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Solve the no connection puzzle

From Rosetta Code
Task
Solve the no connection puzzle
You are encouraged to solve this task according to the task description, using any language you may know.

You are given a box with eight holes labelled A-to-H, connected by fifteen straight lines in the pattern as shown

        A   B
       /|\ /|\
      / | X | \
     /  |/ \|  \
    C - D - E - F
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        G   H

You are also given eight pegs numbered 1-to-8. The idea is to place the pegs in the holes so that the (absolute) difference between any two numbers connected by any line is greater than one.

For example, in this attempt:

        4   7
       /|\ /|\
      / | X | \
     /  |/ \|  \
    8 - 1 - 6 - 2
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        3   5

Note that 7 and 6 are connected and have a difference of 1 so it is not a solution.


Task

Produce and show here one solution to the puzzle.


Related tasks


See also

No Connection Puzzle (youtube).

Ada[edit]

This solution is a bit longer than it actually needs to be; however, it uses tasks to find the solution and the used types and solution-generating functions are well-separated, making it more amenable to other solutions or altering it to display all solutions.

 
With
Ada.Text_IO,
Connection_Types,
Connection_Combinations;
 
procedure main is
Result : Connection_Types.Partial_Board renames Connection_Combinations;
begin
Ada.Text_IO.Put_Line( Connection_Types.Image(Result) );
end;
Pragma Ada_2012;
 
Package Connection_Types with Pure is
 
-- Name of the nodes.
Type Node is (A, B, C, D, E, F, G, H);
 
-- Type for indicating if a node is connected.
Type Connection_List is array(Node) of Boolean
with Size => 8, Object_Size => 8, Pack;
 
Function "&"( Left : Connection_List; Right : Node ) return Connection_List;
 
-- The actual map of the network connections.
Network : Constant Array (Node) of Connection_List:=
(
A => (C|D|E => True, others => False),
B => (D|E|F => True, others => False),
C => (A|D|G => True, others => False),
D => (C|A|B|E|H|G => True, others => False),
E => (D|A|B|F|H|G => True, others => False),
F => (B|E|H => True, others => False),
G => (C|D|E => True, others => False),
H => (D|E|F => True, others => False)
);
 
-- Values of the nodes.
Type Peg is range 1..8;
 
-- Indicator for which values have been assigned.
Type Used_Peg is array(Peg) of Boolean
with Size => 8, Object_Size => 8, Pack;
 
Function "&"( Left : Used_Peg; Right : Peg ) return Used_Peg;
 
 
-- Type describing the layout of the network.
Type Partial_Board is array(Node range <>) of Peg;
Subtype Board is Partial_Board(Node);
 
-- Determines if the given board is a solution or partial-solution.
Function Is_Solution ( Input : Partial_Board ) return Boolean;
 
-- Displays the board as text.
Function Image ( Input : Partial_Board ) Return String;
 
End Connection_Types;
 
Pragma Ada_2012;
 
with Connection_Types;
use Connection_Types;
 
Function Connection_Combinations return Partial_Board;
 
Pragma Ada_2012;
 
Package Body Connection_Types is
 
New_Line : Constant String := ASCII.CR & ASCII.LF;
 
---------------------
-- Solution Test --
---------------------
 
Function Is_Solution( Input : Partial_Board ) return Boolean is
(for all Index in Input'Range =>
(for all Connection in Node'Range =>
(if Network(Index)(Connection) and Connection in Input'Range
then abs (Input(Index) - Input(Connection)) > 1
)
)
);
 
------------------------
-- Concat Operators --
------------------------
 
Function "&"( Left : Used_Peg; Right : Peg ) return Used_Peg is
begin
return Result : Used_Peg := Left do
Result(Right):= True;
end return;
end "&";
 
Function "&"(Left : Connection_List; Right : Node) return Connection_List is
begin
Return Result : Connection_List := Left do
Result(Right):= True;
end return;
end "&";
 
-----------------------
-- IMAGE FUNCTIONS --
-----------------------
 
Function Image(Input : Peg) Return Character is
( Peg'Image(Input)(2) );
 
Function Image(Input : Peg) Return String is
( 1 => Image(Input) );
 
Function Image(Input : Partial_Board; Item : Node) Return String is
( 1 => (if Item not in Input'Range then '*' else Image(Input(Item)) ));
 
Function Image( Input : Partial_Board ) Return String is
A : String renames Image(Input, Connection_Types.A);
B : String renames Image(Input, Connection_Types.B);
C : String renames Image(Input, Connection_Types.C);
D : String renames Image(Input, Connection_Types.D);
E : String renames Image(Input, Connection_Types.E);
F : String renames Image(Input, Connection_Types.F);
G : String renames Image(Input, Connection_Types.G);
H : String renames Image(Input, Connection_Types.H);
begin
return
" "&A&" "&B & New_Line &
" /|\ /|\" & New_Line &
"
/ | X | \" & New_Line &
"
/ |/ \| \" & New_Line &
"
"&C&" - "&D&" - "&E&" - "&F & New_Line &
"
\ |\ /| /" & New_Line &
"
\ | X | /" & New_Line &
"
\|/ \|/" & New_Line &
"
"&G&" "&H & New_Line;
end Image;
 
End Connection_Types;
Function Connection_Combinations return Partial_Board is
 
begin
Return Result : Board do
declare
 
-- The Generate task takes two parameters
-- (1) a list of pegs already in use, and
-- (2) a partial-board
-- and, if the state given is a viable yet incomplete solution, it
-- takes a peg and adds it to the state creating a new task with
-- that peg in its used list.
--
-- When a complete solution is found it is copied into result.
task type Generate(
Pegs : not null access Used_Peg:= new Used_Peg'(others => False);
State : not null access Partial_Board:= new Partial_Board'(Node'Last..Node'First => <>)
) is
end Generate;
 
-- An access to Generate and array thereof, for creating the
-- children tasks.
type Generator is access all Generate;
type Generators is array(Peg range <>) of Generator;
 
-- Gen handles the actual creation of a new task and state.
Function Gen(P : Peg; G : not null access Generate) return Generator is
begin
return (if G.Pegs(P) then null
else new Generate(
Pegs => new Used_Peg'(G.Pegs.all & P),
State => New Partial_Board'(G.All.State.All & P)
)
);
end;
 
task body Generate is
begin
if Is_Solution(State.All) then
-- If the state is a partial board, we make children to
-- complete the calculations.
if State'Length <= Node'Pos(Node'Last) then
declare
Subtasks : Constant Generators:=
(
Gen(1, Generate'Access),
Gen(2, Generate'Access),
Gen(3, Generate'Access),
Gen(4, Generate'Access),
Gen(5, Generate'Access),
Gen(6, Generate'Access),
Gen(7, Generate'Access),
Gen(8, Generate'Access)
);
begin
null;
end;
else
Result:= State.All;
end if;
else
-- The current state is not a solution, so we do not continue it.
Null;
end if;
 
end Generate;
 
Master : Generate;
begin
null;
end;
End return;
End Connection_Combinations;
 
Output:
        4   5
       /|\ /|\
      / | X | \
     /  |/ \|  \
    7 - 1 - 8 - 2
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        3   6

Chapel[edit]

type hole = int;
param A : hole = 1;
param B : hole = A+1;
param C : hole = B+1;
param D : hole = C+1;
param E : hole = D+1;
param F : hole = E+1;
param G : hole = F+1;
param H : hole = G+1;
param starting : int = 0;
const holes : domain(hole) = { A,B,C,D,E,F,G,H };
const graph : [holes] domain(hole) = [ A => { C,D,E },
B => { D,E,F },
C => { A,D,G },
D => { A,B,C,E,G,H },
E => { A,B,D,F,G,H },
F => { B,E,H },
G => { C,D,E },
H => { D,E,F }
];
 
proc check( configuration : [] int, idx : hole ) : bool {
var good = true;
for adj in graph[idx] {
if adj >= idx then continue;
if abs( configuration[idx] - configuration[adj] ) <= 1 {
good = false;
break;
}
}
 
return good;
}
 
proc solve( configuration : [] int, pegs : domain(int), idx : hole = A ) : bool {
for value in pegs {
configuration[idx] = value;
if check( configuration, idx ) {
if idx < holes.size {
var prePegs = pegs;
if solve( configuration, prePegs - value, idx + 1 ){
return true;
}
} else {
return true;
}
}
}
configuration[idx] = starting;
return false;
}
 
proc printBoard( configuration : [] int ){
return
"\n " + configuration[A] + " " + configuration[B]+ "\n" +
" /|\\ /|\\ \n"+
" / | X | \\ \n"+
" / |/ \\| \\ \n"+
" " + configuration[C] +" - " + configuration[D] + " - " + configuration[E] + " - " + configuration[F] + " \n"+
" \\ |\\ /| / \n"+
" \\ | X | / \n"+
" \\|/ \\|/ \n"+
" " + configuration[G] + " " + configuration[H]+ "\n";
 
}
 
 
 
proc main(){
var configuration : [holes] int;
for idx in holes do configuration[idx] = starting;
 
var pegs : domain(int) = {1,2,3,4,5,6,7,8};
solve( configuration, pegs );
 
writeln( printBoard( configuration ) );
 
}
 
       4   5
      /|\ /|\ 
     / | X | \ 
    /  |/ \|  \ 
   7 - 1 - 8 - 2 
    \  |\ /|  / 
     \ | X | / 
      \|/ \|/ 
       3   6

D[edit]

void main() @safe {
import std.stdio, std.math, std.algorithm, std.traits, std.string;
 
enum Peg { A, B, C, D, E, F, G, H }
immutable Peg[2][15] connections =
[[Peg.A, Peg.C], [Peg.A, Peg.D], [Peg.A, Peg.E],
[Peg.B, Peg.D], [Peg.B, Peg.E], [Peg.B, Peg.F],
[Peg.C, Peg.D], [Peg.D, Peg.E], [Peg.E, Peg.F],
[Peg.G, Peg.C], [Peg.G, Peg.D], [Peg.G, Peg.E],
[Peg.H, Peg.D], [Peg.H, Peg.E], [Peg.H, Peg.F]];
 
immutable board = r"
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H"
;
 
Peg[EnumMembers!Peg.length] perm = [EnumMembers!Peg];
do if (connections[].all!(con => abs(perm[con[0]] - perm[con[1]]) > 1))
return board.tr("ABCDEFGH", "%(%d%)".format(perm)).writeln;
while (perm[].nextPermutation);
}
Output:
        2   3
       /|\ /|\
      / | X | \
     /  |/ \|  \
    6 - 0 - 7 - 1
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        4   5

Alternative version[edit]

Using a simple backtracking.

Translation of: Go
import std.stdio, std.algorithm, std.conv, std.string, std.typecons;
 
// Holes A=0, B=1, ..., H=7
// With connections:
const board = r"
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H"
;
 
struct Connection { uint a, b; }
 
immutable Connection[] connections = [
{0, 2}, {0, 3}, {0, 4}, // A to C,D,E
{1, 3}, {1, 4}, {1, 5}, // B to D,E,F
{6, 2}, {6, 3}, {6, 4}, // G to C,D,E
{7, 3}, {7, 4}, {7, 5}, // H to D,E,F
{2, 3}, {3, 4}, {4, 5}, // C-D, D-E, E-F
];
 
alias Pegs = uint[8];
 
int absDiff(in uint a, in uint b) pure nothrow @safe @nogc {
return (a > b) ? (a - b) : (b - a);
}
 
/** Solution is a simple recursive brute force solver,
it stops at the first found solution.
It returns the solution, the number of positions tested,
and the number of pegs swapped. */

Tuple!(Pegs,"p", uint,"tests", uint,"swaps") solve() pure nothrow @safe @nogc {
uint tests = 0, swaps = 0;
Pegs p = [1, 2, 3, 4, 5, 6, 7, 8];
 
bool recurse(in uint i) nothrow @safe @nogc {
if (i >= p.length.signed - 1) {
tests++;
return connections.all!(c => absDiff(p[c.a], p[c.b]) > 1);
}
 
// Try each remain peg from.
foreach (immutable j; i .. p.length) {
swaps++;
swap(p[i], p[j]);
if (recurse(i + 1))
return true;
swap(p[i], p[j]);
}
return false;
}
 
recurse(0);
return typeof(return)(p, tests, swaps);
}
 
void main() {
immutable sol = solve();
board.tr("ABCDEFGH", "%(%d%)".format(sol.p)).writeln;
writeln("Tested ", sol.tests, " positions and did ", sol.swaps, " swaps.");
}
Output:
       3   4
      /|\ /|\
     / | X | \
    /  |/ \|  \
   7 - 1 - 8 - 2
    \  |\ /|  /
     \ | X | /
      \|/ \|/
       5   6
Tested 12094 positions and did 20782 swaps.

Elixir[edit]

Translation of: Ruby

This solution uses HLPsolver from here

# It solved if connected A and B, connected G and H (according to the video).
 
# require HLPsolver
 
adjacent = for i <- -2..2, j <- -2..2, not(i in -1..1 and j in -1..1), do: {i,j}
layout = ~S"""
A - B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G - H
"""
board = """
. 0 0 .
0 1 0 0
. 0 0 .
"""
HLPsolver.solve(board, adjacent, false)
|> Enum.sort |> Enum.map(fn {_,cell} -> cell.value end)
|> Enum.zip(~w[A B C D E F G H])
|> Enum.reduce(layout, fn {n,c},acc -> String.replace(acc, c, to_string(n)) end)
|> IO.puts
Output:
       4 - 6
      /|\ /|\
     / | X | \
    /  |/ \|  \
   7 - 1 - 8 - 2
    \  |\ /|  /
     \ | X | /
      \|/ \|/
       3 - 5

Go[edit]

A simple recursive brute force solution.

package main
 
import (
"fmt"
"strings"
)
 
func main() {
p, tests, swaps := Solution()
fmt.Println(p)
fmt.Println("Tested", tests, "positions and did", swaps, "swaps.")
}
 
// Holes A=0, B=1, …, H=7
// With connections:
const conn = `
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H`

 
var connections = []struct{ a, b int }{
{0, 2}, {0, 3}, {0, 4}, // A to C,D,E
{1, 3}, {1, 4}, {1, 5}, // B to D,E,F
{6, 2}, {6, 3}, {6, 4}, // G to C,D,E
{7, 3}, {7, 4}, {7, 5}, // H to D,E,F
{2, 3}, {3, 4}, {4, 5}, // C-D, D-E, E-F
}
 
type pegs [8]int
 
// Valid checks if the pegs are a valid solution.
// If the absolute difference between any pair of connected pegs is
// greater than one it is a valid solution.
func (p *pegs) Valid() bool {
for _, c := range connections {
if absdiff(p[c.a], p[c.b]) <= 1 {
return false
}
}
return true
}
 
// Solution is a simple recursive brute force solver,
// it stops at the first found solution.
// It returns the solution, the number of positions tested,
// and the number of pegs swapped.
func Solution() (p *pegs, tests, swaps int) {
var recurse func(int) bool
recurse = func(i int) bool {
if i >= len(p)-1 {
tests++
return p.Valid()
}
// Try each remain peg from p[i:] in p[i]
for j := i; j < len(p); j++ {
swaps++
p[i], p[j] = p[j], p[i]
if recurse(i + 1) {
return true
}
p[i], p[j] = p[j], p[i]
}
return false
}
p = &pegs{1, 2, 3, 4, 5, 6, 7, 8}
recurse(0)
return
}
 
func (p *pegs) String() string {
return strings.Map(func(r rune) rune {
if 'A' <= r && r <= 'H' {
return rune(p[r-'A'] + '0')
}
return r
}, conn)
}
 
func absdiff(a, b int) int {
if a > b {
return a - b
}
return b - a
}
Output:

       3   4
      /|\ /|\
     / | X | \
    /  |/ \|  \
   7 - 1 - 8 - 2
    \  |\ /|  /
     \ | X | /
      \|/ \|/
       5   6
Tested 12094 positions and did 20782 swaps.

Haskell[edit]

import Data.List (permutations, intercalate)
 
solution :: [Int]
solution@(a:b:c:d:e:f:g:h:_) = head $ filter isSolution (permutations [1 .. 8])
where
isSolution :: [Int] -> Bool
isSolution (a:b:c:d:e:f:g:h:_) =
all
((> 1) . abs)
[ a - d
, c - d
, g - d
, e - d
, a - c
, c - g
, g - e
, e - a
, b - e
, d - e
, h - e
, f - e
, b - d
, d - h
, h - f
, f - b
]
 
main :: IO ()
main =
mapM_ putStrLn $
let rightShift s
| length s > 3 = s
| otherwise = " " ++ s
in intercalate
"\n"
(zipWith ((. ((" = " ++) . show)) . (:)) ['A' .. 'H'] solution) :
((rightShift . unwords . (show <$>)) <$> [[], [a, b], [c, d, e, f], [g, h]])
Output:
A = 3
B = 4
C = 7
D = 1
E = 8
F = 2
G = 5
H = 6

  3 4
7 1 8 2
  5 6 

J[edit]

Supporting code:

holes=:;:'A B C D E F G H'
 
connections=:".;._2]0 :0
holes e.;:'C D E' NB. A
holes e.;:'D E F' NB. B
holes e.;:'A D G' NB. C
holes e.;:'A B C E G H' NB. D
holes e.;:'A B D F G H' NB. E
holes e.;:'B E H' NB. F
holes e.;:'C D E' NB. G
holes e.;:'D E F' NB. H
)
assert (-:|:) connections NB. catch typos
 
pegs=: 1+(A.&i.~ !)8
 
attempt=: [: <./@(-.&0)@,@:| connections * -/~
 
 
box=:0 :0
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H
)
 
disp=:verb define
rplc&(,holes;&":&>y) box
)

Intermezzo:

   (#~ 1<attempt"1) pegs
3 4 7 1 8 2 5 6
3 5 7 1 8 2 4 6
3 6 7 1 8 2 4 5
3 6 7 1 8 2 5 4
4 3 2 8 1 7 6 5
4 5 2 8 1 7 6 3
4 5 7 1 8 2 3 6
4 6 7 1 8 2 3 5
5 3 2 8 1 7 6 4
5 4 2 8 1 7 6 3
5 4 7 1 8 2 3 6
5 6 7 1 8 2 3 4
6 3 2 8 1 7 4 5
6 3 2 8 1 7 5 4
6 4 2 8 1 7 5 3
6 5 2 8 1 7 4 3

Since there's more than one arrangement where the pegs satisfy the task constraints, and since the task calls for one solution, we will need to pick one of them. We can use the "first" function to satisfy this important constraint.

   disp {. (#~ 1<attempt"1) pegs
3 4
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
5 6
 
 

Video

If we follow the video and also connect A and B as well as G and H, we get only four solutions (which we can see are reflections / rotations of each other):

   (#~ 1<attempt"1) pegs
3 5 7 1 8 2 4 6
4 6 7 1 8 2 3 5
5 3 2 8 1 7 6 4
6 4 2 8 1 7 5 3

The first of these looks like this:

   disp {. (#~ 1<attempt"1) pegs
3 - 5
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
4 - 6
 

For this puzzle, we can also see that the solution can be described as: put the starting and ending numbers in the middle - everything else follows from there. It's perhaps interesting that we get this solution even if we do not explicitly put that logic into our code - it's built into the puzzle itself and is still the only solution no matter how we arrive there.

Java[edit]

The backtracking is getting tiresome, we'll try a stochastic solution for a change.

Works with: Java version 8
import static java.lang.Math.abs;
import java.util.*;
import static java.util.stream.Collectors.toList;
import static java.util.stream.IntStream.range;
 
public class NoConnection {
 
// adopted from Go
static int[][] links = {
{2, 3, 4}, // A to C,D,E
{3, 4, 5}, // B to D,E,F
{2, 4}, // D to C, E
{5}, // E to F
{2, 3, 4}, // G to C,D,E
{3, 4, 5}, // H to D,E,F
};
 
static int[] pegs = new int[8];
 
public static void main(String[] args) {
 
List<Integer> vals = range(1, 9).mapToObj(i -> i).collect(toList());
do {
Collections.shuffle(vals);
for (int i = 0; i < pegs.length; i++)
pegs[i] = vals.get(i);
 
} while (!solved());
 
printResult();
}
 
static boolean solved() {
for (int i = 0; i < links.length; i++)
for (int peg : links[i])
if (abs(pegs[i] - peg) == 1)
return false;
return true;
}
 
static void printResult() {
System.out.printf("  %s %s%n", pegs[0], pegs[1]);
System.out.printf("%s %s %s %s%n", pegs[2], pegs[3], pegs[4], pegs[5]);
System.out.printf("  %s %s%n", pegs[6], pegs[7]);
}
}

(takes about 500 shuffles on average)

       4  5       
    2  8  1  7    
       6  3     

JavaScript[edit]

ES6[edit]

Translation of: Haskell
(() => {
'use strict';
 
// GENERIC FUNCTIONS
 
// permutations :: [a] -> [[a]]
const permutations = xs =>
xs.length ? concatMap(x => concatMap(ys => [
[x].concat(ys)
],
permutations(delete_(x, xs))), xs) : [
[]
];
 
// concatMap :: (a -> [b]) -> [a] -> [b]
const concatMap = (f, xs) => [].concat.apply([], xs.map(f));
 
// delete_ :: Eq a => a -> [a] -> [a]
const delete_ = (x, xs) =>
deleteBy((a, b) => a === b, x, xs);
 
// deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
const deleteBy = (f, x, xs) =>
xs.length > 0 ? (
f(x, xs[0]) ? (
xs.slice(1)
) : [xs[0]].concat(deleteBy(f, x, xs.slice(1)))
) : [];
 
// enumFromTo :: Enum a => a -> a -> [a]
const enumFromTo = (m, n) => {
const [tm, tn] = [typeof m, typeof n];
if (tm === tn) {
const blnS = (tm === 'string'),
base = blnS ? m.codePointAt(0) : m,
end = blnS ? n.codePointAt(0) : n;
 
return Array.from({
length: Math.floor(end - base) + 1
}, (_, i) => blnS ? String.fromCodePoint(base + i) : m + i);
} else return undefined;
};
 
// all :: (a -> Bool) -> [a] -> Bool
const all = (f, xs) => xs.every(f);
 
// abs :: Num a => a -> a
const abs = Math.abs;
 
// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = (p, f, x) => {
let v = x;
while (!p(v)) v = f(v);
return v;
};
 
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = (f, xs, ys) => {
const ny = ys.length;
return (xs.length <= ny ? xs : xs.slice(0, ny))
.map((x, i) => f(x, ys[i]));
}
 
// justifyRight :: Int -> Char -> Text -> Text
const justifyRight = (n, cFiller, strText) =>
n > strText.length ? (
(cFiller.repeat(n) + strText)
.slice(-n)
) : strText;
 
// show :: a -> String
const show = x => JSON.stringify(x);
 
// unwords :: [String] -> String
const unwords = xs => xs.join(' ');
 
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
 
 
// CONNECTION PUZZLE
 
// universe :: [[Int]]
const universe = permutations(enumFromTo(1, 8));
 
// isSolution :: [Int] -> Bool
const isSolution = ([a, b, c, d, e, f, g, h]) =>
all(x => abs(x) > 1, [a - d, c - d, g - d, e - d, a - c, c - g, g - e,
e - a, b - e, d - e, h - e, f - e, b - d, d - h, h - f, f - b
]);
 
// firstSolution :: [Int]
const firstSolution = universe[until(
i => isSolution(universe[i]),
i => i + 1,
0
)];
 
// [Int]
const [a, b, c, d, e, f, g, h] = firstSolution;
 
 
// TEST
return unlines(
zipWith(
(a, n) => a + ' = ' + n.toString(),
enumFromTo('A', 'H'),
firstSolution
)
.concat(
[
[],
[a, b],
[c, d, e, f],
[g, h]
].map(xs => justifyRight(5, ' ', unwords(xs.map(show))))
)
);
})();
Output:
A = 3
B = 4
C = 7
D = 1
E = 8
F = 2
G = 5
H = 6
     
  3 4
7 1 8 2
  5 6

jq[edit]

Works with: jq version 1.4

We present a generate-and-test solver for a slightly more general version of the problem, in which there are N pegs and holes, and in which the connectedness of holes is defined by an array such that holes i and j are connected if and only if [i,j] is a member of the array.

The jq index origin is 0, and so in the following, the pegs and holes are internally numbered from 0 to (N-1) inclusive. That is, we interpret a permutation, p, of 0 .. (N-1) as meaning that the i-th peg is numbered p[i], for i in 0 .. (N-1).

However the pretty-print function shows solutions using the 1-to-8 numbering scheme for pegs, and the A-to-H lettering scheme for holes.

Part 1: Generic functions

# Short-circuit determination of whether (a|condition)
# is true for all a in array:
def forall(array; condition):
def check:
. as $ix
| if $ix == (array|length) then true
elif (array[$ix] | condition) then ($ix + 1) | check
else false
end;
0 | check;
 
# permutations of 0 .. (n-1)
def permutations(n):
# Given a single array, generate a stream by inserting n at different positions:
def insert(m;n):
if m >= 0 then (.[0:m] + [n] + .[m:]), insert(m-1;n) else empty end;
if n==0 then []
elif n == 1 then [1]
else
permutations(n-1) | insert(n-1; n)
end;
 
# Count the number of items in a stream
def count(f): reduce f as $_ (0; .+1);

Part 2: The no-connections puzzle for N pegs and holes

# Generate a stream of solutions.
# Input should be the connections array, i.e. an array of [i,j] pairs;
# N is the number of pegs and holds.
def solutions(N):
def abs: if . < 0 then -. else . end;
 
# Is the proposed permutation (the input) ok?
def ok(connections):
. as $p
| forall( connections;
(($p[.[0]] - $p[.[1]])|abs) != 1 );
 
. as $connections | permutations(N) | select(ok($connections);

Part 3: The 8-peg no-connection puzzle

# The connectedness matrix:
# In this table, 0 represents "A", etc, and an entry [i,j]
# signifies that the holes with indices i and j are connected.
def connections:
[[0, 2], [0, 3], [0, 4],
[1, 3], [1, 4], [1, 5],
[6, 2], [6, 3], [6, 4],
[7, 3], [7, 4], [7, 5],
[2, 3], [3, 4], [4, 5]]
;
 
def solve:
connections | solutions(8);
 
# pretty-print a solution for the 8-peg puzzle
def pp:
def pegs: ["A", "B", "C", "D", "E", "F", "G", "H"];
. as $in
| ("
A B
/|\\ /|\\
/ | X | \\
/ |/ \\| \\
C - D - E - F
\\ |\\ /| /
\\ | X | /
\\|/ \\|/
G H
" | explode) as $board
| (pegs | map(explode)) as $letters
| $letters
| reduce range(0;length) as $i ($board; index($letters[$i]) as $ix | .[$ix] = $in[$i] + 48)
| implode;

Examples:

# To print all the solutions:
# solve | pp
 
# To count the number of solutions:
# count(solve)
 
# jq 1.4 lacks facilities for harnessing generators,
# but the following will suffice here:
def one(f): reduce f as $s
(null; if . == null then $s else . end);
 
one(solve) | pp
 
Output:
$ jq -n -r -f no_connection.jq
 
5 6
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
3 4

Mathematica[edit]

This one simply takes all permutations of the pegs and filters out invalid solutions.

sol = Fold[
Select[#,
Function[perm, Abs[perm[[#2[[1]]]] - perm[[#2[[2]]]]] > 1]] &,
Permutations[
Range[8]], {{1, 3}, {1, 4}, {1, 5}, {2, 4}, {2, 5}, {2, 6}, {3,
4}, {3, 7}, {4, 5}, {4, 7}, {4, 8}, {5, 6}, {5, 7}, {5, 8}, {6,
8}}][[1]];
Print[StringForm[
" `` ``\n /|\\ /|\\\n / | X | \\\n / |/ \\| \\\n`` - `` \
- `` - ``\n \\ |\\ /| /\n \\ | X | /\n \\|/ \\|/\n `` ``",
Sequence @@ sol]];
Output:
    3   4
   /|\ /|\
  / | X | \
 /  |/ \|  \
7 - 1 - 8 - 2
 \  |\ /|  /
  \ | X | /
   \|/ \|/
    5   6

Perl 6[edit]

Using the Warnsdorff algorithm from Solve_a_Hidato_puzzle. The idiosyncratic adjacency diagram is dealt with by the simple expedient of bending the two vertical lines || into two bows )(, such that adjacency can be calculated simply as a distance of 2 or less.

my @adjacent = gather -> $y, $x {
take [$y,$x] if abs($x|$y) > 2;
} for flat -5 .. 5 X -5 .. 5;
 
solveboard q:to/END/;
. _ . . _ .
. . . . . .
_ . _ 1 . _
. . . . . .
. _ . . _ .
END
Output:
  4     3  
           
2   8 1   7
           
  6     5  
18 tries

Phix[edit]

Brute force solution. I ordered the links highest letter first, then grouped by start letter to eliminate things asap. Nothing to eliminate when placing A and B, when placing C, check that CA>1, when placing D, check that DA,DB,DC are all >1, etc.

 
constant txt = """
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H"""
--constant links = "CA DA DB DC EA EB ED FB FE GC GD GE HD HE HF"
constant links = {"","","A","ABC","ABD","BE","CDE","DEF"}
 
function solve(sequence s, integer idx, sequence part)
object res
integer v, p
for i=1 to length(s) do
v = s[i]
for j=1 to length(links[idx]) do
p = links[idx][j]-'@'
if abs(v-part[p])<2 then v=0 exit end if
end for
if v then
if length(s)=1 then return part&v end if
res = solve(s[1..i-1]&s[i+1..$],idx+1,part&v)
if sequence(res) then return res end if
end if
end for
return 0
end function
 
printf(1,substitute_all(txt,"ABCDEFGH",solve("12345678",1,"")))
Output:
        3   4
       /|\ /|\
      / | X | \
     /  |/ \|  \
    7 - 1 - 8 - 2
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        5   6

Prolog[edit]

Works with SWi-Prolog with module clpfd written by Markus Triska

We first compute a list of nodes, with sort this list, and we attribute a value at the nodes.

:- use_module(library(clpfd)).
 
edge(a, c).
edge(a, d).
edge(a, e).
edge(b, d).
edge(b, e).
edge(b, f).
edge(c, d).
edge(c, g).
edge(d, e).
edge(d, g).
edge(d, h).
edge(e, f).
edge(e, g).
edge(e, h).
edge(f, h).
 
connected(A, B) :-
( edge(A,B); edge(B, A)).
 
no_connection_puzzle(Vs) :-
% construct the arranged list of the nodes
bagof(A, B^(edge(A,B); edge(B, A)), Lst),
sort(Lst, L),
length(L, Len),
 
% construct the list of the values
length(Vs, Len),
Vs ins 1..Len,
all_distinct(Vs),
 
% two connected nodes must have values different for more than 1
set_constraints(L, Vs),
label(Vs).
 
 
set_constraints([], []).
 
set_constraints([H | T], [VH | VT]) :-
set_constraint(H, T, VH, VT),
set_constraints(T, VT).
 
 
 
set_constraint(_, [], _, []).
set_constraint(H, [H1 | T1], V, [VH | VT]) :-
connected(H, H1),
( V - VH #> 1; VH - V #> 1),
set_constraint(H, T1, V, VT).
 
set_constraint(H, [H1 | T1], V, [_VH | VT]) :-
\+connected(H, H1),
set_constraint(H, T1, V, VT).
 
 

Output :

 ?- no_connection_puzzle(Vs).
Vs = [4, 3, 2, 8, 1, 7, 6, 5] .

 27 ?- setof(Vs, no_connection_puzzle(Vs), R), length(R, Len).
R = [[3, 4, 7, 1, 8, 2, 5, 6], [3, 5, 7, 1, 8, 2, 4|...], [3, 6, 7, 1, 8, 2|...], [3, 6, 7, 1, 8|...], [4, 3, 2, 8|...], [4, 5, 2|...], [4, 5|...], [4|...], [...|...]|...],
Len = 16.

Python[edit]

A brute force search solution.

from __future__ import print_function
from itertools import permutations
from enum import Enum
 
A, B, C, D, E, F, G, H = Enum('Peg', 'A, B, C, D, E, F, G, H')
 
connections = ((A, C), (A, D), (A, E),
(B, D), (B, E), (B, F),
(G, C), (G, D), (G, E),
(H, D), (H, E), (H, F),
(C, D), (D, E), (E, F))
 
 
def ok(conn, perm):
"""Connected numbers ok?"""
this, that = (c.value - 1 for c in conn)
return abs(perm[this] - perm[that]) != 1
 
 
def solve():
return [perm for perm in permutations(range(1, 9))
if all(ok(conn, perm) for conn in connections)]
 
 
if __name__ == '__main__':
solutions = solve()
print("A, B, C, D, E, F, G, H =", ', '.join(str(i) for i in solutions[0]))
Output:
A, B, C, D, E, F, G, H = 3, 4, 7, 1, 8, 2, 5, 6


All solutions pretty printed

Add the following code after that above:

def pp(solution):
"""Prettyprint a solution"""
boardformat = r"""
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H"""

for letter, number in zip("ABCDEFGH", solution):
boardformat = boardformat.replace(letter, str(number))
print(boardformat)
 
 
if __name__ == '__main__':
for i, s in enumerate(solutions, 1):
print("\nSolution", i, end='')
pp(s)
Extra output
Solution 1
         3   4
        /|\ /|\
       / | X | \
      /  |/ \|  \
     7 - 1 - 8 - 2
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         5   6

Solution 2
         3   5
        /|\ /|\
       / | X | \
      /  |/ \|  \
     7 - 1 - 8 - 2
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         4   6

Solution 3
         3   6
        /|\ /|\
       / | X | \
      /  |/ \|  \
     7 - 1 - 8 - 2
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         4   5

Solution 4
         3   6
        /|\ /|\
       / | X | \
      /  |/ \|  \
     7 - 1 - 8 - 2
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         5   4

Solution 5
         4   3
        /|\ /|\
       / | X | \
      /  |/ \|  \
     2 - 8 - 1 - 7
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         6   5

Solution 6
         4   5
        /|\ /|\
       / | X | \
      /  |/ \|  \
     2 - 8 - 1 - 7
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         6   3

Solution 7
         4   5
        /|\ /|\
       / | X | \
      /  |/ \|  \
     7 - 1 - 8 - 2
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         3   6

Solution 8
         4   6
        /|\ /|\
       / | X | \
      /  |/ \|  \
     7 - 1 - 8 - 2
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         3   5

Solution 9
         5   3
        /|\ /|\
       / | X | \
      /  |/ \|  \
     2 - 8 - 1 - 7
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         6   4

Solution 10
         5   4
        /|\ /|\
       / | X | \
      /  |/ \|  \
     2 - 8 - 1 - 7
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         6   3

Solution 11
         5   4
        /|\ /|\
       / | X | \
      /  |/ \|  \
     7 - 1 - 8 - 2
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         3   6

Solution 12
         5   6
        /|\ /|\
       / | X | \
      /  |/ \|  \
     7 - 1 - 8 - 2
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         3   4

Solution 13
         6   3
        /|\ /|\
       / | X | \
      /  |/ \|  \
     2 - 8 - 1 - 7
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         4   5

Solution 14
         6   3
        /|\ /|\
       / | X | \
      /  |/ \|  \
     2 - 8 - 1 - 7
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         5   4

Solution 15
         6   4
        /|\ /|\
       / | X | \
      /  |/ \|  \
     2 - 8 - 1 - 7
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         5   3

Solution 16
         6   5
        /|\ /|\
       / | X | \
      /  |/ \|  \
     2 - 8 - 1 - 7
      \  |\ /|  /
       \ | X | /
        \|/ \|/
         4   3

Racket[edit]

#lang racket
;; Solve the no connection puzzle. Tim Brown Oct. 2014
 
;; absolute difference of a and b if they are both true
(define (and- a b) (and a b (abs (- a b))))
 
;; Finds the differences of all established connections in the network
(define (network-diffs (A #f) (B #f) (C #f) (D #f) (E #f) (F #f) (G #f) (H #f))
(list (and- A C) (and- A D) (and- A E)
(and- B D) (and- B E) (and- B F)
(and- C D) (and- C G)
(and- D E) (and- D G) (and- D H)
(and- E F) (and- E G) (and- E H)
(and- F G)))
 
;; Make sure there is “no connection” in the network N; return N if good
(define (good-network? N)
(and (for/and ((d (filter values (apply network-diffs N)))) (> d 1)) N))
 
;; possible optimisation is to reverse the arguments to network-diffs, reverse the return value from
;; this function and make this a cons but we're pretty quick here as it is.
(define (find-good-network pegs (n/w null))
(if (null? pegs) n/w
(for*/or ((p pegs))
(define n/w+ (append n/w (list p)))
(and (good-network? n/w+)
(find-good-network (remove p pegs =) n/w+)))))
 
(define (render-puzzle pzl)
(apply printf (regexp-replace* "O" #<<EOS
O O
/|\ /|\
/ | X | \
/ |/ \| \
O - O - O - O
\ |\ /| /
\ | X | /
\|/ \|/
O O~%
EOS
"~a") pzl))
 
(render-puzzle (find-good-network '(1 2 3 4 5 6 7 8)))
Output:
    3   4
   /|\ /|\
  / | X | \
 /  |/ \|  \
7 - 1 - 8 - 2
 \  |\ /|  /
  \ | X | /
   \|/ \|/
    5   6

REXX[edit]

unannotated solutions[edit]

/*REXX program  solves  the  "no-connection"  puzzle   (the puzzle has eight pegs).     */
parse arg limit . /*number of solutions wanted.*/ /* ╔═══════════════════════════╗ */
if limit=='' | limit=="." then limit=1 /* ║ A B ║ */
/* ║ /│\ /│\ ║ */
@. = /* ║ / │ \/ │ \ ║ */
@.1 = 'A C D E' /* ║ / │ /\ │ \ ║ */
@.2 = 'B D E F' /* ║ / │/ \│ \ ║ */
@.3 = 'C A D G' /* ║ C────D────E────F ║ */
@.4 = 'D A B C E G' /* ║ \ │\ /│ / ║ */
@.5 = 'E A B D F H' /* ║ \ │ \/ │ / ║ */
@.6 = 'F B E H' /* ║ \ │ /\ │ / ║ */
@.7 = 'G C D E' /* ║ \│/ \│/ ║ */
@.8 = 'H D E F' /* ║ G H ║ */
cnt=0 /* ╚═══════════════════════════╝ */
do pegs=1 while @.pegs\==''; _=word(@.pegs,1)
subs=0
do #=1 for words(@.pegs) -1 /*create list of node paths.*/
__=word(@.pegs, # + 1); if __>_ then iterate
subs=subs + 1;  !._.subs=__
end /*#*/
 !._.0=subs /*assign the number of the node paths. */
end /*pegs*/
pegs=pegs-1 /*the number of pegs to be seated. */
_=' ' /*_ is used for indenting the output.*/
do a=1 for pegs; if ?('A') then iterate
do b=1 for pegs; if ?('B') then iterate
do c=1 for pegs; if ?('C') then iterate
do d=1 for pegs; if ?('D') then iterate
do e=1 for pegs; if ?('E') then iterate
do f=1 for pegs; if ?('F') then iterate
do g=1 for pegs; if ?('G') then iterate
do h=1 for pegs; if ?('H') then iterate
say _ 'a='a _ 'b='||b _ 'c='c _ 'd='d _ 'e='e _ 'f='f _ 'g='g _ 'h='h
cnt=cnt+1; if cnt==limit then leave a
end /*h*/
end /*g*/
end /*f*/
end /*e*/
end /*d*/
end /*c*/
end /*b*/
end /*a*/
say /*display a blank line to the terminal.*/
s= left('s', cnt\==1) /*handle the case of plurals (or not).*/
say 'found ' cnt " solution"s'.' /*display the number of solutions found*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
?: parse arg node; nn=value(node)
nH=nn+1
do cn=c2d('A') to c2d(node) - 1; if value( d2c(cn) )==nn then return 1
end /*cn*/ /* [↑] see if there any are duplicates.*/
nL=nn-1
do ch=1 for !.node.0 /* [↓] see if there any ¬= ±1 values.*/
$=!.node.ch; fn=value($) /*the node name and its current peg #.*/
if nL==fn | nH==fn then return 1 /*if ≡ ±1, then the node can't be used.*/
end /*ch*/ /* [↑] looking for suitable number. */
return 0 /*the subroutine arg value passed is OK.*/

output   when using the default input:

     a=3      b=4      c=7      d=1      e=8      f=2      g=5      h=6

found  1  solution.

output   when using the input of:   999

     a=3      b=4      c=7      d=1      e=8      f=2      g=5      h=6
     a=3      b=5      c=7      d=1      e=8      f=2      g=4      h=6
     a=3      b=6      c=7      d=1      e=8      f=2      g=4      h=5
     a=3      b=6      c=7      d=1      e=8      f=2      g=5      h=4
     a=4      b=3      c=2      d=8      e=1      f=7      g=6      h=5
     a=4      b=5      c=2      d=8      e=1      f=7      g=6      h=3
     a=4      b=5      c=7      d=1      e=8      f=2      g=3      h=6
     a=4      b=6      c=7      d=1      e=8      f=2      g=3      h=5
     a=5      b=3      c=2      d=8      e=1      f=7      g=6      h=4
     a=5      b=4      c=2      d=8      e=1      f=7      g=6      h=3
     a=5      b=4      c=7      d=1      e=8      f=2      g=3      h=6
     a=5      b=6      c=7      d=1      e=8      f=2      g=3      h=4
     a=6      b=3      c=2      d=8      e=1      f=7      g=4      h=5
     a=6      b=3      c=2      d=8      e=1      f=7      g=5      h=4
     a=6      b=4      c=2      d=8      e=1      f=7      g=5      h=3
     a=6      b=5      c=2      d=8      e=1      f=7      g=4      h=3

found  16  solutions.

annotated solutions[edit]

Usage note:   if the   limit   (the 1st argument)   is negative, a diagram (node graph) is shown.

/*REXX program  solves  the  "no-connection"  puzzle   (the puzzle has eight pegs).     */
@abc='ABCDEFGHIJKLMNOPQRSTUVWXYZ'
parse arg limit . /*number of solutions wanted.*/ /* ╔═══════════════════════════╗ */
if limit=='' | limit=="." then limit=1 /* ║ A B ║ */
oLimit=limit; limit=abs(limit) /* ║ /│\ /│\ ║ */
@. = /* ║ / │ \/ │ \ ║ */
@.1 = 'A C D E' /* ║ / │ /\ │ \ ║ */
@.2 = 'B D E F' /* ║ / │/ \│ \ ║ */
@.3 = 'C A D G' /* ║ C────D────E────F ║ */
@.4 = 'D A B C E G' /* ║ \ │\ /│ / ║ */
@.5 = 'E A B D F H' /* ║ \ │ \/ │ / ║ */
@.6 = 'F B E H' /* ║ \ │ /\ │ / ║ */
@.7 = 'G C D E' /* ║ \│/ \│/ ║ */
@.8 = 'H D E F' /* ║ G H ║ */
cnt=0 /* ╚═══════════════════════════╝ */
do pegs=1 while @.pegs\==''; _=word(@.pegs, 1)
subs=0
do #=1 for words(@.pegs) -1 /*create list of node paths.*/
__=word(@.pegs, #+1); if __>_ then iterate
subs=subs + 1;  !._.subs=__
end /*#*/
 !._.0=subs /*assign the number of the node paths. */
end /*pegs*/
pegs=pegs - 1 /*the number of pegs to be seated. */
_=' ' /*_ is used for indenting the output. */
do a=1 for pegs; if ?('A') then iterate
do b=1 for pegs; if ?('B') then iterate
do c=1 for pegs; if ?('C') then iterate
do d=1 for pegs; if ?('D') then iterate
do e=1 for pegs; if ?('E') then iterate
do f=1 for pegs; if ?('F') then iterate
do g=1 for pegs; if ?('G') then iterate
do h=1 for pegs; if ?('H') then iterate
call showNodes
cnt=cnt+1; if cnt==limit then leave a
end /*h*/
end /*g*/
end /*f*/
end /*e*/
end /*d*/
end /*c*/
end /*b*/
end /*a*/
say /*display a blank line to the terminal.*/
s=left('s', cnt\==1) /*handle the case of plurals (or not).*/
say 'found ' cnt " solution"s'.' /*display the number of solutions found*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
?: parse arg node; nn=value(node)
nH=nn+1
do cn=c2d('A') to c2d(node)-1; if value( d2c(cn) )==nn then return 1
end /*cn*/ /* [↑] see if there're any duplicates.*/
nL=nn-1
do ch=1 for !.node.0 /* [↓] see if there any ¬= ±1 values.*/
$=!.node.ch; fn=value($) /*the node name and its current peg #.*/
if nL==fn | nH==fn then return 1 /*if ≡ ±1, then the node can't be used.*/
end /*ch*/ /* [↑] looking for suitable number. */
return 0 /*the subroutine arg value passed is OK*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
showNodes: _=left('', 5) /*_ is used for padding the output. */
show=0 /*indicates no graph has been found yet*/
do box=1 for sourceline() while oLimit<0 /*Negative? Then display the diagram. */
xw=sourceline(box) /*get a source line of this program. */
p2=lastpos('*', xw) /*the position of last asterisk.*/
p1=lastpos('*', xw, max(1, p2-1) ) /* " " " penultimate " */
if pos('╔', xw)\==0 then show=1 /*Have found the top-left box corner ? */
if \show then iterate /*Not found? Then skip this line. */
xb=substr(xw, p1+1, p2-p1-2) /*extract the "box" part of line. */
xt=xb /*get a working copy of the box. */
do jx=1 for pegs /*do a substitution for all the pegs. */
@=substr(@abc, jx, 1) /*get the name of the peg (A ──► Z). */
xt=translate(xt,value(@),@) /*substitute the peg name with a value.*/
end /*jx*/ /* [↑] graph is limited to 26 nodes.*/
say _ xb _ _ xt /*display one line of the graph. */
if pos('╝', xw)\==0 then return /*Is this last line of graph? Then stop*/
end /*box*/
say _ 'a='a _ 'b='||b _ 'c='c _ 'd='d _ ' e='e _ 'f='f _ 'g='g _ 'h='h
return

output when using the input of:   -3

       ╔═══════════════════════════╗              ╔═══════════════════════════╗
       ║          A    B           ║              ║          3    4           ║
       ║         /│\  /│\          ║              ║         /│\  /│\          ║
       ║        / │ \/ │ \         ║              ║        / │ \/ │ \         ║
       ║       /  │ /\ │  \        ║              ║       /  │ /\ │  \        ║
       ║      /   │/  \│   \       ║              ║      /   │/  \│   \       ║
       ║     C────D────E────F      ║              ║     7────1────8────2      ║
       ║      \   │\  /│   /       ║              ║      \   │\  /│   /       ║
       ║       \  │ \/ │  /        ║              ║       \  │ \/ │  /        ║
       ║        \ │ /\ │ /         ║              ║        \ │ /\ │ /         ║
       ║         \│/  \│/          ║              ║         \│/  \│/          ║
       ║          G    H           ║              ║          5    6           ║
       ╚═══════════════════════════╝              ╚═══════════════════════════╝
       ╔═══════════════════════════╗              ╔═══════════════════════════╗
       ║          A    B           ║              ║          3    5           ║
       ║         /│\  /│\          ║              ║         /│\  /│\          ║
       ║        / │ \/ │ \         ║              ║        / │ \/ │ \         ║
       ║       /  │ /\ │  \        ║              ║       /  │ /\ │  \        ║
       ║      /   │/  \│   \       ║              ║      /   │/  \│   \       ║
       ║     C────D────E────F      ║              ║     7────1────8────2      ║
       ║      \   │\  /│   /       ║              ║      \   │\  /│   /       ║
       ║       \  │ \/ │  /        ║              ║       \  │ \/ │  /        ║
       ║        \ │ /\ │ /         ║              ║        \ │ /\ │ /         ║
       ║         \│/  \│/          ║              ║         \│/  \│/          ║
       ║          G    H           ║              ║          4    6           ║
       ╚═══════════════════════════╝              ╚═══════════════════════════╝
       ╔═══════════════════════════╗              ╔═══════════════════════════╗
       ║          A    B           ║              ║          3    6           ║
       ║         /│\  /│\          ║              ║         /│\  /│\          ║
       ║        / │ \/ │ \         ║              ║        / │ \/ │ \         ║
       ║       /  │ /\ │  \        ║              ║       /  │ /\ │  \        ║
       ║      /   │/  \│   \       ║              ║      /   │/  \│   \       ║
       ║     C────D────E────F      ║              ║     7────1────8────2      ║
       ║      \   │\  /│   /       ║              ║      \   │\  /│   /       ║
       ║       \  │ \/ │  /        ║              ║       \  │ \/ │  /        ║
       ║        \ │ /\ │ /         ║              ║        \ │ /\ │ /         ║
       ║         \│/  \│/          ║              ║         \│/  \│/          ║
       ║          G    H           ║              ║          4    5           ║
       ╚═══════════════════════════╝              ╚═══════════════════════════╝

found  3  solutions.

Ruby[edit]

Be it Golden Frogs jumping on trancendental lilly pads, or a Knight on a board, or square pegs into round holes this is essentially a Hidato Like Problem, so I use HLPSolver:

 
# Solve No Connection Puzzle
#
# Nigel_Galloway
# October 6th., 2014
require 'HLPSolver'
ADJACENT = [[0,0]]
A,B,C,D,E,F,G,H = [0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]
 
board1 = <<EOS
. 0 0 .
0 0 1 0
. 0 0 .
 
EOS

g = HLPsolver.new(board1)
g.board[A[0]][A[1]].adj = [B,G,H,F]
g.board[B[0]][B[1]].adj = [A,C,G,H]
g.board[C[0]][C[1]].adj = [B,E,F,H]
g.board[D[0]][D[1]].adj = [F]
g.board[E[0]][E[1]].adj = [C]
g.board[F[0]][F[1]].adj = [A,C,D,G]
g.board[G[0]][G[1]].adj = [A,B,F,H]
g.board[H[0]][H[1]].adj = [A,B,C,G]
g.solve
 
Output:
Problem:
     0  0
  0  0  1  0
     0  0

Solution:
     5  3
  2  8  1  7
     6  4

Tcl[edit]

Library: Tcllib (Package: struct::list)
package require Tcl 8.6
package require struct::list
 
proc haveAdjacent {a b c d e f g h} {
expr {
[edge $a $c] ||
[edge $a $d] ||
[edge $a $e] ||
[edge $b $d] ||
[edge $b $e] ||
[edge $b $f] ||
[edge $c $d] ||
[edge $c $g] ||
[edge $d $e] ||
[edge $d $g] ||
[edge $d $h] ||
[edge $e $f] ||
[edge $e $g] ||
[edge $e $h] ||
[edge $f $h]
}
}
proc edge {x y} {
expr {abs($x-$y) == 1}
}
 
set layout [string trim {
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H
} \n]
struct::list foreachperm p {1 2 3 4 5 6 7 8} {
if {![haveAdjacent {*}$p]} {
puts [string map [join [
lmap name {A B C D E F G H} val $p {list $name $val}
]] $layout]
break
}
}
Output:
        3   4
       /|\ /|\ 
      / | X | \ 
     /  |/ \|  \ 
    7 - 1 - 8 - 2
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        5   6

XPL0[edit]

include c:\cxpl\codes;
 
int Hole, Max, I;
char Box(8), Str;
def A, B, C, D, E, F, G, H;
[for Hole:= 0 to 7 do Box(Hole):= Hole+1;
Max:= 7;
while abs(Box(D)-Box(A)) < 2 or abs(Box(D)-Box(C)) < 2 or
abs(Box(D)-Box(G)) < 2 or abs(Box(D)-Box(E)) < 2 or
abs(Box(A)-Box(C)) < 2 or abs(Box(C)-Box(G)) < 2 or
abs(Box(G)-Box(E)) < 2 or abs(Box(E)-Box(A)) < 2 or
abs(Box(E)-Box(B)) < 2 or abs(Box(E)-Box(H)) < 2 or
abs(Box(E)-Box(F)) < 2 or abs(Box(B)-Box(D)) < 2 or
abs(Box(D)-Box(H)) < 2 or abs(Box(H)-Box(F)) < 2 or
abs(Box(F)-Box(B)) < 2 do
loop [I:= Box(0); \next permutation
for Hole:= 0 to Max-1 do Box(Hole):= Box(Hole+1);
Box(Max):= I;
if I # Max+1 then [Max:= 7; quit]
else Max:= Max-1];
Str:= "
# #
/|\ /|\
/ | X | \
/ |/ \| \
# - # - # - #
\ |\ /| /
\ | X | /
\|/ \|/
# #
";
Hole:= 0; I:= 0;
repeat if Str(I)=^# then [Str(I):= Box(Hole)+^0; Hole:= Hole+1];
I:= I+1;
until Hole = 8;
Text(0, Str);
]
Output:
    5   6
   /|\ /|\
  / | X | \
 /  |/ \|  \
7 - 1 - 8 - 2
 \  |\ /|  /
  \ | X | /
   \|/ \|/
    3   4

zkl[edit]

Translation of: D
const PegA=0, PegB=1, PegC=2, PegD=3, PegE=4, PegF=5, PegG=6, PegH=7;
connections:=T(
T(PegA, PegC), T(PegA, PegD), T(PegA, PegE),
T(PegB, PegD), T(PegB, PegE), T(PegB, PegF),
T(PegC, PegD), T(PegD, PegE), T(PegE, PegF),
T(PegG, PegC), T(PegG, PegD), T(PegG, PegE),
T(PegH, PegD), T(PegH, PegE), T(PegH, PegF) );
CZ:=connections.len();
#<<< // Use "raw" string in a "here doc" so \ isn't a quote char
board:=
0'$ A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H$;
#<<< // end "here doc"
 
perm:=T(PegA,PegB,PegC,PegD,PegE,PegF,PegG,PegH); // Peg[8]
foreach p in (Utils.Helpers.permuteW(perm)){ // permutation iterator
if(connections.filter1('wrap([(a,b)]){ (p[a] - p[b]).abs()<=1 })) continue;
board.translate("ABCDEFGH",p.apply('+(1)).concat()).println();
break; // comment out to see all 16 solutions
}

The filter1 method stops on the first True, so it acts like a conditional or.

Output:
        5   6
       /|\ /|\
      / | X | \
     /  |/ \|  \
    7 - 1 - 8 - 2
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        3   4