Table of Lehmer Codes for Swindler's Gambit

Table of Lehmer Codes

The stack is written left-to-right, bottom-to-top. (So cba has c at the bottom, b in the middle, and a at the top.)

Code	Permutation
Permuting a
0	a
Permuting ba
1	ab
Permuting cba
2	bca
3	bac
4	acb
5	abc
Permuting dcba
6	cdba
7	cdab
8	cbda
9	cbad
10	cadb
11	cabd
12	bdca
13	bdac
14	bcda
15	bcad
16	badc
17	bacd
18	adcb
19	adbc
20	acdb
21	acbd
22	abdc
23	abcd
Permuting edcba
24	decba
25	decab
26	debca
27	debac
28	deacb
29	deabc
30	dceba
31	dceab
32	dcbea
33	dcbae
34	dcaeb
35	dcabe
36	dbeca
37	dbeac
38	dbcea
39	dbcae
40	dbaec
41	dbace
42	daecb
43	daebc
44	daceb
45	dacbe
46	dabec
47	dabce
48	cedba
49	cedab
50	cebda
51	cebad
52	ceadb
53	ceabd
54	cdeba
55	cdeab
56	cdbea
57	cdbae
58	cdaeb
59	cdabe
60	cbeda
61	cbead
62	cbdea
63	cbdae
64	cbaed
65	cbade
66	caedb
67	caebd
68	cadeb
69	cadbe
70	cabed
71	cabde
72	bedca
73	bedac
74	becda
75	becad
76	beadc
77	beacd
78	bdeca
79	bdeac
80	bdcea
81	bdcae
82	bdaec
83	bdace
84	bceda
85	bcead
86	bcdea
87	bcdae
88	bcaed
89	bcade
90	baedc
91	baecd
92	badec
93	badce
94	baced
95	bacde
96	aedcb
97	aedbc
98	aecdb
99	aecbd
100	aebdc
101	aebcd
102	adecb
103	adebc
104	adceb
105	adcbe
106	adbec
107	adbce
108	acedb
109	acebd
110	acdeb
111	acdbe
112	acbed
113	acbde
114	abedc
115	abecd
116	abdec
117	abdce
118	abced
119	abcde
Permuting fedcba
120	efdcba
121	efdcab
122	efdbca
123	efdbac
124	efdacb
125	efdabc
126	efcdba
127	efcdab
128	efcbda
129	efcbad
130	efcadb
131	efcabd
132	efbdca
133	efbdac
134	efbcda
135	efbcad
136	efbadc
137	efbacd
138	efadcb
139	efadbc
140	efacdb
141	efacbd
142	efabdc
143	efabcd
144	edfcba
145	edfcab
146	edfbca
147	edfbac
148	edfacb
149	edfabc
150	edcfba
151	edcfab
152	edcbfa
153	edcbaf
154	edcafb
155	edcabf
156	edbfca
157	edbfac
158	edbcfa
159	edbcaf
160	edbafc
161	edbacf
162	edafcb
163	edafbc
164	edacfb
165	edacbf
166	edabfc
167	edabcf
168	ecfdba
169	ecfdab
170	ecfbda
171	ecfbad
172	ecfadb
173	ecfabd
174	ecdfba
175	ecdfab
176	ecdbfa
177	ecdbaf
178	ecdafb
179	ecdabf
180	ecbfda
181	ecbfad
182	ecbdfa
183	ecbdaf
184	ecbafd
185	ecbadf
186	ecafdb
187	ecafbd
188	ecadfb
189	ecadbf
190	ecabfd
191	ecabdf
192	ebfdca
193	ebfdac
194	ebfcda
195	ebfcad
196	ebfadc
197	ebfacd
198	ebdfca
199	ebdfac
200	ebdcfa
201	ebdcaf
202	ebdafc
203	ebdacf
204	ebcfda
205	ebcfad
206	ebcdfa
207	ebcdaf
208	ebcafd
209	ebcadf
210	ebafdc
211	ebafcd
212	ebadfc
213	ebadcf
214	ebacfd
215	ebacdf
216	eafdcb
217	eafdbc
218	eafcdb
219	eafcbd
220	eafbdc
221	eafbcd
222	eadfcb
223	eadfbc
224	eadcfb
225	eadcbf
226	eadbfc
227	eadbcf
228	eacfdb
229	eacfbd
230	eacdfb
231	eacdbf
232	eacbfd
233	eacbdf
234	eabfdc
235	eabfcd
236	eabdfc
237	eabdcf
238	eabcfd
239	eabcdf
240	dfecba
241	dfecab
242	dfebca
243	dfebac
244	dfeacb
245	dfeabc
246	dfceba
247	dfceab
248	dfcbea
249	dfcbae
250	dfcaeb
251	dfcabe
252	dfbeca
253	dfbeac
254	dfbcea
255	dfbcae
256	dfbaec
257	dfbace
258	dfaecb
259	dfaebc
260	dfaceb
261	dfacbe
262	dfabec
263	dfabce
264	defcba
265	defcab
266	defbca
267	defbac
268	defacb
269	defabc
270	decfba
271	decfab
272	decbfa
273	decbaf
274	decafb
275	decabf
276	debfca
277	debfac
278	debcfa
279	debcaf
280	debafc
281	debacf
282	deafcb
283	deafbc
284	deacfb
285	deacbf
286	deabfc
287	deabcf
288	dcfeba
289	dcfeab
290	dcfbea
291	dcfbae
292	dcfaeb
293	dcfabe
294	dcefba
295	dcefab
296	dcebfa
297	dcebaf
298	dceafb
299	dceabf
300	dcbfea
301	dcbfae
302	dcbefa
303	dcbeaf
304	dcbafe
305	dcbaef
306	dcafeb
307	dcafbe
308	dcaefb
309	dcaebf
310	dcabfe
311	dcabef
312	dbfeca
313	dbfeac
314	dbfcea
315	dbfcae
316	dbfaec
317	dbface
318	dbefca
319	dbefac
320	dbecfa
321	dbecaf
322	dbeafc
323	dbeacf
324	dbcfea
325	dbcfae
326	dbcefa
327	dbceaf
328	dbcafe
329	dbcaef
330	dbafec
331	dbafce
332	dbaefc
333	dbaecf
334	dbacfe
335	dbacef
336	dafecb
337	dafebc
338	dafceb
339	dafcbe
340	dafbec
341	dafbce
342	daefcb
343	daefbc
344	daecfb
345	daecbf
346	daebfc
347	daebcf
348	dacfeb
349	dacfbe
350	dacefb
351	dacebf
352	dacbfe
353	dacbef
354	dabfec
355	dabfce
356	dabefc
357	dabecf
358	dabcfe
359	dabcef
360	cfedba
361	cfedab
362	cfebda
363	cfebad
364	cfeadb
365	cfeabd
366	cfdeba
367	cfdeab
368	cfdbea
369	cfdbae
370	cfdaeb
371	cfdabe
372	cfbeda
373	cfbead
374	cfbdea
375	cfbdae
376	cfbaed
377	cfbade
378	cfaedb
379	cfaebd
380	cfadeb
381	cfadbe
382	cfabed
383	cfabde
384	cefdba
385	cefdab
386	cefbda
387	cefbad
388	cefadb
389	cefabd
390	cedfba
391	cedfab
392	cedbfa
393	cedbaf
394	cedafb
395	cedabf
396	cebfda
397	cebfad
398	cebdfa
399	cebdaf
400	cebafd
401	cebadf
402	ceafdb
403	ceafbd
404	ceadfb
405	ceadbf
406	ceabfd
407	ceabdf
408	cdfeba
409	cdfeab
410	cdfbea
411	cdfbae
412	cdfaeb
413	cdfabe
414	cdefba
415	cdefab
416	cdebfa
417	cdebaf
418	cdeafb
419	cdeabf
420	cdbfea
421	cdbfae
422	cdbefa
423	cdbeaf
424	cdbafe
425	cdbaef
426	cdafeb
427	cdafbe
428	cdaefb
429	cdaebf
430	cdabfe
431	cdabef
432	cbfeda
433	cbfead
434	cbfdea
435	cbfdae
436	cbfaed
437	cbfade
438	cbefda
439	cbefad
440	cbedfa
441	cbedaf
442	cbeafd
443	cbeadf
444	cbdfea
445	cbdfae
446	cbdefa
447	cbdeaf
448	cbdafe
449	cbdaef
450	cbafed
451	cbafde
452	cbaefd
453	cbaedf
454	cbadfe
455	cbadef
456	cafedb
457	cafebd
458	cafdeb
459	cafdbe
460	cafbed
461	cafbde
462	caefdb
463	caefbd
464	caedfb
465	caedbf
466	caebfd
467	caebdf
468	cadfeb
469	cadfbe
470	cadefb
471	cadebf
472	cadbfe
473	cadbef
474	cabfed
475	cabfde
476	cabefd
477	cabedf
478	cabdfe
479	cabdef
480	bfedca
481	bfedac
482	bfecda
483	bfecad
484	bfeadc
485	bfeacd
486	bfdeca
487	bfdeac
488	bfdcea
489	bfdcae
490	bfdaec
491	bfdace
492	bfceda
493	bfcead
494	bfcdea
495	bfcdae
496	bfcaed
497	bfcade
498	bfaedc
499	bfaecd
500	bfadec
501	bfadce
502	bfaced
503	bfacde
504	befdca
505	befdac
506	befcda
507	befcad
508	befadc
509	befacd
510	bedfca
511	bedfac
512	bedcfa
513	bedcaf
514	bedafc
515	bedacf
516	becfda
517	becfad
518	becdfa
519	becdaf
520	becafd
521	becadf
522	beafdc
523	beafcd
524	beadfc
525	beadcf
526	beacfd
527	beacdf
528	bdfeca
529	bdfeac
530	bdfcea
531	bdfcae
532	bdfaec
533	bdface
534	bdefca
535	bdefac
536	bdecfa
537	bdecaf
538	bdeafc
539	bdeacf
540	bdcfea
541	bdcfae
542	bdcefa
543	bdceaf
544	bdcafe
545	bdcaef
546	bdafec
547	bdafce
548	bdaefc
549	bdaecf
550	bdacfe
551	bdacef
552	bcfeda
553	bcfead
554	bcfdea
555	bcfdae
556	bcfaed
557	bcfade
558	bcefda
559	bcefad
560	bcedfa
561	bcedaf
562	bceafd
563	bceadf
564	bcdfea
565	bcdfae
566	bcdefa
567	bcdeaf
568	bcdafe
569	bcdaef
570	bcafed
571	bcafde
572	bcaefd
573	bcaedf
574	bcadfe
575	bcadef
576	bafedc
577	bafecd
578	bafdec
579	bafdce
580	bafced
581	bafcde
582	baefdc
583	baefcd
584	baedfc
585	baedcf
586	baecfd
587	baecdf
588	badfec
589	badfce
590	badefc
591	badecf
592	badcfe
593	badcef
594	bacfed
595	bacfde
596	bacefd
597	bacedf
598	bacdfe
599	bacdef
600	afedcb
601	afedbc
602	afecdb
603	afecbd
604	afebdc
605	afebcd
606	afdecb
607	afdebc
608	afdceb
609	afdcbe
610	afdbec
611	afdbce
612	afcedb
613	afcebd
614	afcdeb
615	afcdbe
616	afcbed
617	afcbde
618	afbedc
619	afbecd
620	afbdec
621	afbdce
622	afbced
623	afbcde
624	aefdcb
625	aefdbc
626	aefcdb
627	aefcbd
628	aefbdc
629	aefbcd
630	aedfcb
631	aedfbc
632	aedcfb
633	aedcbf
634	aedbfc
635	aedbcf
636	aecfdb
637	aecfbd
638	aecdfb
639	aecdbf
640	aecbfd
641	aecbdf
642	aebfdc
643	aebfcd
644	aebdfc
645	aebdcf
646	aebcfd
647	aebcdf
648	adfecb
649	adfebc
650	adfceb
651	adfcbe
652	adfbec
653	adfbce
654	adefcb
655	adefbc
656	adecfb
657	adecbf
658	adebfc
659	adebcf
660	adcfeb
661	adcfbe
662	adcefb
663	adcebf
664	adcbfe
665	adcbef
666	adbfec
667	adbfce
668	adbefc
669	adbecf
670	adbcfe
671	adbcef
672	acfedb
673	acfebd
674	acfdeb
675	acfdbe
676	acfbed
677	acfbde
678	acefdb
679	acefbd
680	acedfb
681	acedbf
682	acebfd
683	acebdf
684	acdfeb
685	acdfbe
686	acdefb
687	acdebf
688	acdbfe
689	acdbef
690	acbfed
691	acbfde
692	acbefd
693	acbedf
694	acbdfe
695	acbdef
696	abfedc
697	abfecd
698	abfdec
699	abfdce
700	abfced
701	abfcde
702	abefdc
703	abefcd
704	abedfc
705	abedcf
706	abecfd
707	abecdf
708	abdfec
709	abdfce
710	abdefc
711	abdecf
712	abdcfe
713	abdcef
714	abcfed
715	abcfde
716	abcefd
717	abcedf
718	abcdfe
719	abcdef

Generating Code

/** iterator yielding 1, 1, 2, 6, 24, ... */
struct Factorial {
    acc: usize, n: usize
}

impl Factorial {
    fn new() -> Self { Factorial { acc: 1, n: 1 } }
}

impl Iterator for Factorial {
    type Item = usize;
    fn next(&mut self) -> Option<usize> {
        let val = self.acc;
        self.acc *= self.n;
        self.n += 1;
        Some(val)
    }
}

fn factorial(x: usize) -> usize {
    if x == 0 {
        // sorry. it works better this way in these cases
        0
    } else {
        Factorial::new().nth(x).unwrap()
    }
}


/** Fn to take a stack and a value and perform a shuffling of the last few elems */
fn ixed_factorial<T: Clone>(mut value: usize, stack: &mut [T]) -> Result<(), String> {
    let mut strides: Vec<usize> = Factorial::new().take_while(|&x| x <= value).collect();

    // want only the last few elems of the stack
    if stack.len() < strides.len() {
        Err("Manipulating too many elements on the stack!")?
    }
    let stride_offset = stack.len() - strides.len();
    let mut edit_target = &mut stack[stride_offset..];
    let mut swap = edit_target.to_vec();

    while let Some(divisor) = strides.pop() {
        let index = value / divisor;
        value %= divisor;
        edit_target[0] = swap.remove(index);
        edit_target = &mut edit_target[1..];
    }

    Ok(())
}

fn main() {
    
    let max_len = 6;
    let template = {
        let mut tmp = ('a'..=(b'a' + max_len as u8) as char).collect::<Vec<char>>();
        tmp.reverse();
        tmp
    };
    
    println!("<table>");
    println!("<tr><th>Code</th><th>Permutation</th></tr>");

    for x in 1..=max_len {
        let len = template.len();
        let slice = &template[len - x..];

        println!("<tr><th colspan=\"2\">Permuting <code>{}</code></th></tr>", slice.iter().collect::<String>());
        let fact = factorial(x);
        let prev_fact = factorial(x-1);
        
        for code in prev_fact..fact {
            let mut permed = slice.to_owned();
            ixed_factorial(code, &mut permed).unwrap();
            println!("<tr><td>{}</td> <td><code>{}</code></td></tr>", code, permed.iter().collect::<String>());
        }
    }
    
    println!("</table>");
}