@# reverse=: |. same_perimeter=: e. (,&:rotations reverse) (3, 1, 8)same_perimeter(8, 1, 3) 1 (18, 8, 14, 10, 12, 17, 19)same_perimeter(8, 14, 10, 12, 17, 19, 18) 1
Secondly: <lang J> edge_to_node=: 3 :0
assert. 2 = #/.~ , y [ 'expect each node to appear twice'
oel=. 1 2 {. y
Y=. }. y
while. # Y do.
i =. <. -: 1 i.~ , Y (e."1) {: oel
assert. 0 < # i [ 'isolated edge detected'
oel =. oel , i { Y
Y =. i ({. , (}.~ >:)~) Y
end.
~. , oel
) </lang>
boxdraw_j_ 0
]TESTS=: ([: < _2 ]\ ".);._2'{}'-.~0 :0
{(1, 11), (7, 11), (1, 7)}
{(11, 23), (1, 17), (17, 23), (1, 11)}
{(8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)}
{(1, 3), (9, 11), (3, 11), (1, 11)}
)
┌────┬─────┬─────┬────┐
│1 11│11 23│ 8 14│1 3│
│7 11│ 1 17│17 19│9 11│
│1 7│17 23│10 12│3 11│
│ │ 1 11│10 14│1 11│
│ │ │12 17│ │
│ │ │ 8 18│ │
│ │ │18 19│ │
└────┴─────┴─────┴────┘
edge_to_node ::('failure'"_)&.> TESTS
┌──────┬──────────┬───────────────────┬───────┐
│1 11 7│11 23 17 1│8 14 10 12 17 19 18│failure│
└──────┴──────────┴───────────────────┴───────┘
edge_to_node _1 {:: TESTS
|assertion failure: edge_to_node
| 2=#/.~,y['expect each node to appear twice'
Julia
<lang julia>iseq(f, g) = any(n -> f == circshift(g, n), 1:length(g))
function toface(evec)
try
ret, edges = collect(evec[1]), copy(evec[2:end])
while !isempty(edges)
i = findfirst(x -> ret[end] == x[1] || ret[end] == x[2], edges)
push!(ret, ret[end] == edges[i][1] ? edges[i][2] : edges[i][1])
deleteat!(edges, i)
end
return ret[1:end-1]
catch
println("Invalid edges vector: $evec")
exit(1)
end
end
const faces1 = [
[[8, 1, 3], [1, 3, 8]], [[18, 8, 14, 10, 12, 17, 19], [8, 14, 10, 12, 17, 19, 18]]
]
const faces2 = [
[(1, 11), (7, 11), (1, 7)], [(11, 23), (1, 17), (17, 23), (1, 11)], [(8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)], [(1, 3), (9, 11), (3, 11), (1, 11)]
]
for faces in faces1
println("Faces are ", iseq(faces[1], faces[2]) ? "" : "not ", "equivalent.")
end
for face in faces2
println(toface(face))
end
</lang>
- Output:
Faces are equivalent.
Faces are equivalent.
[1, 11, 7]
[11, 23, 17, 1]
[8, 14, 10, 12, 17, 19, 18]
Invalid edges vector: Tuple{Int64,Int64}[(1, 3), (9, 11), (3, 11), (1, 11)]
Lua
<lang lua>-- support function T(t) return setmetatable(t, {__index=table}) end table.eql = function(t,u) if #t~=#u then return false end for i=1,#t do if t[i]~=u[i] then return false end end return true end table.rol = function(t,n) local s=T{} for i=1,#t do s[i]=t[(i+n-1)%#t+1] end return s end table.rev = function(t) local s=T{} for i=1,#t do s[#t-i+1]=t[i] end return s end
-- 1 function pfeq(pf1, pf2)
if #pf1 ~= #pf2 then return false end -- easy case
for w = 0,1 do -- exhaustive cases
local pfw = pf1 -- w:winding
if w==1 then pfw=pfw:rev() end
for r = 0,#pfw do
local pfr = pfw -- r:rotate
if r>0 then pfr=pfr:rol(r) end
if pf2:eql(pfr) then return true end
end
end
return false
end
Q = T{8, 1, 3} R = T{1, 3, 8} U = T{18, 8, 14, 10, 12, 17, 19} V = T{8, 14, 10, 12, 17, 19, 18} print("pfeq(Q,R): ", pfeq(Q, R)) print("pfeq(U,V): ", pfeq(U, V))
-- 2 function ef2pf(ef)
local pf, hse = T{}, T{} -- hse:hash of sorted edges
for i,e in ipairs(ef) do table.sort(e) hse[e]=e end
local function nexte(e)
if not e then return ef[1] end
for k,v in pairs(hse) do
if e[2]==v[1] then return v end
if e[2]==v[2] then v[1],v[2]=v[2],v[1] return v end
end
end
local e = nexte()
while e do
pf[#pf+1] = e[1]
hse[e] = nil
e = nexte(e)
end
if #pf ~= #ef then pf=T{"failed to convert edge format to perimeter format"} end
return pf
end
E = {{1, 11}, {7, 11}, {1, 7}} F = {{11, 23}, {1, 17}, {17, 23}, {1, 11}} G = {{8, 14}, {17, 19}, {10, 12}, {10, 14}, {12, 17}, {8, 18}, {18, 19}} H = {{1, 3}, {9, 11}, {3, 11}, {1, 11}} print("ef2pf(E): ", ef2pf(E):concat(",")) print("ef2pf(F): ", ef2pf(F):concat(",")) print("ef2pf(G): ", ef2pf(G):concat(",")) print("ef2pf(H): ", ef2pf(H):concat(","))</lang>
- Output:
pfeq(Q,R): true pfeq(U,V): true ef2pf(E): 1,11,7 ef2pf(F): 11,23,17,1 ef2pf(G): 8,14,10,12,17,19,18 ef2pf(H): failed to convert edge format to perimeter format
Nim
<lang Nim>import algorithm, strutils
type
Perimeter = seq[int] Face = tuple[name: char; perimeter: Perimeter] Edge = tuple[first, last: int]
const None = -1 # No point.
- ---------------------------------------------------------------------------------------------------
func isSame(p1, p2: Perimeter): bool =
## Return "true" if "p1" and "p2" represent the same face.
if p1.len != p2.len: return false
for p in p1: if p notin p2: return false
var start = p2.find(p1[0]) if p1 == p2[start..^1] & p2[0..<start]: return true
let p3 = reversed(p2) start = p3.find(p1[0]) if p1 == p3[start..^1] & p3[0..<start]: return true
- ---------------------------------------------------------------------------------------------------
func `$`(perimeter: Perimeter): string =
## Convert a perimeter to a string.
'(' & perimeter.join(", ") & ')'
func `$`(face: Face): string =
## Convert a perimeter formatted face to a string. face.name & $face.perimeter
- ---------------------------------------------------------------------------------------------------
func toPerimeter(edges: seq[Edge]): Perimeter =
## Convert a list of edges to perimeter representation. ## Return an empty perimeter if the list of edges doesn’t represent a face.
var edges = edges let firstEdge = edges.pop() # First edge taken in account. var nextPoint = firstEdge.first # Next point to search in remaining edges. result.add(nextpoint)
while edges.len > 0:
# Search an edge.
var idx = None
for i, e in edges:
if e.first == nextPoint or e.last == nextPoint:
idx = i
nextPoint = if nextpoint == e.first: e.last else: e.first
break
if idx == None:
return @[] # No edge found containing "newPoint".
# Add next point to perimeter and remove the edge. result.add(nextPoint) edges.del(idx)
# Check that last added point is the expected one. if nextPoint != firstEdge.last: return @[]
- ———————————————————————————————————————————————————————————————————————————————————————————————————
when isMainModule:
# List of pairs of perimeter formatted faces to compare.
const FP = [(('P', @[8, 1, 3]), ('R', @[1, 3, 8])),
(('U', @[18, 8, 14, 10, 12, 17, 19]), ('V', @[8, 14, 10, 12, 17, 19, 18]))]
echo "Perimeter comparison:" for (p1, p2) in FP: echo p1, if isSame(p1[1], p2[1]): " is same as " else: "is not same as", p2
# List of edge formatted faces.
const FE = {'E': @[(1, 11), (7, 11), (1, 7)],
'F': @[(11, 23), (1, 17), (17, 23), (1, 11)],
'G': @[(8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)],
'H': @[(1, 3), (9, 11), (3, 11), (1, 11)]}
echo "" echo "Conversion from edge to perimeter format:" for (faceName, edges) in FE: let perimeter = edges.toPerimeter() echo faceName, ": ", if perimeter.len == 0: "Invalid edge list" else: $perimeter</lang>
- Output:
Perimeter comparison: P(8, 1, 3) is same as R(1, 3, 8) U(18, 8, 14, 10, 12, 17, 19) is same as V(8, 14, 10, 12, 17, 19, 18) Conversion from edge to perimeter format: E: (1, 11, 7) F: (1, 17, 23, 11) G: (18, 8, 14, 10, 12, 17, 19) H: Invalid edge list
Perl
<lang perl>use strict; use warnings; use feature 'say'; use Set::Scalar; use Set::Bag; use Storable qw(dclone);
sub show { my($pts) = @_; my $p='( '; $p .= '(' . join(' ',@$_) . ') ' for @$pts; $p.')' }
sub check_equivalence {
my($a, $b) = @_; Set::Scalar->new(@$a) == Set::Scalar->new(@$b)
}
sub edge_to_periphery {
my $a = dclone \@_;
my $bag_a = Set::Bag->new;
for my $p (@$a) {
$bag_a->insert( @$p[0] => 1);
$bag_a->insert( @$p[1] => 1);
}
2 != @$bag_a{$_} and return 0 for keys %$bag_a;
my $b = shift @$a;
while ($#{$a} > 0) {
for my $k (0..$#{$a}) {
my $v = @$a[$k];
if (@$v[0] == @$b[-1]) {
push @$b, @$v[1];
splice(@$a,$k,1);
last
} elsif (@$v[1] == @$b[-1]) {
push @$b, @$v[0];
splice(@$a,$k,1);
last
}
}
}
@$b;
}
say 'Perimeter format equality checks:'; for ([[8, 1, 3], [1, 3, 8]],
[[18, 8, 14, 10, 12, 17, 19], [8, 14, 10, 12, 17, 19, 18]]) {
my($a, $b) = @$_;
say '(' . join(', ', @$a) . ') equivalent to (' . join(', ', @$b) . ')? ',
check_equivalence($a, $b) ? 'True' : 'False';
}
say "\nEdge to perimeter format translations:"; for ([[1, 11], [7, 11], [1, 7]],
[[11, 23], [1, 17], [17, 23], [1, 11]],
[[8, 14], [17, 19], [10, 12], [10, 14], [12, 17], [8, 18], [18, 19]],
[[1, 3], [9, 11], [3, 11], [1, 11]]) {
say show($_) . ' ==> (' . (join ' ', edge_to_periphery(@$_) or 'Invalid edge format') . ')'
}</lang>
- Output:
Perimeter format equality checks: (8, 1, 3) equivalent to (1, 3, 8)? True (18, 8, 14, 10, 12, 17, 19) equivalent to (8, 14, 10, 12, 17, 19, 18)? True Edge to perimeter format translations: ( (1 11) (7 11) (1 7) ) ==> (1 11 7) ( (11 23) (1 17) (17 23) (1 11) ) ==> (11 23 17 1) ( (8 14) (17 19) (10 12) (10 14) (12 17) (8 18) (18 19) ) ==> (8 14 10 12 17 19 18) ( (1 3) (9 11) (3 11) (1 11) ) ==> Invalid edge format
Phix
with javascript_semantics function perequiv(sequence a, b) -- Works by aligning and rotating in one step, so theoretically much faster on massive sets. -- (ahem, faster than multiple rotates, index-only loops would obviously be even faster...) bool res = (length(a)==length(b)) if res and length(a)>0 then integer k = find(a[1],b) if k=0 then res = false else -- align with a (ie make b[1]==a[1], by -- rotating b k places in one operation) b = b[k..$]&b[1..k-1] if a!=b then -- eg {8,3,4,5} <=> {8,5,4,3}, ie -- rotate *and* keep in alignment. b[2..$] = reverse(b[2..$]) res = (a==b) end if end if end if -- return res return {"false","true"}[res+1] end function function edge2peri(sequence edges) sequence was = edges, res = {} string error = "" integer lnk = 0 if length(edges)<2 then error = "too short" else -- edges = sort(deep_copy(edges)) -- (see note below) res = deep_copy(edges[1]) edges = edges[2..$] lnk = res[2] while length(edges) and error="" do bool found = false for i=1 to length(edges) do integer k = find(lnk,edges[i]) if k then lnk = edges[i][3-k] edges[i..i] = {} if edges={} then if lnk!=res[1] then error = "oh dear" end if else if find(lnk,res) then error = "oops" end if res &= lnk end if found = true exit end if end for if not found then error = "bad link" exit end if end while end if if length(error) then res = {error,res,lnk,edges,was} end if return res end function constant ptests = {{{8, 1, 3}, {1, 3, 8}}, {{18, 8, 14, 10, 12, 17, 19}, {8, 14, 10, 12, 17, 19, 18}}, -- (check our results below against Go etc) {{1,11,7},{1,7,11}}, {{11,23,17,1},{1,11,23,17}}} for i=1 to length(ptests) do sequence {p,q} = ptests[i] printf(1,"%v equivalent to %v: %s\n",{p,q,perequiv(p,q)}) end for constant etests = {{{1, 11}, {7, 11}, {1, 7}}, {{11, 23}, {1, 17}, {17, 23}, {1, 11}}, {{8, 14}, {17, 19}, {10, 12}, {10, 14}, {12, 17}, {8, 18}, {18, 19}}, {{1, 3}, {9, 11}, {3, 11}, {1, 11}}} for i=1 to length(etests) do printf(1,"%v\n",{edge2peri(etests[i])}) end for
- Output:
(second part matches Julia/Perl: un-comment that sort above to match Go/Python/zkl)
{8,1,3} equivalent to {1,3,8}: true
{18,8,14,10,12,17,19} equivalent to {8,14,10,12,17,19,18}: true
{1,11,7} equivalent to {1,7,11}: true
{11,23,17,1} equivalent to {1,11,23,17}: true
{1,11,7}
{11,23,17,1}
{8,14,10,12,17,19,18}
{"bad link",{1,3,11,9},9,{{1,11}},{{1,3},{9,11},{3,11},{1,11}}}
Python
<lang python>def perim_equal(p1, p2):
# Cheap tests first
if len(p1) != len(p2) or set(p1) != set(p2):
return False
if any(p2 == (p1[n:] + p1[:n]) for n in range(len(p1))):
return True
p2 = p2[::-1] # not inplace
return any(p2 == (p1[n:] + p1[:n]) for n in range(len(p1)))
def edge_to_periphery(e):
edges = sorted(e)
p = list(edges.pop(0)) if edges else []
last = p[-1] if p else None
while edges:
for n, (i, j) in enumerate(edges):
if i == last:
p.append(j)
last = j
edges.pop(n)
break
elif j == last:
p.append(i)
last = i
edges.pop(n)
break
else:
#raise ValueError(f'Invalid edge format: {e}')
return ">>>Error! Invalid edge format<<<"
return p[:-1]
if __name__ == '__main__':
print('Perimeter format equality checks:')
for eq_check in [
{ 'Q': (8, 1, 3),
'R': (1, 3, 8)},
{ 'U': (18, 8, 14, 10, 12, 17, 19),
'V': (8, 14, 10, 12, 17, 19, 18)} ]:
(n1, p1), (n2, p2) = eq_check.items()
eq = '==' if perim_equal(p1, p2) else '!='
print(' ', n1, eq, n2)
print('\nEdge to perimeter format translations:')
edge_d = {
'E': {(1, 11), (7, 11), (1, 7)},
'F': {(11, 23), (1, 17), (17, 23), (1, 11)},
'G': {(8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)},
'H': {(1, 3), (9, 11), (3, 11), (1, 11)}
}
for name, edges in edge_d.items():
print(f" {name}: {edges}\n -> {edge_to_periphery(edges)}")</lang>
- Output:
Perimeter format equality checks:
Q == R
U == V
Edge to perimeter format translations:
E: {(7, 11), (1, 11), (1, 7)}
-> [1, 7, 11]
F: {(11, 23), (1, 11), (1, 17), (17, 23)}
-> [1, 11, 23, 17]
G: {(8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)}
-> [8, 14, 10, 12, 17, 19, 18]
H: {(1, 11), (9, 11), (1, 3), (3, 11)}
-> >>>Error! Invalid edge format<<<
Raku
(formerly Perl 6)
<lang perl6>sub check-equivalence ($a, $b) { so $a.Bag eqv $b.Bag }
sub edge-to-periphery (@a is copy) {
return Nil unless @a.List.Bag.values.all == 2;
my @b = @a.shift.flat;
while @a > 1 {
for @a.kv -> $k, $v {
if $v[0] == @b.tail {
@b.push: $v[1];
@a.splice($k,1);
last
}
elsif $v[1] == @b.tail {
@b.push: $v[0];
@a.splice($k,1);
last
}
}
}
@b
}
say 'Perimeter format equality checks:';
for (8, 1, 3), (1, 3, 8),
(18, 8, 14, 10, 12, 17, 19), (8, 14, 10, 12, 17, 19, 18)
-> $a, $b {
say "({$a.join: ', '}) equivalent to ({$b.join: ', '})? ",
check-equivalence($a, $b)
}
say "\nEdge to perimeter format translations:";
for ((1, 11), (7, 11), (1, 7)),
((11, 23), (1, 17), (17, 23), (1, 11)),
((8, 14), (17, 19), (10, 12), (10, 14), (12, 17), (8, 18), (18, 19)),
((1, 3), (9, 11), (3, 11), (1, 11))
{
.gist.print;
say " ==> ({.&edge-to-periphery || 'Invalid edge format'})";
}</lang>
- Output:
Perimeter format equality checks: (8, 1, 3) equivalent to (1, 3, 8)? True (18, 8, 14, 10, 12, 17, 19) equivalent to (8, 14, 10, 12, 17, 19, 18)? True Edge to perimeter format translations: ((1 11) (7 11) (1 7)) ==> (1 11 7) ((11 23) (1 17) (17 23) (1 11)) ==> (11 23 17 1) ((8 14) (17 19) (10 12) (10 14) (12 17) (8 18) (18 19)) ==> (8 14 10 12 17 19 18) ((1 3) (9 11) (3 11) (1 11)) ==> (Invalid edge format)
Wren
<lang ecmascript>import "./sort" for Sort import "./seq" for Lst import "./fmt" for Fmt
// Check two perimeters are equal. var perimEqual = Fn.new { |p1, p2|
var le = p1.count
if (le != p2.count) return false
for (p in p1) {
if (!p2.contains(p)) return false
}
// use copy to avoid mutating 'p1'
var c = p1.toList
for (r in 0..1) {
for (i in 0...le) {
if (Lst.areEqual(c, p2)) return true
// do circular shift to right
Lst.rshift(c)
}
// now process in opposite direction
Lst.reverse(c) // reverses 'c' in place
}
return false
}
var faceToPerim = Fn.new { |face|
// use copy to avoid mutating 'face'
var le = face.count
if (le == 0) return []
var edges = List.filled(le, null)
for (i in 0...le) {
// check edge pairs are in correct order
if (face[i][1] <= face[i][0]) return []
edges[i] = [face[i][0], face[i][1]]
}
// sort edges in ascending order
var cmp = Fn.new { |e1, e2|
if (e1[0] != e2[0]) {
return (e1[0] - e2[0]).sign
}
return (e1[1] - e2[1]).sign
}
Sort.insertion(edges, cmp)
var first = edges[0][0]
var last = edges[0][1]
var perim = [first, last]
// remove first edge
edges.removeAt(0)
le = le - 1
while (le > 0) {
var i = 0
var outer = false
var cont = false
for (e in edges) {
var found = false
if (e[0] == last) {
perim.add(e[1])
last = e[1]
found = true
} else if (e[1] == last) {
perim.add(e[0])
last = e[0]
found = true
}
if (found) {
// remove i'th edge
edges.removeAt(i)
le = le - 1
if (last == first) {
if (le == 0) {
outer = true
break
} else {
return []
}
}
cont = true
break
}
i = i + 1
}
if (outer && !cont) break
}
return perim[0..-2]
}
System.print("Perimeter format equality checks:") var areEqual = perimEqual.call([8, 1, 3], [1, 3, 8]) System.print(" Q == R is %(areEqual)") areEqual = perimEqual.call([18, 8, 14, 10, 12, 17, 19], [8, 14, 10, 12, 17, 19, 18]) System.print(" U == V is %(areEqual)") var e = [[7, 11], [1, 11], [1, 7]] var f = [[11, 23], [1, 17], [17, 23], [1, 11]] var g = [[8, 14], [17, 19], [10, 12], [10, 14], [12, 17], [8, 18], [18, 19]] var h = [[1, 3], [9, 11], [3, 11], [1, 11]] System.print("\nEdge to perimeter format translations:") var i = 0 for (face in [e, f, g, h]) {
var perim = faceToPerim.call(face)
if (perim.isEmpty) {
Fmt.print(" $c => Invalid edge format", i + 69) // 'E' is ASCII 69
} else {
Fmt.print(" $c => $n", i + 69, perim)
}
}</lang>
- Output:
Perimeter format equality checks: Q == R is true U == V is true Edge to perimeter format translations: E => [1, 7, 11] E => [1, 11, 23, 17] E => [8, 14, 10, 12, 17, 19, 18] E => Invalid edge format
zkl
<lang zkl>fcn perimSame(p1, p2){
if(p1.len() != p2.len()) return(False);
False == p1.filter1('wrap(p){ (not p2.holds(p)) })
}
fcn edge_to_periphery(faces){
edges:=faces.copy().sort(fcn(a,b){ if(a[0]!=b[0]) a[0]<b[0] else a[1]<b[1] });
p,last := ( if(edges) edges.pop(0).copy() else T ), ( p and p[-1] or Void );
while(edges){
foreach i,j in (edges){
if (i==last){ p.append( last=j ); edges.del(__iWalker.idx); break; }
else if(j==last){ p.append( last=i ); edges.del(__iWalker.idx); break; }
}
fallthrough{ return(">>>Error! Invalid edge format<<<") }
}
p[0,-1] // last element not part of result
}</lang> <lang zkl>println("Perimeter format equality checks:"); ps:=T( T( T(8,1,3), T(1,3,8) ),
T( T(18, 8, 14, 10, 12, 17, 19), T(8, 14, 10, 12, 17, 19, 18) ) );
foreach p1,p2 in (ps)
{ println(pp(p1), " equivalent to ", pp(p2), "? ", perimSame(p1,p2)) }
println("\nEdge to perimeter format translations:"); edge_d:=T(
T(T( 1, 11), T( 7, 11), T( 1, 7) ),
T(T(11, 23), T( 1, 17), T(17, 23), T( 1, 11) ),
T(T( 8, 14), T(17, 19), T(10, 12), T(10, 14), T(12, 17), T(8, 18), T(18, 19) ),
T(T( 1, 3), T( 9, 11), T( 3, 11), T( 1, 11) ),
);
foreach edges in (edge_d)
{ println(ppp(edges), " --> ", edge_to_periphery(edges)) }
fcn pp(a){ a.concat(", ","(",")") } fcn ppp(edges){ pp(edges.apply(pp)) }</lang>
- Output:
Perimeter format equality checks: (8, 1, 3) equivalent to (1, 3, 8)? True (18, 8, 14, 10, 12, 17, 19) equivalent to (8, 14, 10, 12, 17, 19, 18)? True Edge to perimeter format translations: ((1 11), (7 11), (1 7)) --> L(1,7,11) ((11 23), (1 17), (17 23), (1 11)) --> L(1,11,23,17) ((8 14), (17 19), (10 12), (10 14), (12 17), (8 18), (18 19)) --> L(8,14,10,12,17,19,18) ((1 3), (9 11), (3 11), (1 11)) --> >>>Error! Invalid edge format<<<