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Intersecting number wheels

Intersecting number wheels
You are encouraged to solve this task according to the task description, using any language you may know.

A number wheel has:

• A name which is an uppercase letter.
• A set of ordered values which are either numbers or names.

A number is generated/yielded from a named wheel by:

1. Starting at the first value of the named wheel and advancing through subsequent values and wrapping around to the first value to form a "wheel":
1.a If the value is a number, yield it.
1.b If the value is a name, yield the next value from the named wheel
1.c Advance the position of this wheel.

Given the wheel

A: 1 2 3

the number 1 is first generated, then 2, then 3, 1, 2, 3, 1, ...

Note: When more than one wheel is defined as a set of intersecting wheels then the first named wheel is assumed to be the one that values are generated from.

Examples

Given the wheels:

A: 1 B 2
B: 3 4

The series of numbers generated starts:

1, 3, 2, 1, 4, 2, 1, 3, 2, 1, 4, 2, 1, 3, 2...

The intersections of number wheels can be more complex, (and might loop forever), and wheels may be multiply connected.

Note: If a named wheel is referenced more than once by one or many other wheels, then there is only one position of the wheel that is advanced by each and all references to it.

E.g.

A:  1 D D
D:  6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Generate and show the first twenty terms of the sequence of numbers generated from these groups:

Intersecting Number Wheel group:
A:  1 2 3

Intersecting Number Wheel group:
A:  1 B 2
B:  3 4

Intersecting Number Wheel group:
A:  1 D D
D:  6 7 8

Intersecting Number Wheel group:
A:  1 B C
B:  3 4
C:  5 B

11l

Translation of: Python
F nextfrom(&w, =name)
L
V nxt = w[name]
w[name] = w[name][1..] + w[name][0.<1]
I nxt C ‘0’..‘9’
R nxt
name = nxt

L(group) |‘A: 1 2 3
A: 1 B 2; B: 3 4
A: 1 D D; D: 6 7 8
A: 1 B C; B: 3 4; C: 5 B’.split("\n")
print("Intersecting Number Wheel group:\n "group)
[String = [String]] wheel
V first = ‘’
L(w) group.split(‘;’)
V s = w.trim(‘ ’).split(‘ ’)
V name = s
wheel[name[0 .< (len)-1]] = s[1..]
first = I first == ‘’ {name[0 .< (len)-1]} E first
V gen = (0.<20).map(i -> nextfrom(&@wheel, @first)).join(‘ ’)
print(" Generates:\n "gen" ...\n")
Output:
Intersecting Number Wheel group:
A: 1 2 3
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
A: 1 B 2; B: 3 4
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
A: 1 D D; D: 6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
A: 1 B C; B: 3 4; C: 5 B
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...

ALGOL 68

BEGIN
# a number wheel element #
MODE NWELEMENT = UNION( CHAR # wheel name #, INT # wheel value # );
# a number wheel #
MODE NW = STRUCT( CHAR name, REF INT position, FLEX[ 1 : 0 ]NWELEMENT values );
# get the next value from a number wheel in an array of number wheels #
# note: invalid wheel names will cause subscript range errors #
OP NEXT = ( []NW wheels )INT:
BEGIN
INT result;
BOOL found := FALSE;
INT w := LWB wheels; # start with the first wheel #
IF position OF wheels[ w ] > UPB values OF wheels[ w ] THEN
# passed the end of the wheel, go back to the start #
position OF wheels[ w ] := LWB values OF wheels[ w ]
FI;
NWELEMENT e = ( values OF wheels[ w ] )[ position OF wheels[ w ] ];
position OF wheels[ w ] +:= 1;
CASE e
IN ( INT n ): BEGIN result := n; found := TRUE END
, ( CHAR c ): BEGIN
w := LWB wheels;
WHILE name OF wheels[ w ] /= c DO w +:= 1 OD
END
ESAC
OD;
result
END # NEXT # ;
# prints the first n values from an array of wheels #
PROC show = ( INT n, []NW wheels )VOID:
BEGIN
print( ( "First ", whole( n, 0 ), " values from the Intersecting Number Wheels:" ) );
FOR i FROM LWB wheels TO UPB wheels DO
print( ( newline, " ", name OF wheels[ i ], ":" ) );
FOR v FROM LWB values OF wheels[ i ] TO UPB values OF wheels[ i ] DO
CASE ( values OF wheels[ i ] )[ v ]
IN ( INT n ): print( ( " ", whole( n, 0 ) ) )
, ( CHAR c ): print( ( " ", c ) )
ESAC
OD
OD;
print( ( newline, " " ) );
FOR i TO n DO print( ( " ", whole( NEXT wheels, 0 ) ) ) OD;
print( ( newline, newline ) )
END # show # ;
# show some wheels in action #
show( 20, ( NW( "A", LOC INT := 1, ( 1, 2, 3 ) ) ) );
show( 20, ( NW( "A", LOC INT := 1, ( 1, "B", 2 ) )
, NW( "B", LOC INT := 1, ( 3, 4 ) ) ) );
show( 20, ( NW( "A", LOC INT := 1, ( 1, "D", "D" ) )
, NW( "D", LOC INT := 1, ( 6, 7, 8 ) ) ) );
show( 20, ( NW( "A", LOC INT := 1, ( 1, "B", "C" ) )
, NW( "B", LOC INT := 1, ( 3, 4 ) )
, NW( "C", LOC INT := 1, ( 5, "B" ) ) ) )
END
Output:
First 20 values from the Intersecting Number Wheels:
A: 1 2 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

First 20 values from the Intersecting Number Wheels:
A: 1 B 2
B: 3 4
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

First 20 values from the Intersecting Number Wheels:
A: 1 D D
D: 6 7 8
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

First 20 values from the Intersecting Number Wheels:
A: 1 B C
B: 3 4
C: 5 B
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

AutoHotkey

obj1 := {"A":[1, 2, 3]}
obj2 := {"A":[1, "B", 2] , "B":[3, 4]}
obj3 := {"A":[1, "D", "D"] , "D":[6, 7, 8]}
obj4 := {"A":[1, "B", "C"] , "B":[3, 4] , "C":[5, "B"]}

loop 4
{
str := ""
for k, v in obj%A_Index% {
str .= "{" k " : "
for i, t in v
str .= t ","
str := Trim(str, ",") "}, "
}
str := Trim(str, ", ")
x := INW(obj%A_Index%)
result .= str "`n" x.1 "`n" x.2 "`n------`n"
}
MsgBox % result
return

INW(obj, num:=20){
sets := [], ptr := []
for k, v in obj {
if A_Index=1
s := k, s1 := k
%k% := v, sets.Push(k), ptr[k] := 0
}
loop % num {
ptr[s]++
while !((v := %s%[ptr[s]]) ~= "\d") {
s := %s%[ptr[s]]
ptr[s]++
}
key .= s "." ptr[s] ", "
result .= %s%[ptr[s]] " "
s := s1
for i, set in sets
ptr[set] := ptr[set] = %set%.count() ? 0 : ptr[set]
}
return [key, result]
}
Output:
{A : 1,2,3}
A.1, A.2, A.3, A.1, A.2, A.3, A.1, A.2, A.3, A.1, A.2, A.3, A.1, A.2, A.3, A.1, A.2, A.3, A.1, A.2,
1    2    3    1    2    3    1    2    3    1    2    3    1    2    3    1    2    3    1    2
------
{A : 1,B,2}, {B : 3,4}
A.1, B.1, A.3, A.1, B.2, A.3, A.1, B.1, A.3, A.1, B.2, A.3, A.1, B.1, A.3, A.1, B.2, A.3, A.1, B.1,
1    3    2    1    4    2    1    3    2    1    4    2    1    3    2    1    4    2    1    3
------
{A : 1,D,D}, {D : 6,7,8}
A.1, D.1, D.2, A.1, D.3, D.1, A.1, D.2, D.3, A.1, D.1, D.2, A.1, D.3, D.1, A.1, D.2, D.3, A.1, D.1,
1    6    7    1    8    6    1    7    8    1    6    7    1    8    6    1    7    8    1    6
------
{A : 1,B,C}, {B : 3,4}, {C : 5,B}
A.1, B.1, C.1, A.1, B.2, B.1, A.1, B.2, C.1, A.1, B.1, B.2, A.1, B.1, C.1, A.1, B.2, B.1, A.1, B.2,
1    3    5    1    4    3    1    4    5    1    3    4    1    3    5    1    4    3    1    4
------

C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

struct Wheel {
char *seq;
int len;
int pos;
};

struct Wheel *create(char *seq) {
struct Wheel *w = malloc(sizeof(struct Wheel));
if (w == NULL) {
return NULL;
}

w->seq = seq;
w->len = strlen(seq);
w->pos = 0;

return w;
}

char cycle(struct Wheel *w) {
char c = w->seq[w->pos];
w->pos = (w->pos + 1) % w->len;
return c;
}

struct Map {
struct Wheel *v;
struct Map *next;
char k;
};

struct Map *insert(char k, struct Wheel *v, struct Map *head) {
struct Map *m = malloc(sizeof(struct Map));
if (m == NULL) {
return NULL;
}

m->k = k;
m->v = v;

return m;
}

struct Wheel *find(char k, struct Map *m) {
struct Map *ptr = m;

while (ptr != NULL) {
if (ptr->k == k) {
return ptr->v;
}
ptr = ptr->next;
}

return NULL;
}

void printOne(char k, struct Map *m) {
struct Wheel *w = find(k, m);
char c;

if (w == NULL) {
printf("Missing the wheel for: %c\n", k);
exit(1);
}

c = cycle(w);
if ('0' <= c && c <= '9') {
printf(" %c", c);
} else {
printOne(c, m);
}
}

void exec(char start, struct Map *m) {
struct Wheel *w;
int i;

if (m == NULL) {
printf("Unable to proceed.");
return;
}

for (i = 0; i < 20; i++) {
printOne(start, m);
}
printf("\n");
}

void group1() {
struct Wheel *a = create("123");

struct Map *m = insert('A', a, NULL);

exec('A', m);
}

void group2() {
struct Wheel *a = create("1B2");
struct Wheel *b = create("34");

struct Map *m = insert('A', a, NULL);
m = insert('B', b, m);

exec('A', m);
}

void group3() {
struct Wheel *a = create("1DD");
struct Wheel *d = create("678");

struct Map *m = insert('A', a, NULL);
m = insert('D', d, m);

exec('A', m);
}

void group4() {
struct Wheel *a = create("1BC");
struct Wheel *b = create("34");
struct Wheel *c = create("5B");

struct Map *m = insert('A', a, NULL);
m = insert('B', b, m);
m = insert('C', c, m);

exec('A', m);
}

int main() {
group1();
group2();
group3();
group4();

return 0;
}
Output:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

C#

using System;
using System.Collections.Generic;
using System.Linq;

public static class IntersectingNumberWheels
{
public static void Main() {
TurnWheels(('A', "123")).Take(20).Print();
TurnWheels(('A', "1B2"), ('B', "34")).Take(20).Print();
TurnWheels(('A', "1DD"), ('D', "678")).Take(20).Print();
TurnWheels(('A', "1BC"), ('B', "34"), ('C', "5B")).Take(20).Print();
}

static IEnumerable<char> TurnWheels(params (char name, string values)[] wheels) {
var data = wheels.ToDictionary(wheel => wheel.name, wheel => wheel.values.Loop().GetEnumerator());
var primary = data[wheels.name];
while (true) {
yield return Turn(primary);
}

char Turn(IEnumerator<char> sequence) {
sequence.MoveNext();
char c = sequence.Current;
return char.IsDigit(c) ? c : Turn(data[c]);
}
}

static IEnumerable<T> Loop<T>(this IEnumerable<T> seq) {
while (true) {
foreach (T element in seq) yield return element;
}
}

static void Print(this IEnumerable<char> sequence) => Console.WriteLine(string.Join(" ", sequence));
}
Output:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

C++

Translation of: D
#include <initializer_list>
#include <iostream>
#include <map>
#include <vector>

struct Wheel {
private:
std::vector<char> values;
size_t index;

public:
Wheel() : index(0) {
// empty
}

Wheel(std::initializer_list<char> data) : values(data), index(0) {
//values.assign(data);
if (values.size() < 1) {
throw new std::runtime_error("Not enough elements");
}
}

char front() {
return values[index];
}

void popFront() {
index = (index + 1) % values.size();
}
};

struct NamedWheel {
private:
std::map<char, Wheel> wheels;

public:
void put(char c, Wheel w) {
wheels[c] = w;
}

char front(char c) {
char v = wheels[c].front();
while ('A' <= v && v <= 'Z') {
v = wheels[v].front();
}
return v;
}

void popFront(char c) {
auto v = wheels[c].front();
wheels[c].popFront();

while ('A' <= v && v <= 'Z') {
auto d = wheels[v].front();
wheels[v].popFront();
v = d;
}
}
};

void group1() {
Wheel w({ '1', '2', '3' });
for (size_t i = 0; i < 20; i++) {
std::cout << ' ' << w.front();
w.popFront();
}
std::cout << '\n';
}

void group2() {
Wheel a({ '1', 'B', '2' });
Wheel b({ '3', '4' });

NamedWheel n;
n.put('A', a);
n.put('B', b);

for (size_t i = 0; i < 20; i++) {
std::cout << ' ' << n.front('A');
n.popFront('A');
}
std::cout << '\n';
}

void group3() {
Wheel a({ '1', 'D', 'D' });
Wheel d({ '6', '7', '8' });

NamedWheel n;
n.put('A', a);
n.put('D', d);

for (size_t i = 0; i < 20; i++) {
std::cout << ' ' << n.front('A');
n.popFront('A');
}
std::cout << '\n';
}

void group4() {
Wheel a({ '1', 'B', 'C' });
Wheel b({ '3', '4' });
Wheel c({ '5', 'B' });

NamedWheel n;
n.put('A', a);
n.put('B', b);
n.put('C', c);

for (size_t i = 0; i < 20; i++) {
std::cout << ' ' << n.front('A');
n.popFront('A');
}
std::cout << '\n';
}

int main() {
group1();
group2();
group3();
group4();

return 0;
}
Output:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

D

import std.exception;
import std.range;
import std.stdio;

struct Wheel {
private string[] values;
private uint index;

invariant {
enforce(index < values.length, "index out of range");
}

this(string[] value...) in {
enforce(value.length > 0, "Cannot create a wheel with no elements");
} body {
values = value;
}

enum empty = false;

auto front() {
return values[index];
}

void popFront() {
index = (index + 1) % values.length;
}
}

struct NamedWheel {
private Wheel[char] wheels;
char m;

this(char c, Wheel w) {
m = c;
}

void add(char c, Wheel w) {
wheels[c] = w;
}

enum empty = false;

auto front() {
auto v = wheels[m].front;
char c = v;
while ('A' <= c && c <= 'Z') {
v = wheels[c].front;
c = v;
}
return v;
}

void popFront() {
auto v = wheels[m].front;
wheels[m].popFront;

char c = v;
while ('A' <= c && c <= 'Z') {
auto d = wheels[c].front;
wheels[c].popFront;
c = d;
}
}
}

void group1() {
auto a = Wheel("1", "2", "3");
a.take(20).writeln;
}

void group2() {
auto a = Wheel("1", "B", "2");
auto b = Wheel("3", "4");

auto n = NamedWheel('A', a);

n.take(20).writeln;
}

void group3() {
auto a = Wheel("1", "D", "D");
auto d = Wheel("6", "7", "8");

auto n = NamedWheel('A', a);

n.take(20).writeln;
}

void group4() {
auto a = Wheel("1", "B", "C");
auto b = Wheel("3", "4");
auto c = Wheel("5", "B");

auto n = NamedWheel('A', a);

n.take(20).writeln;
}

void main() {
group1();
group2();
group3();
group4();
}
Output:
["1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2"]
["1", "3", "2", "1", "4", "2", "1", "3", "2", "1", "4", "2", "1", "3", "2", "1", "4", "2", "1", "3"]
["1", "6", "7", "1", "8", "6", "1", "7", "8", "1", "6", "7", "1", "8", "6", "1", "7", "8", "1", "6"]
["1", "3", "5", "1", "4", "3", "1", "4", "5", "1", "3", "4", "1", "3", "5", "1", "4", "3", "1", "4"]

F#

// Wheels within wheels. Nigel Galloway: September 30th., 2019.
let N(n)=fun()->n
let wheel(n:(unit->int)[])=let mutable g= -1 in (fun()->g<-(g+1)%n.Length; n.[g]())
let A1=wheel[|N(1);N(2);N(3)|]
for n in 0..20 do printf "%d " (A1())
printfn ""
let B2=wheel[|N(3);N(4)|]
let A2=wheel[|N(1);B2;N(2)|]
for n in 0..20 do printf "%d " (A2())
printfn ""
let D3=wheel[|N(6);N(7);N(8)|]
let A3=wheel[|N(1);D3;D3|]
for n in 0..20 do printf "%d " (A3())
printfn ""
let B4=wheel[|N(3);N(4)|]
let C4=wheel[|N(5);B4|]
let A4=wheel[|N(1);B4;C4|]
for n in 0..20 do printf "%d " (A4())
printfn ""

Output:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 2
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 7
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 5

Factor

An attempt has been made to simplify the interface as much as possible by creating a natural literal syntax for number wheel groups. This should be useful for exploring these types of sequences in the future. nw-parser is an EBNF grammar that turns

"A: 1 B C\nB: 3 4\nC: 5 B"

into

{
{ "A" T{ number-wheel { seq T{ circular { seq { 1 "B" "C" } } } } { i 0 } } }
{ "B" T{ number-wheel { seq T{ circular { seq { 3 4 } } } } { i 0 } } }
{ "C" T{ number-wheel { seq T{ circular { seq { 5 "B" } } } } { i 0 } } }
}

⁠— a dictionary-like structure that is transformed into a lazy list which yields the expected sequence elements.

Works with: Factor version 0.99 2019-07-10
USING: accessors assocs circular io kernel lists lists.lazy math
math.parser multiline peg.ebnf prettyprint prettyprint.custom
sequences strings ;
IN: rosetta-code.number-wheels

TUPLE: group pretty list ;

C: <group> group

M: group pprint* pretty>> write ;

TUPLE: number-wheel seq i ;

: <number-wheel> ( seq -- number-wheel )
<circular> 0 number-wheel boa ;

: yield ( assoc -- n )
dup first first [ dup integer? ]
[ dupd of [ i>> ] [ [ 1 + ] change-i seq>> nth ] bi ] until
nip ;

: number-wheel>lazy ( assoc -- list )
0 lfrom swap [ yield nip ] curry lmap-lazy ;

EBNF: nw-parser [=[
num = [0-9]+ => [[ >string string>number ]]
name = [a-zA-Z]+ => [[ >string ]]
wheel = (" "~ (num | name))+ "\n"?
=> [[ but-last first <number-wheel> ]]
group = (name ":"~ wheel)+ => [[ number-wheel>lazy ]]
]=]

SYNTAX: NUMBER-WHEELS: parse-here dup nw-parser <group> suffix! ;

: .take ( n group -- )
list>> ltake list>array [ pprint bl ] each "..." print ;

Now the interface defined above may be used:

USING: generalizations io kernel prettyprint
rosetta-code.number-wheels ;

NUMBER-WHEELS:
A: 1 2 3
;

NUMBER-WHEELS:
A: 1 B 2
B: 3 4
;

NUMBER-WHEELS:
A: 1 D D
D: 6 7 8
;

NUMBER-WHEELS:
A: 1 B C
B: 3 4
C: 5 B
;

[
"Intersecting number wheel group:" print
[ . ] [ "Generates:" print 20 swap .take nl ] bi
] 4 napply
Output:
Intersecting number wheel group:
A: 1 2 3
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting number wheel group:
A: 1 B 2
B: 3 4
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting number wheel group:
A: 1 D D
D: 6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting number wheel group:
A: 1 B C
B: 3 4
C: 5 B
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...

Go

package main

import (
"fmt"
"sort"
"strconv"
)

type wheel struct {
next int
values []string
}

type wheelMap = map[string]wheel

func generate(wheels wheelMap, start string, maxCount int) {
count := 0
w := wheels[start]
for {
s := w.values[w.next]
v, err := strconv.Atoi(s)
w.next = (w.next + 1) % len(w.values)
wheels[start] = w
if err == nil {
fmt.Printf("%d ", v)
count++
if count == maxCount {
fmt.Println("...\n")
return
}
} else {
for {
w2 := wheels[s]
ss := s
s = w2.values[w2.next]
w2.next = (w2.next + 1) % len(w2.values)
wheels[ss] = w2
v, err = strconv.Atoi(s)
if err == nil {
fmt.Printf("%d ", v)
count++
if count == maxCount {
fmt.Println("...\n")
return
}
break
}
}
}
}
}

func printWheels(wheels wheelMap) {
var names []string
for name := range wheels {
names = append(names, name)
}
sort.Strings(names)
fmt.Println("Intersecting Number Wheel group:")
for _, name := range names {
fmt.Printf("  %s: %v\n", name, wheels[name].values)
}
fmt.Print(" Generates:\n ")
}

func main() {
wheelMaps := []wheelMap{
{
"A": {0, []string{"1", "2", "3"}},
},
{
"A": {0, []string{"1", "B", "2"}},
"B": {0, []string{"3", "4"}},
},
{
"A": {0, []string{"1", "D", "D"}},
"D": {0, []string{"6", "7", "8"}},
},
{
"A": {0, []string{"1", "B", "C"}},
"B": {0, []string{"3", "4"}},
"C": {0, []string{"5", "B"}},
},
}
for _, wheels := range wheelMaps {
printWheels(wheels)
generate(wheels, "A", 20)
}
}
Output:
Intersecting Number Wheel group:
A: [1 2 3]
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
A: [1 B 2]
B: [3 4]
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
A: [1 D D]
D: [6 7 8]
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
A: [1 B C]
B: [3 4]
C: [5 B]
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...

Defining a unit movement of the interlocking wheels as a recursive descent, terminating at the first digit found, and printing a map-accumulation of that recursion over a list of given length but arbitrary content.

import Data.Char (isDigit)
import Data.List (mapAccumL)
import qualified Data.Map.Strict as M
import Data.Maybe (fromMaybe)

---------------- INTERSECTING NUMBER WHEELS --------------

clockWorkTick ::
M.Map Char String ->
(M.Map Char String, Char)
clockWorkTick = flip click 'A'
where
click wheels name
| isDigit name = (wheels, name)
| otherwise =
( click
. flip
(M.insert name . leftRotate)
wheels
)
\$ fromMaybe ['?'] \$ M.lookup name wheels

leftRotate :: [a] -> [a]
leftRotate = take . length <*> (tail . cycle)

--------------------------- TEST -------------------------
main :: IO ()
main = do
let wheelSets =
[ [('A', "123")],
[('A', "1B2"), ('B', "34")],
[('A', "1DD"), ('D', "678")],
[('A', "1BC"), ('B', "34"), ('C', "5B")]
]
putStrLn "State of each wheel-set after 20 clicks:\n"
mapM_ print \$
fmap
( flip
(mapAccumL (const . clockWorkTick))
(replicate 20 undefined)
. M.fromList
)
wheelSets
putStrLn "\nInitial state of the wheel-sets:\n"
mapM_ print wheelSets
Output:
State of each wheel-set after 20 clicks:

(fromList [('A',"312")],"12312312312312312312")
(fromList [('A',"21B"),('B',"43")],"13214213214213214213")
(fromList [('A',"D1D"),('D',"786")],"16718617816718617816")
(fromList [('A',"C1B"),('B',"34"),('C',"5B")],"13514314513413514314")

Initial state of the wheel-sets:

[('A',"123")]
[('A',"1B2"),('B',"34")]
[('A',"1DD"),('D',"678")]
[('A',"1BC"),('B',"34"),('C',"5B")]

J

Implementation:

wheelgroup=:{{
yield_wheelgroup_=: {{
i=. wheels i.<;y
j=. i{inds
k=. ".;y
l=. j{k
inds=: ((#k)|1+j) i} inds
if. l e. wheels
do.yield l
else.{.".;l
end.
}}
gen_wheelgroup_=: {{
yield wheel
}}
grp=. cocreate ''
coinsert__grp 'wheelgroup'
specs__grp=: cut each boxopen m
wheel__grp=: ;{.wheels__grp=: {.every specs__grp
init__grp=: {{('inds';wheels)=:(0#~#specs);}.each specs}}
init__grp''
('gen_',(;grp),'_')~
}}

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
task 'A 1 B 2';'B 3 4'
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
task 'A 1 D D';'D 6 7 8'
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
task 'A 1 B C';'B 3 4';'C 5 B'
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

Java

package intersectingNumberWheels;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.stream.IntStream;

public class WheelController {
private static final String IS_NUMBER = "[0-9]";
private static final int TWENTY = 20;
private static Map<String, WheelModel> wheelMap;

public static void advance(String wheel) {
WheelModel w = wheelMap.get(wheel);
if (w.list.get(w.position).matches(IS_NUMBER)) {
w.printThePosition();
} else {
String wheelName = w.list.get(w.position);
}
}

public static void run() {
System.out.println(wheelMap);
System.out.println();
wheelMap.clear();
}

public static void main(String[] args) {
wheelMap = new HashMap<>();
wheelMap.put("A", new WheelModel("A", "1", "2", "3"));
run();
wheelMap.put("A", new WheelModel("A", "1", "B", "2"));
wheelMap.put("B", new WheelModel("B", "3", "4"));
run();
wheelMap.put("A", new WheelModel("A", "1", "D", "D"));
wheelMap.put("D", new WheelModel("D", "6", "7", "8"));
run();
wheelMap.put("A", new WheelModel("A", "1", "B", "C"));
wheelMap.put("B", new WheelModel("B", "3", "4"));
wheelMap.put("C", new WheelModel("C", "5", "B"));
run();
}

}

class WheelModel {
String name;
List<String> list;
int position;
int endPosition;
private static final int INITIAL = 0;

public WheelModel(String name, String... values) {
super();

this.name = name.toUpperCase();
this.list = new ArrayList<>();
for (String value : values) {
}
this.position = INITIAL;
this.endPosition = this.list.size() - 1;
}

@Override
public String toString() {
return list.toString();
}

if (this.position == this.endPosition) {
this.position = INITIAL;// new beginning
} else {
}
}

public void printThePosition() {
System.out.print(" " + this.list.get(position));
}
}

Output: {A=[1, 2, 3]}

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

{A=[1, B, 2], B=[3, 4]}

1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

{A=[1, D, D], D=[6, 7, 8]}

1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

{A=[1, B, C], B=[3, 4], C=[5, B]}

1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

JavaScript

Map-accumulation of a recursive digit-search, over an array of given length and arbitrary contents.

Translation of: Python
(() => {
'use strict';

// main :: IO ()
const main = () => {

// clockWorkTick :: Dict -> (Dict, Char)
const clockWorkTick = wheelMap => {
// The new configuration of the wheels, tupled with
// a digit found by recursive descent from a single
// click of the first wheel.
const click = wheels => wheelName => {
const
wheel = wheels[wheelName] || ['?'],
v = wheel;
return bool(click)(Tuple)(isDigit(v) || '?' === v)(
insertDict(wheelName)(
leftRotate(wheel)
)(wheels)
)(v);
};
return click(wheelMap)('A');
};

// leftRotate ::[a] -> [a]
const leftRotate = xs =>
// The head of the list appended
// to the tail of of the list.
0 < xs.length ? (
xs.slice(1).concat(xs)
) : [];

// TEST -------------------------------------------
// State of each wheel-set after 20 clicks,
// paired with the resulting series of characters.

const tuple = uncurry(Tuple);
const wheelLists = [
[tuple('A', '123')],
[tuple('A', '1B2'), tuple('B', '34')],
[tuple('A', '1DD'), tuple('D', '678')],
[tuple('A', '1BC'), tuple('B', '34'), tuple('C', '5B')]
];

console.log([
'Series and state of each wheel-set after 20 clicks:\n',
unlines(
map(tuples => showWheels(
mapAccumL(
compose(constant, clockWorkTick)
)(dictFromList(tuples))(replicate(20)(''))
))(wheelLists)
),
'\nInitial state of each wheel-set:\n',
map(map(compose(
JSON.stringify,
dictFromList,
x => [Array.from(x)]
)))(wheelLists).join('\n')
].join('\n'));
};

// DISPLAY FORMATTING ---------------------------------

// showWheels :: (Dict, [Char]) -> String
const showWheels = tpl =>
JSON.stringify(
Array.from(secondArrow(concat)(tpl))
);

// GENERIC FUNCTIONS ----------------------------------

// Tuple (,) :: a -> b -> (a, b)
const Tuple = a => b => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});

// bool :: a -> a -> Bool -> a
const bool = f => t => p =>
p ? t : f;

// compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
const compose = (...fs) =>
x => fs.reduceRight((a, f) => f(a), x);

// concat :: [[a]] -> [a]
// concat :: [String] -> String
const concat = xs =>
0 < xs.length ? (() => {
const unit = 'string' !== typeof xs ? (
[]
) : '';
return unit.concat.apply(unit, xs);
})() : [];

// constant :: a -> b -> a
const constant = k => _ => k;

// dictFromList :: [(k, v)] -> Dict
const dictFromList = kvs =>
Object.fromEntries(kvs);

// secondArrow :: (a -> b) -> ((c, a) -> (c, b))
const secondArrow = f => xy =>
// A function over a simple value lifted
// to a function over a tuple.
// f (a, b) -> (a, f(b))
Tuple(xy)(
f(xy)
);

// insertDict :: String -> a -> Dict -> Dict
const insertDict = k => v => dct =>
Object.assign({}, dct, {
[k]: v
});

// isDigit :: Char -> Bool
const isDigit = c => {
const n = c.codePointAt(0);
return 48 <= n && 57 >= n;
};

// map :: (a -> b) -> [a] -> [b]
const map = f => xs =>
(Array.isArray(xs) ? (
xs
) : xs.split('')).map(f);

// Map-accumulation is a combination of map and a catamorphism;
// it applies a function to each element of a list, passing an
// accumulating parameter from left to right, and returning a final
// value of this accumulator together with the new list.

// mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
const mapAccumL = f => acc => xs =>
xs.reduce((a, x) => {
const pair = f(a)(x);
return Tuple(pair)(a.concat(pair));
}, Tuple(acc)([]));

// replicate :: Int -> a -> [a]
const replicate = n => x =>
Array.from({
length: n
}, () => x);

// uncurry :: (a -> b -> c) -> ((a, b) -> c)
const uncurry = f =>
(x, y) => f(x)(y);

// unlines :: [String] -> String
const unlines = xs => xs.join('\n');

// MAIN ---
return main();
})();
Output:
Series and state of each wheel-set after 20 clicks:

[{"A":"312"},"12312312312312312312"]
[{"A":"21B","B":"43"},"13214213214213214213"]
[{"A":"D1D","D":"786"},"16718617816718617816"]
[{"A":"C1B","B":"34","C":"5B"},"13514314513413514314"]

Initial state of each wheel-set:

{"A":"123"}
{"A":"1B2"},{"B":"34"}
{"A":"1DD"},{"D":"678"}
{"A":"1BC"},{"B":"34"},{"C":"5B"}

Julia

const d1 = Dict("A" => [["1", "2", "3"], 1])
const d2 = Dict("A" => [["1", "B", "2"], 1], "B" => [["3", "4"], 1])
const d3 = Dict("A" => [["1", "D", "D"], 1], "D" => [["6", "7", "8"], 1])
const d4 = Dict("A" => [["1", "B", "C"], 1], "B" => [["3", "4"], 1],
"C" => [["5", "B"], 1])

function getvalue!(wheelname, allwheels)
wheel = allwheels[wheelname]
s = wheel[wheel]
wheel = mod1(wheel + 1, length(wheel))
return haskey(allwheels, s) ? getvalue!(s, allwheels) : s
end

function testwheels(wheels, numterms = 20, firstwheel = "A")
println("\nNumber Wheels:")
for k in sort(collect(keys(wheels)))
print("\$k: [")
for s in wheels[k]
print(s, " ")
end
println("\b]")
end
print("Output: ")
for _ in 1:numterms
print(getvalue!(firstwheel, wheels), " ")
end
println("...")
end

foreach(testwheels, [d1, d2, d3, d4])

Output:
Number Wheels:
A: [1 2 3]
Output: 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Number Wheels:
A: [1 B 2]
B: [3 4]
Output: 1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Number Wheels:
A: [1 D D]
D: [6 7 8]
Output: 1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Number Wheels:
A: [1 B C]
B: [3 4]
C: [5 B]
Output: 1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...

Kotlin

Translation of: Java
import java.util.Collections
import java.util.stream.IntStream

object WheelController {
private val IS_NUMBER = "[0-9]".toRegex()
private const val TWENTY = 20
private var wheelMap = mutableMapOf<String, WheelModel>()

val w = wheelMap[wheel]
if (w!!.list[w.position].matches(IS_NUMBER)) {
w.printThePosition()
} else {
val wheelName = w.list[w.position]
}
}

private fun run() {
println(wheelMap)
IntStream.rangeClosed(1, TWENTY)
println()
wheelMap.clear()
}

@JvmStatic
fun main(args: Array<String>) {
wheelMap["A"] = WheelModel("1", "2", "3")
run()
wheelMap["A"] = WheelModel("1", "B", "2")
wheelMap["B"] = WheelModel("3", "4")
run()
wheelMap["A"] = WheelModel("1", "D", "D")
wheelMap["D"] = WheelModel("6", "7", "8")
run()
wheelMap["A"] = WheelModel("1", "B", "C")
wheelMap["B"] = WheelModel("3", "4")
wheelMap["C"] = WheelModel("5", "B")
run()
}
}

internal class WheelModel(vararg values: String?) {
var list = mutableListOf<String>()
var position: Int
private var endPosition: Int

override fun toString(): String {
return list.toString()
}

if (position == endPosition) {
position = INITIAL // new beginning
} else {
}
}

fun printThePosition() {
print(" \${list[position]}")
}

companion object {
private const val INITIAL = 0
}

init {
position = INITIAL
endPosition = list.size - 1
}
}
Output:
{A=[1, 2, 3]}
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
{A=[1, B, 2], B=[3, 4]}
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
{A=[1, D, D], D=[6, 7, 8]}
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
{A=[1, B, C], B=[3, 4], C=[5, B]}
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

Maple

with(ArrayTools):

module Wheel()
option object;
local spokes := Array([1,2,3]);
local currentSpoke := 1;

export currentValue::static := proc(self::Wheel)
local valueOut;
if type(self:-spokes[self:-currentSpoke], integer) then
valueOut := self:-spokes[self:-currentSpoke]:
else
valueOut := currentValue(self:-spokes[self:-currentSpoke]):
end if:
rotate(self):
return valueOut;
end proc:

export rotate::static := proc(self::Wheel)
if self:-currentSpoke = ArrayNumElems(self:-spokes) then self:-currentSpoke := 1:
else self:-currentSpoke += 1: end if:
end proc:

export ModuleApply::static := proc()
Object(Wheel, _passed);
end proc:

export ModuleCopy::static := proc(new::Wheel, proto::Wheel, spo::Array, curr::integer, \$)
new:-spokes := spo:
new:-currentSpoke := curr:
end proc:
end module:

A := Wheel(Array([1,2,3]), 1):

seq(currentValue(A), 1..20);

A := Wheel(Array([1,B,2]), 1):
B := Wheel(Array([3,4]), 1):

seq(currentValue(A), 1..20);

A := Wheel(Array([1,d,d]), 1):
d := Wheel(Array([6,7,8]), 1):

seq(currentValue(A), 1..20);

A := Wheel(Array([1,b,C]), 1):
b := Wheel(Array([3,4]), 1):
C := Wheel(Array([5,b]), 1):

seq(currentValue(A), 1..20);

Output:

1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2
1, 3, 2, 1, 4, 2, 1, 3, 2, 1, 4, 2, 1, 3, 2, 1, 4, 2, 1, 3
1, 6, 7, 1, 8, 6, 1, 7, 8, 1, 6, 7, 1, 8, 6, 1, 7, 8, 1, 6
1, 3, 5, 1, 4, 3, 1, 4, 5, 1, 3, 4, 1, 3, 5, 1, 4, 3, 1, 4

Nim

import strutils, tables

type

ElemKind = enum eValue, eWheel

Elem = object
case kind: ElemKind
of eValue:
value: Natural
of eWheel:
name: char

Wheel = ref object
elems: seq[Elem]
index: Natural

Wheels = Table[char, Wheel]

WheelDescription = tuple[name: char; elems: string]

func initWheels(wheels: openArray[WheelDescription]): Wheels =
## Initialize a table of wheels from an array of wheel descriptions.

for (name, elems) in wheels:
let wheel = new(Wheel)
for e in elems.splitWhitespace():
if e.isUpperAscii():
else:
result[name] = wheel

func next(wheels: Wheels; name: char): Natural =
## Return the next element from a wheel.

let wheel = wheels[name]
let elem = wheel.elems[wheel.index]
wheel.index = (wheel.index + 1) mod wheel.elems.len
result = case elem.kind
of eValue: elem.value
of eWheel: wheels.next(elem.name)

when isMainModule:

proc generate(wheelList: openArray[WheelDescription]; count: Positive) =
## Create the wheels from their description, then display
## the first "count" values generated by wheel 'A'.

let wheels = wheelList.initWheels()
for (name, elems) in wheelList:
echo name, ": ", elems
echo "generates:"
for _ in 1..count:
stdout.write ' ', wheels.next('A')
echo '\n'

{'A': "1 2 3"}.generate(20)
{'A': "1 B 2", 'B': "3 4"}.generate(20)
{'A': "1 D D", 'D': "6 7 8"}.generate(20)
{'A': "1 B C", 'B': "3 4", 'C': "5 B"}.generate(20)
Output:
A: 1 2 3
generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

A: 1 B 2
B: 3 4
generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

A: 1 D D
D: 6 7 8
generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

A: 1 B C
B: 3 4
C: 5 B
generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

Perl

Translation of: Julia
use strict;
use warnings;
use feature 'say';

sub get_next {
my(\$w,%wheels) = @_;
my \$wh = \@{\$wheels{\$w}}; # reference, not a copy
my \$value = \$\$wh[\$\$wh];
\$\$wh = (\$\$wh+1) % @{\$\$wh};
defined \$wheels{\$value} ? get_next(\$value,%wheels) : \$value;
}

sub spin_wheels {
my(%wheels) = @_;
say "\$_: " . join ', ', @{\${\$wheels{\$_}}} for sort keys %wheels;
print get_next('A', %wheels) . ' ' for 1..20; print "\n\n";
}

spin_wheels(%\$_) for
(
{'A' => [['1', '2', '3'], 0]},
{'A' => [['1', 'B', '2'], 0], 'B' => [['3', '4'], 0]},
{'A' => [['1', 'D', 'D'], 0], 'D' => [['6', '7', '8'], 0]},
{'A' => [['1', 'B', 'C'], 0], 'B' => [['3', '4'], 0], 'C' => [['5', 'B'], 0]},
);
Output:
A: 1, 2, 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

A: 1, B, 2
B: 3, 4
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

A: 1, D, D
D: 6, 7, 8
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

A: 1, B, C
B: 3, 4
C: 5, B
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

Phix

with javascript_semantics
function terms(sequence wheels, integer n)
sequence res = repeat(' ',n),
pos = repeat(2,length(wheels)),
wvs = vslice(wheels,1)
integer wheel = 1, rdx = 1
while rdx<=n do
integer p = pos[wheel],
c = wheels[wheel][p]
p = iff(p=length(wheels[wheel])?2:p+1)
pos[wheel] = p
if c>'9' then
wheel = find(c,wvs)
else
res[rdx] = c
rdx += 1
wheel = 1
end if
end while
return res
end function

constant wheels = {{"A123"},
{"A1B2","B34"},
{"A1DD","D678"},
{"A1BC","B34","C5B"}}

for i=1 to length(wheels) do
?terms(wheels[i],20)
end for
Output:
"12312312312312312312"
"13214213214213214213"
"16718617816718617816"
"13514314513413514314"

Python

Python: Original class and generator based

from itertools import islice

class INW():
"""
Intersecting Number Wheels
represented as a dict mapping
name to tuple of values.
"""

def __init__(self, **wheels):
self._wheels = wheels
self.isect = {name: self._wstate(name, wheel)
for name, wheel in wheels.items()}

def _wstate(self, name, wheel):
"Wheel state holder"
assert all(val in self._wheels for val in wheel if type(val) == str), \
pos = 0
ln = len(wheel)
while True:
nxt, pos = wheel[pos % ln], pos + 1
yield next(self.isect[nxt]) if type(nxt) == str else nxt

def __iter__(self):
base_wheel_name = next(self.isect.__iter__())
yield from self.isect[base_wheel_name]

def __repr__(self):
return f"{self.__class__.__name__}({self._wheels})"

def __str__(self):
txt = "Intersecting Number Wheel group:"
for name, wheel in self._wheels.items():
txt += f"\n {name+':':4}" + ' '.join(str(v) for v in wheel)
return txt

def first(iter, n):
"Pretty print first few terms"
return ' '.join(f"{nxt}" for nxt in islice(iter, n))

if __name__ == '__main__':
for group in[
{'A': (1, 2, 3)},
{'A': (1, 'B', 2),
'B': (3, 4)},
{'A': (1, 'D', 'D'),
'D': (6, 7, 8)},
{'A': (1, 'B', 'C'),
'B': (3, 4),
'C': (5, 'B')}, # 135143145...
]:
w = INW(**group)
print(f"{w}\n Generates:\n {first(w, 20)} ...\n")
Output:
Intersecting Number Wheel group:
A:  1 2 3
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
A:  1 B 2
B:  3 4
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
A:  1 D D
D:  6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
A:  1 B C
B:  3 4
C:  5 B
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...

Python: Simplified procedural

def nextfrom(w, name):
while True:
nxt, w[name] = w[name], w[name][1:] + w[name][:1]
if '0' <= nxt <= '9':
return nxt
name = nxt

if __name__ == '__main__':
for group in '''
A: 1 2 3
A: 1 B 2; B: 3 4
A: 1 D D; D: 6 7 8
A: 1 B C; B: 3 4; C: 5 B'''
.strip().split('\n'):
print(f"Intersecting Number Wheel group:\n {group}")
wheel, first = {}, None
for w in group.strip().split(';'):
name, *values = w.strip().split()
wheel[name[:-1]] = values
first = name[:-1] if first is None else first
gen = ' '.join(nextfrom(wheel, first) for i in range(20))
print(f" Generates:\n {gen} ...\n")
Output:
Intersecting Number Wheel group:
A: 1 2 3
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
A: 1 B 2; B: 3 4
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
A: 1 D D; D: 6 7 8
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
A: 1 B C; B: 3 4; C: 5 B
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...

And Again

This time the nextfromr function is recursive and it will only work for single character names and numbers due to character string rotation being used.
Input is just a list of Python dicts, and depends on c-python dicts being odered by key insertion order.

def nextfromr(w, name):
nxt, w[name] = w[name], w[name][1:] + w[name][:1]
return nxt if '0' <= nxt <= '9' else nextfromr(w, nxt)

if __name__ == '__main__':
for group in [{'A': '123'},
{'A': '1B2', 'B': '34'},
{'A': '1DD', 'D': '678'},
{'A': '1BC', 'B': '34', 'C': '5B'},]:
print(f"Intersecting Number Wheel group:\n {group}")
first = next(group.__iter__())
gen = ' '.join(nextfromr(group, first) for i in range(20))
print(f" Generates:\n {gen} ...\n")
Output:
Intersecting Number Wheel group:
{'A': '123'}
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
{'A': '1B2', 'B': '34'}
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
{'A': '1DD', 'D': '678'}
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
{'A': '1BC', 'B': '34', 'C': '5B'}
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...

Python: Functional composition

Defining a unit rotation of the wheel-set as a recursive descent, and taking a map-accumulation of this recursion over a list of specific length and arbitrary content.

Works with: Python version 3.7
'''Intersecting number wheels'''

from itertools import cycle, islice
from functools import reduce

# clockWorkTick :: Dict -> (Dict, Char)
def clockWorkTick(wheelMap):
'''The new state of the wheels, tupled with a
digit found by recursive descent from a single
click of the first wheel.'''

def click(wheels):
def go(wheelName):
wheel = wheels.get(wheelName, ['?'])
v = wheel
return (Tuple if v.isdigit() or '?' == v else click)(
insertDict(wheelName)(leftRotate(wheel))(wheels)
)(v)
return go
return click(wheelMap)('A')

# leftRotate :: [a] -> String
def leftRotate(xs):
''' A string shifted cyclically towards
the left by one position.
'''

return ''.join(islice(cycle(xs), 1, 1 + len(xs)))

# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''First twenty values from each set of test wheels.'''

wheelMaps = [dict(kvs) for kvs in [
[('A', "123")],
[('A', "1B2"), ('B', "34")],
[('A', "1DD"), ('D', "678")],
[('A', "1BC"), ('B', "34"), ('C', "5B")]
]]
print('New state of wheel sets, after 20 clicks of each:\n')
for wheels, series in [
mapAccumL(compose(const)(clockWorkTick))(
dct
)(' ' * 20) for dct in wheelMaps
]:
print((wheels, ''.join(series)))

print('\nInital states:')
for x in wheelMaps:
print(x)

# ----------------------- GENERIC ------------------------

# Tuple (,) :: a -> b -> (a, b)
def Tuple(x):
'''Constructor for a pair of values,
possibly of two different types.
'''

return lambda y: (
x + (y,)
) if isinstance(x, tuple) else (x, y)

# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
'''Right to left function composition.'''
return lambda f: lambda x: g(f(x))

# const :: a -> b -> a
def const(k):
'''The latter of two arguments,
'''

return lambda _: k

# insertDict :: String -> a -> Dict -> Dict
def insertDict(k):
'''A new dictionary updated with a (k, v) pair.'''
def go(v, dct):
return dict(dct, **{k: v})
return lambda v: lambda dct: go(v, dct)

# mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
def mapAccumL(f):
'''A tuple of an accumulation and a map
with accumulation from left to right.
'''

def nxt(a, x):
tpl = f(a)(x)
return tpl, a + [tpl]

def go(acc):
def g(xs):
return reduce(nxt, xs, (acc, []))
return g
return go

# MAIN ---
if __name__ == '__main__':
main()
Output:
New state of wheel sets, after 20 clicks of each:

({'A': '312'}, '12312312312312312312')
({'A': '21B', 'B': '43'}, '13214213214213214213')
({'A': 'D1D', 'D': '786'}, '16718617816718617816')
({'A': 'C1B', 'B': '34', 'C': '5B'}, '13514314513413514314')

Inital states:
{'A': '123'}
{'A': '1B2', 'B': '34'}
{'A': '1DD', 'D': '678'}
{'A': '1BC', 'B': '34', 'C': '5B'}

Quackery

As the contents of a wheel (e.g. [ 1 B 2 ]) is just Quackery code, wheels can be extended in interesting ways.

They could, for example, contain a nest that randomly selects a wheel to advance; [ 1 [ 2 random table [ B C ] ] 2 ] would do the same as [ 1 B 2 ], except that on the second click of the wheel, instead of always advancing wheel B, [ 2 random table [ B C ] ] would be evaluated, causing either wheel B or wheel C to advance arbitrarily.

[ ]this[ ]done[
dup dip
[ nested join
swap put ]
do ] is wheel ( --> n )

[ ]'[
]'[ nested
' [ wheel ]
swap join
swap replace ] is newwheel ( --> )

forward is A forward is B forward is C
forward is D ( and so on, as required )

[ wheel [ 1 2 3 ] ] resolves A ( --> n )

[ wheel [ 3 4 ] ] resolves B ( --> n )

[ wheel [ 5 B ] ] resolves C ( --> n )

[ wheel [ 6 7 8 ] ] resolves D ( --> n )

20 times [ A echo sp ] cr

newwheel A [ 1 B 2 ]
20 times [ A echo sp ] cr

newwheel A [ 1 D D ]
20 times [ A echo sp ] cr

newwheel A [ 1 B C ]
newwheel B [ 3 4 ] ( As B has been used already )
( it's state may be [ 4 3 ]. )
( So we reset it to [ 3 4 ]. )

20 times [ A echo sp ] cr
Output:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

Raku

(formerly Perl 6) A succinct Raku example using a few additional language features. Wheels are implemented as infinite repeating sequences, allowing a single iterator to keep track of the current position. This means the code contains no position tracking whatsoever.

#| advance rotates a named wheel \$n by consuming an item from an infinite sequence. It is called
#| from within a gather block and so can use take in order to construct an infinite, lazy sequence
#| of result values
given \$g{\$n}.pull-one {
when /\d/ { take \$_ }
default { samewith \$g, \$_ } # samewith re-calls this function with new parameters
}
}

#| Input groups are a hash containing each wheel name as the key, and a list of values constructed
#| using <> to split on whitespace. They are transformed using xx * to repeat the list infinitely.
#| We then retrieve the underlying iterator in order for wheel position to be persistent. Each group
#| is then aggregated into a lazy output sequence using an infinite loop inside a gather block.
[
{A => <1 2 3>},
{A => <1 B 2>, B => <3 4>},
{A => <1 D D>, D => <6 7 8>},
{A => <1 B C>, B => <3 4>, C => <5 B>},
]
#| %() converts a list of pairs produced by map into a hash. \$^k and \$^v are implicit variables.
#| They are processed in alphabetical order and make the block arity 2, called with two vars.
#| .kv gets the list of wheel names and wheel values from the input entry
==> map({ %(.kv.map: { \$^k => (|\$^v xx *).iterator }) })
#| gather constructs a lazy sequence, in which we infinitely loop advancing wheel A
==> map({ gather { loop { advance \$_, 'A' }} })
#| state variables are only initialised once, and are kept between invocations.
==> map({ state \$i = 1; say "Group {\$i++}, First 20 values: \$_[^20]" })

Output:
Group 1, First 20 values: 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
Group 2, First 20 values: 1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
Group 3, First 20 values: 1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
Group 4, First 20 values: 1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

REXX

Quite a bit of the REXX code deals with detecting of errors   (and issuing error messages)   in the specification and
generation/construction of the wheel sets.

This REXX program uses   numbers   (any form),   not   digits   (for the values on the wheels).

/*REXX program  expresses numbers  from  intersecting number wheels  (or wheel sets).   */
@.= /*initialize array to hold the wheels. */
parse arg lim @.1 /*obtain optional arguments from the CL*/
if lim='' | lim="," then lim= 20 /*Not specified? Then use the default.*/
if @.1='' | @.1="," then do; @.1= ' A: 1 2 3 '
@.2= ' A: 1 B 2, B: 3 4 '
@.3= ' A: 1 D D, D: 6 7 8 '
@.4= ' A: 1 B C, B: 3 4, C: 5 B '
end
do i=1 while @.i\=''; call run /*construct wheel set and "execute" it.*/
end /*i*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
error: procedure; say; say; say '***error***' arg(1); say; say; exit 12
isLet: procedure; parse arg y; return datatype(y, 'M') & length(y)==1 /*is a letter? */
isNum: procedure; parse arg y; return datatype(y, 'N') /*is a number? */
/*──────────────────────────────────────────────────────────────────────────────────────*/
run: @wn= 'wheel name'; first=; @noColon= "wheel name not followed by a colon:"
@gn= 'gear name' ; gear.=; say copies("═", 79)
say 'building wheel group for: ' @.i; wheels= space(@.i); upper wheels
do #=1 while wheels\=''; parse var wheels w gears "," wheels; L= length(w)
if L==2 then do;  !.#= left(w, 1) /*obtain the one─character gear name. */
if right(w, 1)\==':' then call error @noColon w
if \isLet(!.#) then call error @wn "not a letter:" w
end
else call error "first token isn't a" @wn':' w
if #==1 then first= !.1 /*Is this is the 1st wheel set? Use it*/
if first=='' then call error "no wheel name was specified."
n= !.# /*obtain the name of the 1st wheel set.*/
gear.n.0= 1 /*initialize default 1st gear position.*/
say ' setting gear.name:' n " gears=" gears
do g=1 for words(gears); _= word(gears, g)
if isNum(_) | isLet(_) then do; gear.n.g= _; iterate; end
call error @gn "isn't a number or a gear name:" _
end /*g*/
end /*#*/
say; say center(' running the wheel named ' first" ", 79, '─'); \$=
do dummy=0 by 0 until words(\$)==lim; n= first
z= gear.n.0; x= gear.n.z; z= z + 1
gear.n.0= z; if gear.n.z=='' then gear.n.0= 1
if isNum(x) then do; \$= \$ x; iterate; end /*found a number, use it.*/
xx= x /*different gear, keep switching 'til X*/
do forever; nn= xx
if gear.nn.0=='' then call error "a gear is using an unknown gear name:" x
zz= gear.nn.0; xx= gear.nn.zz
zz= zz + 1; gear.nn.0= zz; if gear.nn.zz=='' then gear.nn.0= 1
if isNum(xx) then do; \$= \$ xx; iterate dummy; end
end /*forever*/ /* [↑] found a number, now use FIRST.*/
end /*dummy*/ /*"DUMMY" is needed for the ITERATE. */
say '('lim "results): " strip(\$); say; say; return
output   when using the default inputs:
═══════════════════════════════════════════════════════════════════════════════
building wheel group for:   A:  1 2 3
setting gear.name: A     gears= 1 2 3

───────────────────────── running the wheel named  A ──────────────────────────
(20 results):  1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

═══════════════════════════════════════════════════════════════════════════════
building wheel group for:   A:  1 B 2,    B:  3 4
setting gear.name: A     gears= 1 B 2
setting gear.name: B     gears= 3 4

───────────────────────── running the wheel named  A ──────────────────────────
(20 results):  1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

═══════════════════════════════════════════════════════════════════════════════
building wheel group for:   A:  1 D D,    D:  6 7 8
setting gear.name: A     gears= 1 D D
setting gear.name: D     gears= 6 7 8

───────────────────────── running the wheel named  A ──────────────────────────
(20 results):  1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

═══════════════════════════════════════════════════════════════════════════════
building wheel group for:   A:  1 B C,    B:  3 4,    C:  5 B
setting gear.name: A     gears= 1 B C
setting gear.name: B     gears= 3 4
setting gear.name: C     gears= 5 B

───────────────────────── running the wheel named  A ──────────────────────────
(20 results):  1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

Ruby

groups = [{A: [1, 2, 3]},
{A: [1, :B, 2], B: [3, 4]},
{A: [1, :D, :D], D: [6, 7, 8]},
{A: [1, :B, :C], B: [3, 4], C: [5, :B]} ]

groups.each do |group|
p group
wheels = group.transform_values(&:cycle)
res = 20.times.map do
el = wheels[:A].next
el = wheels[el].next until el.is_a?(Integer)
el
end
puts res.join(" "),""
end

Output:
{:A=>[1, 2, 3]}
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

{:A=>[1, :B, 2], :B=>[3, 4]}
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3

{:A=>[1, :D, :D], :D=>[6, 7, 8]}
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6

{:A=>[1, :B, :C], :B=>[3, 4], :C=>[5, :B]}
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

Visual Basic .NET

Translation of: C#
Imports System.Runtime.CompilerServices

Module Module1

<Extension()>
Iterator Function Loopy(Of T)(seq As IEnumerable(Of T)) As IEnumerable(Of T)
While True
For Each element In seq
Yield element
Next
End While
End Function

Iterator Function TurnWheels(ParamArray wheels As (name As Char, values As String)()) As IEnumerable(Of Char)
Dim data = wheels.ToDictionary(Function(wheel) wheel.name, Function(wheel) wheel.values.Loopy.GetEnumerator)
Dim primary = data(wheels(0).name)

Dim Turn As Func(Of IEnumerator(Of Char), Char) = Function(sequence As IEnumerator(Of Char))
sequence.MoveNext()
Dim c = sequence.Current
Return If(Char.IsDigit(c), c, Turn(data(c)))
End Function

While True
Yield Turn(primary)
End While
End Function

<Extension()>
Sub Print(sequence As IEnumerable(Of Char))
Console.WriteLine(String.Join(" ", sequence))
End Sub

Sub Main()
TurnWheels(("A", "123")).Take(20).Print()
TurnWheels(("A", "1B2"), ("B", "34")).Take(20).Print()
TurnWheels(("A", "1DD"), ("D", "678")).Take(20).Print()
TurnWheels(("A", "1BC"), ("B", "34"), ("C", "5B")).Take(20).Print()
End Sub

End Module
Output:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4

Wren

Translation of: Go
Library: Wren-dynamic
Library: Wren-sort
Library: Wren-fmt
import "/dynamic" for Struct
import "/sort" for Sort
import "/fmt" for Fmt

var Wheel = Struct.create("Wheel", ["next", "values"])

var generate = Fn.new { |wheels, start, maxCount|
var count = 0
var w = wheels[start]
while (true) {
var s = w.values[w.next]
var v = Num.fromString(s)
w.next = (w.next + 1) % w.values.count
wheels[start] = w
if (v) {
System.write("%(v) ")
count = count + 1
if (count == maxCount) {
System.print("...\n")
return
}
} else {
while (true) {
var w2 = wheels[s]
var ss = s
s = w2.values[w2.next]
w2.next = (w2.next + 1) % w2.values.count
wheels[ss] = w2
v = Num.fromString(s)
if (v) {
System.write("%(v) ")
count = count + 1
if (count == maxCount) {
System.print("...\n")
return
}
break
}
}
}
}
}

var printWheels = Fn.new { |wheels|
var names = []
Sort.quick(names)
System.print("Intersecting Number Wheel group:")
for (name in names) {
Fmt.print(" \$s: \$n", name, wheels[name].values)
}
System.write(" Generates:\n ")
}

var wheelMaps = [
{
"A": Wheel.new(0, ["1", "2", "3"])
},
{
"A": Wheel.new(0, ["1", "B", "2"]),
"B": Wheel.new(0, ["3", "4"])
},
{
"A": Wheel.new(0, ["1", "D", "D"]),
"D": Wheel.new(0, ["6", "7", "8"])
},
{
"A": Wheel.new(0, ["1", "B", "C"]),
"B": Wheel.new(0, ["3", "4"]),
"C": Wheel.new(0, ["5", "B"])
}
]
for (wheels in wheelMaps) {
printWheels.call(wheels)
generate.call(wheels, "A", 20)
}
Output:
Intersecting Number Wheel group:
A: [1, 2, 3]
Generates:
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ...

Intersecting Number Wheel group:
A: [1, B, 2]
B: [3, 4]
Generates:
1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3 ...

Intersecting Number Wheel group:
A: [1, D, D]
D: [6, 7, 8]
Generates:
1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6 ...

Intersecting Number Wheel group:
A: [1, B, C]
B: [3, 4]
C: [5, B]
Generates:
1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4 ...

zkl

fcn intersectingNumberWheelsW(wheels){ // ("A":(a,b,"C"), "C":(d,e) ...)
ws:=wheels.pump(Dictionary(),fcn([(k,v)]){ return(k,Walker.cycle(v)) }); // new Dictionary
Walker.zero().tweak(fcn(w,wheels){
while(1){
w=wheels[w].next(); // increment wheel w
if(Int.isType(w)) return(w);
}
}.fp("A",ws)) // assume wheel A exists and is always first
}
wheelSets:=T( Dictionary("A",T(1,2,3)),
Dictionary("A",T(1,"B",2), "B",T(3,4)),
Dictionary("A",T(1,"D","D"), "D",T(6,7,8)),
Dictionary("A",T(1,"B","C"), "C",T(5,"B"), "B",T(3,4)) );
foreach ws in (wheelSets){
println("Wheel set:");
ws.pump(String,fcn([(k,v)]){ "  %s: %s\n".fmt(k,v.concat(" ")) }).print();
println("-->",intersectingNumberWheelsW(ws).walk(20).concat(" "));
}
Output:
Wheel set:
A: 1 2 3
-->1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
Wheel set:
A: 1 B 2
B: 3 4
-->1 3 2 1 4 2 1 3 2 1 4 2 1 3 2 1 4 2 1 3
Wheel set:
A: 1 D D
D: 6 7 8
-->1 6 7 1 8 6 1 7 8 1 6 7 1 8 6 1 7 8 1 6
Wheel set:
A: 1 B C
C: 5 B
B: 3 4
-->1 3 5 1 4 3 1 4 5 1 3 4 1 3 5 1 4 3 1 4