Ce défi consiste à trouver la plus longue chaîne de mots anglais où les 3 premiers caractères du mot suivant correspondent aux 3 derniers caractères du dernier mot. Vous utiliserez un dictionnaire commun disponible dans les distributions Linux qui peut être téléchargé ici:

https://www.dropbox.com/s/8tyzf94ps37tzp7/words?dl=0

qui a 99171 mots anglais. Si votre Linux local /usr/share/dict/wordsest le même fichier (a md5sum == cbbcded3dc3b61ad50c4e36f79c37084), vous pouvez l'utiliser.

Les mots ne peuvent être utilisés qu'une seule fois dans une réponse.

EDIT: les lettres doivent correspondre exactement, y compris les majuscules / minuscules, les apostrophes et les accents.

Un exemple de réponse valide est: idea deadpan panoramic micra craftsman mantra traffic fiche qui donnerait 8.

La réponse avec la chaîne de mots valide la plus longue sera la gagnante. En cas d'égalité, la première réponse l'emportera. Votre réponse doit énumérer la chaîne de mots que vous avez trouvée et (bien sûr) le programme que vous avez écrit pour le faire.

Java, heuristique privilégiant le sommet qui induit le plus grand graphe: 1825 1855 1873

Le code ci-dessous s'exécute en moins de 10 minutes et trouve le chemin suivant:

[wad, wadis, dis, dismay, may, mayfly, flywheels, elsewhere, erecting, ingratiate, ateliers, ersatzes, zest, esthetic, tickled, ledger, germicide, idealizes, zestful, fulling, ingrains, institute, uterine, ineptness, essaying, ingeniously, slyness, essences, cessations, onshore, ores, resoundingly, glycerine, inertness, essay, say, saying, ingenuous, ousted, tediously, sly, slyest, estrogen, genuflecting, ingestion, ionizer, zeros, roses, sesames, mes, meshed, hedonist, isthmuses, sesame, amending, ingredient, entrapment, enthuses, session, ionosphere, erectness, essayist, isthmus, mustaches, hesitatingly, glycogen, generation, ions, onset, settable, blew, lewder, deriding, ingratiates, testicles, lessen, sensitization, ionization, ionizing, ingratiating, ingenious, ouster, terrorizing, ingest, estranges, gesticulating, ingrates, testis, tissue, sue, suede, edelweiss, issuing, ingraining, ingrown, owner, nerdiest, estimation, ionospheres, rescue, cue, cueing, ingesting, ingot, got, gotten, tensor, sorrowing, ingratiated, tedious, ousting, ingratiatingly, glycerin, ringside, identifiable, bleariest, ester, terminological, calibrator, torrent, entraps, apse, pseudonym, nymphomania, niacin, cinema, emailed, led, ledges, gesticulates, testicle, clement, entail, ail, ailment, enter, terrains, inspires, restaurateur, euros, rosiest, estimates, tester, termite, iterator, torture, urethras, raspiest, estimator, tore, oregano, anointment, enthuse, useful, fulfil, filmstrip, riposte, stereotyped, pedicure, urea, readmits, itself, elf, elfin, finagles, lesbians, answerable, bleat, eatery, erythrocytes, testosterone, one, ones, nest, esteemed, medicine, inextricable, blessed, sediment, entry, try, tryout, outsources, cesarians, answered, redressed, seducer, cervical, calumniates, test, establishment, entombment, enthusiastic, tickles, lessens, ensemble, blemishes, hesitant, antic, tick, ickiest, estimable, blemished, hedgehog, hogan, gantlet, letdown, own, ownership, hippest, estates, testates, testiest, establishes, hes, hesitates, testable, bleakest, esthetes, testament, entice, iceberg, erg, ergonomic, microscope, operatives, vestibules, lesser, serenade, adenoidal, dales, lest, estrangement, entrap, raptures, resourceful, fulsome, omen, menswear, earthliest, established, hedges, gestates, testy, styes, yeshivot, voter, terrible, blender, derides, descent, enticed, cedillas, lass, assailable, bleacher, hermit, mite, item, temperas, rash, ashtray, rayon, yonder, dermis, mismanage, agendas, dash, ashy, shy, shyster, terrapins, insatiable, bleeder, derives, vestment, entangle, glen, lengthens, ensconced, ceded, deduced, cedars, arsenic, nice, ice, iced, cedar, daredevil, villa, llamas, masseuse, use, useable, bleach, achievable, bleached, hedonistic, tic, ticker, kerchieves, vessel, sell, ell, elliptic, ticket, kettles, lessee, seeps, epsilon, longboat, oath, atherosclerosis, sisterhood, oodles, lesson, sonatas, tassel, selvage, age, agent, entranced, cedes, descender, deranges, gestures, restraint, interment, enthused, seduced, cedilla, llama, amalgam, gamut, mutable, blend, endear, earthy, thymus, mussel, seltzer, zero, erodes, despot, potful, fulfillment, enthrall, allot, lotus, tussle, sledgehammered, redolent, entrapped, pedestal, talk, alkalis, listen, tended, deductible, bleeped, pedigree, reentered, redistribute, uterus, rustproofed, fed, fedora, oranges, gesundheit, either, herdsman, manes, nestles, lessor, sorrowful, fullback, acknowledges, gestured, redoubtable, blended, deduces, cesareans, answer, werewolves, vesper, perseveres, restructures, reside, ideogram, rammed, meddlesome, omens, ensign, ignores, restrains, insolent, entanglement, entrenchment, enticement, entomological, calligraphy, physical, calico, iconoclast, astringent, entertainment, entrant, antennas, nasty, stymie, miens, enslave, averred, redefine, inexorable, blenched, hedgerow, rowboat, oat, oaten, tend, endears, arson, songwriter, terminable, blent, entreaty, atypical, calypso, psoriasis, sister, term, ermine, ineligible, bleaker, kerosene, enema, emancipator, tormentor, torrider, derailment, entertains, instil, tildes, destine, inelegant, anthropomorphic, hiccup, cupolas, lastingly, glycerol, rollback, acknowledgment, entombed, bedridden, denser, servicewomen, menopause, used, sedatives, vesicle, clearinghouse, user, servant, antipodes, descry, crystalline, inexpedient, enthusiast, astonishment, entirety, etymological, calendared, redbreast, astronomer, merinos, nosedove, overpay, pay, paymaster, termagant, antiaircraft, aftercare, ares, resentful, fulcrum, rumpus, pushcart, artiste, stethoscopes, pesetas, taste, steadfast, astride, ides, destitute, utensil, silvan, vanguard, ardent, entryway, waysides, despair, airdrop, ropes, pestered, redder, derangement, entered, redeemed, medullas, lasagnas, nasal, salsas, sashay, hay, haymow, mow, mowed, wedder, derringer, germane, anemic, microfilmed, media, diatom, tomboys, oyster, terminator, toreador, dorsal, salespeople, pleased, sedater, terabit, bitten, tentacle, clergyman, manifesto, stomach, achoo, hoopla, plaza, azalea, leaven, vendor, dormant, antiparticle, cleared, redraft, afterword, ordains, insufficient, entitlement, entomb, ombudsmen, men, mental, tallyhos, hospice, icecap, cape, aperitif, tiffed, fedoras, rasped, pediatric, rickshaw, hawker, keratin, tinctures, reset, setback, acknowledgement, enthronement, entwine, inexact, actor, torpedos, dosed, sedan, dancer, cerebrum, rumple, plea, leach, ache, cheaper, per, periscopes, pestilent, entreat, eater, terser, serape, ape, apes, pesky, skycap, capped, pederast, astuter, terrace, acetaminophen, henchmen, menopausal, saltcellar, lard, ardor, dormice, icebound, underbrush, ushered, redrew, rewound, underclass, assassin, sinew, newscast, astrologer, gerund, undertaken, ken, kens, ensnared, redcap, cappuccinos, nostrum, rum, rumored, redraw, rawhide, identical, calcine, inertia, tiara, arabesque, queerer, reruns, unsold, oldie, diesel, selectmen, mentored, redden, dental, talon, longhand, and, androgen, genome, omelet, lethal, hallucinogenic, nickname, amen, menhaden, denudes, despaired, redevelop, lope, operas, rasp, aspired, redskin, kindergartens, ensnares, resultant, anthropological, callus, lustful, fulcra, crammed, mediocre, crepes, pesticide, ideas, eastbound, under, derrières, respired, rediscovered, redundant, antihero, erode, ode, odes, described, bedevil, villager, gerrymander, deride, ideograph, aphid, hid, hides, describes, besides, despoil, oilskin, kingdom, dominant, ant, antipasti, stiffens, ensured, redeemer, merchant, antiwar, warped, pederasty, stylus, lush, usher, her, hereafter, terrapin, pinnacle, clerical, caliber, bereave, avenger, geriatric, rickshas, haste, stereoscopes, pester, termini, initiator, tortures, restorer, reran, ransomed, medulla, llanos, nostril, rill, illogical, calif, lifer, fervor, vortex, textures, resister, termed, medieval, valor, lord, ordered, rediscover, verbatim, times, mesdames, mescal, caliper, periscope, opera, erasures, restart, artichokes, kestrel, reliant, antebellum, lumbago, agog, goggle, gleeful, fulfill, illustrator, tor, torque, questionnaires, resumed, mediator, tort, orthodoxy, oxymora, oratorio, riot, iotas, taster, terrific, fiche, checkpoint, interloper, perfumes, mesas, sassafras, rasher, heraldry, drywall, all, allergens, ensnare, area, rearm, armchair, airman, manufactures, resurface, acerbic, bicycle, cleverer, rerun, runt, untidy, idyllic, lichens, ensures, resend, endemic, microchip, hippopotamus, muscatel, telecast, astronaut, autopilot, lot, loth, other, heros, rosin, single, gleamed, mediaeval, valet, lettered, redound, underside, ideological, calliper, perihelia, liaison, sonic, nicknames, messenger, germicides, descendant, antigen, genital, tall, allergen, gentleman, mangos, gossipped, pedicures, resistant, antlered, redeveloped, pedagogical, calligrapher, heroins, inside, idea, deafen, fen, fencer, cerebra, bravuras, rascal, calculus, lusher, herbivores, resins, instill, illicit, citric, ricochet, heterodoxy, oxygen, generic, rice, icebox, box, boxcar, cartography, physique, quell, ellipsis, sis, sisal, sallow, lowbrow, rowel, well, elliptical, calf, alfresco, scow, cow, cowboy, boy, boyfriend, end, endeared, red, redesign, ignoramus, musket, kettledrum, rump, umped, pedlar, larvas, vassal, salmonellas, last, astronomical, calfskin, kingfisher, hereupon, ponchos, hospital, talisman, mantel, telethon, honcho, chomped, pedant, antitoxins, instant, antipastos, tossup, superintend, endangered, redskins, instigator, torpor, portico, icon, conquistador, dormer, merganser, seraphic, hiccuped, pedagogue, guerrillas, laser, sera, eraser, seraph, aphasic, sickbed, bed, bedsores, resign, ignorant, anthropocentric, richer, herdsmen, menu, enures, resuscitator, tornado, ado, adobe, obeisant, anthill, illegal, gallon, longshoremen, menace, ace, acetylene, enemas, mas, mascot, cot, cotton, tonsures, restores, result, ultraviolet, letterbox, boxer, xerography, physiological, calmer, merchantmen, mentor, torus, russet, settee, teenager, gerbil, billfold, old, olden, denatures, resubmit, mitten, ten, tenon, nonchalant, antique, queasy, asymmetric, ricksha, shanghai, haircut, cutups, upsides, descriptor, torpid, pidgin, gins, instep, tepee, peeper, perturb, urbane, anemia, miasmas, mascaras, raspy, spy, spyglass, assures, resonator, tortilla, llano, anon, nontechnical, calabash, ashram, rampart, arthropod, podia, diagram, ramp, amp, amphitheatres, resistor, tortillas, lasagna, gnat, natal, talc, alcoholic, licensee, seemed, medical, calm, almanac, nacho, choreography, phylum, lumbar, barman, mannequins, insures, respires, resound, underarm, armatures, resides, desideratum, tumult, ultrasound, underdog, dogcatcher, herald, alderwoman, mandarins, insecticides, desires, respirator, torrid, rid, rides, descant, anticlimax, maximum, mum, mummer, meringue, guesser, sermon, monogram, ramrod, rodeo, deodorant, antelopes, peso, esophagus, gusset, setups, upshot, hotel, telescope, open, penicillin, lingos, gossip, sip, siphon, honor, normal, maltreat, eaten, tenet, nether, herpes, pesticides, descend, endow, downfall, alleyway, way, waylay, layman, manicures, reshuffle, flea, lea, leash, ashen, henchman, mandolin, linchpins, inscribes, bestow, townspeople, plectrum, rumbas, baste, sternum, numb, umbilici, icicle, cleaver, vertebra, brains, insouciant, antidepressant, anthem, hemoglobin, binocular, largos, gossamer, mermaid, aid, aides, desperado, adopt, opt, optima, imam, mambos, bosun, sun, sunspot, potpourris, risky, sky, skyscraper, perturbed, bedraggle, glee, lee, leech, echo, choreographer, heraldic, dictum, tumid, midday, day, daybed, bedsides, desktop, topknot, notepaper, periodical, calendar, dare, areas, easel, selfsame, amebas, basins, ins, insulin, linnet, nettlesome, omegas, gasp, aspartame, amend, endures, researcher, herbal, balsas, sass, assault, ultimatum, tumor, mortgagor, gores, resort, orthopaedic, dictatorship, hipper, person, sonar, narc, arc, archduke, ukelele, elegant, anther, hereabout, outfox, fox, foxtrot, rotogravures, restaurant, antechamber, beret, retriever, verbena, enamor, morsel, sellout, outmaneuver, vertical, call, allergenic, niche, chessman, mandolins, insipid, pidgins, install, allures, rescind, indignant, antithetical, calicos, cosmonaut, auto, utopia, piano, another, heretical, calk, alkali, alibi, ibis, bistro, troupe, upend, endorser, serviceman, mandarin, rind, inductee, teepee, pee, peekaboo, bootstrap, rape, apertures, resin, singular, larval, valiant, antiperspirant, antipasto, stop, topical, calisthenic, nicer, cervix, vixen, xenophobic, bicep, cephalic, licit, citizenship, hippopotami, amigos, gospel, pellet, letups, upstart, artificer, cerebellum, lumberman, manic, nicknamed, medic, dickie, kielbasas, sash, ash, ashcan, cannon, nonskid, kid, kidnaper, perjures, resolver, vernacular, larkspur, puree, reefer, ferret, retains, insofar, far, fart, artisan, sandbag, bagel, gelatin, tinsel, selectman, manacle, clever, versus, sustains, inscribed, bedpan, pandemic, microprocessor, sorbet, bet, betcha, char, harem, remodel, deli, elicit, citadel, deliver, verandas, dashikis, kisser, servicemen, menthol, holiday, daydreamer, merchantman, manikins, insane, anew, newsprint, interwove, overreach, achieve, even, venom, nomad, mad, madrigal, gala, alarm, armpit, pitchman, manor, northbound, underbid, bidet, detox, toxemia, miasma, smarten, tenderloins, insult, ultra, travel, velvet, veteran, random, domino, inopportune, uneconomic, microbes, bestir, tiro, ironware, arena, enamel, melodramas, mastodon, don, donut, nut, nutmeg, meg, megalopolis, lissom, sombre, breathe, therefrom, romper, performer, merman, mangrove, overshadow, downcast, astir, tiros, rostra, trachea, heaven, ventricle, clergywoman, maneuver, verbal, ballad, ladyship, hippie, pie, piebald, alderman, manatee, teethe, thereupon, poncho, choicer, ceramic, microscopic, picayune, uneaten, tendon, donor, northeast, astound, underpass, assessor, sorghum, hum, human, mantra, trainee, needlepoint, interplay, laywoman, mannikin, kinsman, mantillas, lassie, sieve, ever, verdigris, risen, sensor, sorrel, relabel, belabor, borsch, schlep, leprechauns, unsnap, nap, napkin, kin, kingpin, pinkeye, eyeglass, assemblyman, manikin, kingship, hip, hippos, postpartum, tumbrel, relic, lichee, heehaw, haw, hawser, servicewoman, many, anyhow, howsoever, vertex, text, extra, trap, rap, rapper, periwig, wigwag, wag, wagon, gonorrhea, heave, aver, vermin, minesweeper, perplex, lexicon, congas, gastronomic, microfiche, cheapen, pentathlon, longhair, air, aircraft, aft, aftertaste, stem, tempos, postwar, war, wart, article, clear, earshot, hotshot, hotbed, bedlam, lam, lambkin, kindergarten, tenser, serum, rumor, mortar, tarmac, macabre, breech, echos, hostel, telescopic, pickerel, relay, laypeople, pleas, east, astronomic, micra, crackpot, pot, potato, atom, tombed, bedbug, bugaboo, bootleg, leg, legato, atop, topple, plethora, orangutang, angora, orangutan, tan, tandem, democrat, rat, rattan, tang, angry, gryphon, honeybee, bee, beeswax, waxen, xenon, nonplus, lustre, trellis, lisle, sleepwear, earwig, wig, wigwam, wampum, pummel, melanomas, massacre, cretin, tin, tint, interviewee, wee, weeper, persimmon, monsignori, origin, gingham, ham, hamper, pericardia, diarrhea, heartthrob, rob, robes, besom, sombreros, rosebud, bud, budgerigar, garret, retrodden, denim, nimbus, bus, bushel, helmet, metaphor, horsefly, flypaper, peritonea, near, ear, earlobes, bestowal, wall, allay, layout, outlast, astrakhan, handicapper, perusal, saltpetre, tremor, moribund, undercut, cut, cutoff, off, offal, falcon, con, consul, sultan, tannin, ninepin, pinball, allegro, grommet, metro, trot, rot, rotten, tenpin, pineapple, plectra, transit, sitar, tar, taro, arousal, salmon, moneybag, bagpipe, ipecac, cache, checkout, outrun, runaround, undersea, sea, sear, earache, cherub, rub, rubicund, underpin, pin, pint, intagli, glib, lib, libel, bellyache, cherubim, bimbos, bosuns, unsound, undertow, tow, towel, wellington, ton, tonsil, silicon, concoct, octet, tetrahedra, drachmae, maestri, tripos, possum, sum, sumac, macro, crocus, custom, tom, tomcat, catsup, sup, superstar, tarpaulin, linchpin, pinpoint, intercom, comet, met, metacarpus, pussycat, catastrophe, phenomenon, nonverbal, ballpoint, interurban, bani, animal, malt, altar, tartar, tarot, rotund, undergrad, radio, diocesan, sandbar, bar, barren, renewal, walkout, outstrip, ripen, pen, pencil, cilantro, trout, outran, rancor, corncob, cob, cobra, bra, brag, rag, ragas, gas, gasohol, holdout, output, put, putsch, schwas, was, waste, stereo, reoccur, cur, curb, urban, ban, bantam, tam, tamp, ampul, pullout, outwit, wit, withal, halo, alohas, hasp, asparagus, gusto, stove, overlap, lapel, pelvis, visit, sit, sitcom, compendia, diadem, demigod, god, goddam, dam, dampen, pennon, non, noncom, compel, pelican, cancan, can, cancel, celesta, starlit, lit, litmus, muscat, cat, catnap, naphtha, than, handcar, carpel, pellagra, grammar, mar, mariachi, chichi, chi, chimp, imp, impel, pelvic, vicar, car, caribou, bourgeoisie, siesta, stab, tab, tabu, abut, but, butterfat, fat, fathom, homespun, pun, puns, unsheathe, the, theorem, remove, overtax, tax, taxicab, cab, cabal, balsam, sambas, basal, salamis, missal, salt, altho, tho, thou, housebound, underground, underclassman, man, mannikins, insectivores, resonant, antelope, operator, torn, ornamental, tallow, low, lowered, reddens, enshrine, inefficient, entertainer, nerves, vestiges, gesturing, ingested, tediousness, essentials]

Idées fondamentales

Dans Approximation des chemins et cycles dirigés les plus longs , Bjorklund, Husfeldt et Khanna, Lecture Notes in Computer Science (2004), 222-233, les auteurs proposent que dans les graphiques à expansion clairsemée, un long chemin puisse être trouvé par une recherche gourmande qui sélectionne à chaque pas le voisin de la queue actuelle du chemin qui s'étend sur le plus grand sous-graphe de G ', où G' est le graphique d'origine avec les sommets du chemin actuel supprimés. Je ne suis pas sûr d'un bon moyen de tester si un graphe est un graphe expanseur, mais nous avons certainement affaire à un graphe clairsemé, et puisque son noyau est d'environ 20000 sommets et qu'il a un diamètre de seulement 15, il doit avoir une bonne propriétés d'expansion. J'adopte donc cette heuristique gourmande.

Étant donné un graphique G(V, E), nous pouvons trouver combien de sommets sont accessibles à partir de chaque sommet en utilisant Floyd-Warshall dans le Theta(V^3)temps, ou en utilisant l'algorithme de Johnson dans le Theta(V^2 lg V + VE)temps. Cependant, je sais que nous avons affaire à un graphique qui a un très grand composant fortement connecté (SCC), alors j'adopte une approche différente. Si nous identifions les SCC en utilisant l'algorithme de Tarjan, nous obtenons également un tri topologique pour le graphique compressé G_c(V_c, E_c), qui sera beaucoup plus petit, dans le O(E)temps. Puisqu'il G_cs'agit d'un DAG, nous pouvons calculer l'accessibilité G_cdans le O(V_c^2 + E_c)temps. (J'ai découvert par la suite que cela est indiqué dans l'exercice 26-2.8 du CLR ).

Étant donné que le facteur dominant dans le temps d'exécution est E, je l'optimise en insérant des nœuds factices pour les préfixes / suffixes. Donc plutôt que 151 * 64 = 9664 bords des mots finissant -res aux mots commençant res, j'ai 151 bords des mots se terminant par -res à # res # et 64 bords de # res # aux mots commençant par res- .

Et enfin, comme chaque recherche prend environ 4 minutes sur mon ancien PC, j'essaie de combiner les résultats avec les longs trajets précédents. C'est beaucoup plus rapide et c'est ma meilleure solution actuelle.

Code

org/cheddarmonk/math/graph/Graph.java:

package org.cheddarmonk.math.graph;

import java.util.Set;

public interface Graph<V> {
    public Set<V> getAdjacent(V node);
    public double getWeight(V from, V to);
}

org/cheddarmonk/math/graph/MutableGraph.java:

package org.cheddarmonk.math.graph;

import java.util.*;

public class MutableGraph<V> implements Graph<V> {
    private Map<V, Map<V, Double>> edgesBySource = new HashMap<V, Map<V, Double>>();

    public void addEdge(V from, V to, double weight) {
        if (!edgesBySource.containsKey(to)) edgesBySource.put(to, new HashMap<V, Double>());
        Map<V, Double> e = edgesBySource.get(from);
        if (e == null) edgesBySource.put(from, e = new HashMap<V, Double>());
        if (e.containsKey(to)) throw new IllegalArgumentException("There is already an edge between the vertices");
        e.put(to, weight);
    }

    @Override
    public Set<V> getAdjacent(V node) {
        Map<V, Double> e = edgesBySource.get(node);
        if (e == null) throw new IllegalArgumentException("node doesn't appear to be in the graph");
        return Collections.unmodifiableSet(e.keySet());
    }

    @Override
    public double getWeight(V from, V to) {
        Map<V, Double> e = edgesBySource.get(from);
        if (e == null) throw new IllegalArgumentException("from doesn't appear to be in the graph");
        if (!edgesBySource.containsKey(to)) throw new IllegalArgumentException("to doesn't appear to be in the graph");

        Double c = e.get(to);
        return c == null ? 0 : c.doubleValue();
    }
}

org/cheddarmonk/math/graph/StronglyConnectedComponents.java:

package org.cheddarmonk.math.graph;

import java.util.*;

/**
* A helper class for finding the strongly connected components of a graph using Tarjan's algorithm.
* http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm
*/
public class StronglyConnectedComponents<V> {
    private final Graph<V> g;
    private List<Set<V>> topologicallySortedSccs = new ArrayList<Set<V>>();

    private final LinkedList<V> S = new LinkedList<V>();
    private final Set<V> S2 = new HashSet<V>();
    private final Map<V, Integer> index = new HashMap<V, Integer>();
    private final Map<V, Integer> lowlink = new HashMap<V, Integer>();

    private StronglyConnectedComponents(Graph<V> g) {
        this.g = g;
    }

    private void strongConnect(V v) {
        int idx = index.size();
        index.put(v, idx);
        lowlink.put(v, idx);

        S.push(v);
        S2.add(v);

        for (V w : g.getAdjacent(v)) {
            if (!index.containsKey(w)) {
                strongConnect(w);
                if (lowlink.get(w) < lowlink.get(v)) {
                    lowlink.put(v, lowlink.get(w));
                }
            }
            else if (S2.contains(w)) {
                if (index.get(w) < lowlink.get(v)) {
                    lowlink.put(v, index.get(w));
                }
            }
        }

        if (lowlink.get(v).equals(index.get(v))) {
            Set<V> scc = new HashSet<V>();
            V w;
            do {
                w = S.pop();
                S2.remove(w);
                scc.add(w);
            } while (!w.equals(v));

            topologicallySortedSccs.add(scc);
        }
    }

    public static <V> List<Set<V>> analyse(Graph<V> g, Set<V> sources) {
        if (g == null) throw new IllegalArgumentException("g");

        StronglyConnectedComponents<V> scc = new StronglyConnectedComponents<V>(g);
        for (V v : sources) {
            if (!scc.index.containsKey(v)) {
                scc.strongConnect(v);
            }
        }

        return scc.topologicallySortedSccs;
    }
}

org/cheddarmonk/ppcg/PPCG.java:

package org.cheddarmonk.ppcg;

import java.io.*;
import java.util.*;
import org.cheddarmonk.math.graph.*;

public class PPCG44922 {
    private static final String path = "/usr/share/dict/words";
    private static Set<String> allWords;
    private static Graph<String> fullGraph;

    public static void main(String[] args) {
        loadGraph();

        Random rnd = new Random();
        rnd.setSeed(8104951619088972997L);
        List<String> a = search(rnd);
        rnd.setSeed(-265860022884114241L);
        List<String> b = search(rnd);
        List<String> chain = spliceChains(a, b);
        System.out.println(chain.size());
        System.out.println(chain);
    }

    private static List<String> search(Random rnd) {
        List<String> chain = new ArrayList<String>();
        chain.add(selectOptimalReachabilityCount(fullGraph, allWords, rnd));
        while (true) {
            String tail = chain.get(chain.size() - 1);
            FilteredGraph g = new FilteredGraph(chain);

            // We know that tail only has one successor, so skip ahead.
            Set<String> candidates = new HashSet<String>(fullGraph.getAdjacent(suffix(tail)));
            candidates.removeAll(chain);
            if (candidates.isEmpty()) break;

            chain.add(selectOptimalReachabilityCount(g, candidates, rnd));
        }

        Iterator<String> it = chain.iterator();
        while (it.hasNext()) {
            if (it.next().charAt(0) == '#') it.remove();
        }
        return chain;
    }

    private static List<String> spliceChains(List<String> a, List<String> b) {
        Set<String> intersect = new HashSet<String>(b);
        intersect.retainAll(a);
        if (intersect.isEmpty()) return null;

        // Splice the longest bits. To avoid cycles, we look for intersection points which have the same set of reached intersection points.
        // Thus to get from one to the next we can take either route without violating the unique occurrence of each element in the spliced chain.
        Set<String> left = new HashSet<String>();
        Set<String> right = new HashSet<String>();
        List<String> newChain = new ArrayList<String>();

        // NB We assume that either a(0) and b(0) are the same or neither is in intersect.
        // This is a safe assumption in practice because they're both "wad".
        int idxA = 0, idxB = 0, nextA = 0, nextB = 0;
        while (idxA < a.size()) {
            nextA++;
            while (nextA < a.size() && !intersect.contains(a.get(nextA))) nextA++;
            String tailA = nextA < a.size() ? a.get(nextA) : "";
            left.add(tailA);

            nextB++;
            while (nextB < b.size() && !intersect.contains(b.get(nextB))) nextB++;
            String tailB = nextB < b.size() ? b.get(nextB) : "";
            right.add(tailB);

            if (left.equals(right) && tailA.equals(tailB)) {
                // We take the longer of idxA to nextA-1 or idxB to nextB - 1.
                if (nextA - idxA > nextB - idxB) newChain.addAll(a.subList(idxA, nextA));
                else newChain.addAll(b.subList(idxB, nextB));

                idxA = nextA;
                idxB = nextB;
            }
        }

        if (new HashSet<String>(newChain).size() == newChain.size()) return newChain;
        throw new IllegalStateException();
    }

    private static void loadGraph() {
        Set<String> words = new HashSet<String>();
        Set<String> prefixes = new HashSet<String>();
        Set<String> suffixes = new HashSet<String>();
        try {
            BufferedReader br = new BufferedReader(new InputStreamReader(new FileInputStream(path), "UTF-8"));
            String line;
            while ((line = br.readLine()) != null) {
                if (line.length() >= 3) {
                    words.add(line);
                    prefixes.add(prefix(line));
                    suffixes.add(suffix(line));
                }
            }
            br.close();
        }
        catch (IOException ioe) {
            throw new RuntimeException(ioe);
        }

        // Filter down to a core with decent reachability.
        prefixes.retainAll(suffixes);
        MutableGraph<String> g = new MutableGraph<String>();
        Iterator<String> it = words.iterator();
        while (it.hasNext()) {
            String line = it.next();
            if (prefixes.contains(prefix(line)) && prefixes.contains(suffix(line))) {
                // In the interests of keeping the number of edges down, I insert fake vertices.
                g.addEdge(prefix(line), line, 1);
                g.addEdge(line, suffix(line), 1);
            }
            else it.remove();
        }

        fullGraph = g;
        allWords = Collections.unmodifiableSet(words);
    }

    private static String prefix(String word) {
        return "#" + word.substring(0, 3) + "#";
    }

    private static String suffix(String word) {
        return "#" + word.substring(word.length() - 3, word.length()) + "#";
    }

    private static <V> Map<V, Integer> reachabilityCount(Graph<V> g, Set<V> sources) {
        List<Set<V>> sccs = StronglyConnectedComponents.analyse(g, sources);
        int n = sccs.size();

        // Within a strongly connected component, each vertex can reach each other vertex.
        // Then we need to also take into account the other SCCs which they can reach.
        // We can exploit the fact that we already have a topological sort of the DAG of SCCs to do this efficiently.
        Map<V, Integer> index = new HashMap<V, Integer>();
        for (int i = 0; i < n; i++) {
            for (V v : sccs.get(i)) index.put(v, i);
        }

        BitSet[] reachableSccs = new BitSet[n];
        Map<V, Integer> reachabilityCounts = new HashMap<V, Integer>();
        for (int i = 0; i < n; i++) {
            Set<V> scc = sccs.get(i);
            reachableSccs[i] = new BitSet(n);
            reachableSccs[i].set(i);
            for (V v : scc) {
                for (V w : g.getAdjacent(v)) {
                    int j = index.get(w);
                    if (j < i) reachableSccs[i].or(reachableSccs[j]);
                }
            }

            int count = 0;
            for (int j = reachableSccs[i].nextSetBit(0); j >= 0; j = reachableSccs[i].nextSetBit(j+1)) {
                count += sccs.get(j).size();
            }
            for (V v : scc) {
                reachabilityCounts.put(v, count);
            }
        }

        return reachabilityCounts;
    }

    private static <V extends Comparable<? super V>> V selectOptimalReachabilityCount(Graph<V> g, Set<V> candidates, Random rnd) {
        Map<V, Integer> r = reachabilityCount(g, candidates);

        int max = 0;
        List<V> attaining = new ArrayList<V>();
        for (V candidate : candidates) {
            int score = r.get(candidate);
            if (score > max) {
                max = score;
                attaining.clear();
            }
            if (score == max) attaining.add(candidate);
        }

        return selectRandom(attaining, rnd);
    }

    private static <T extends Comparable<? super T>> T selectRandom(Collection<T> elts, Random rnd) {
        List<T> deterministic = new ArrayList<T>(elts);
        Collections.sort(deterministic);
        Collections.shuffle(deterministic, rnd);
        return deterministic.get(0);
    }

    private static class FilteredGraph implements Graph<String> {
        private final Set<String> filteredVertices;

        public FilteredGraph(Collection<String> filteredVertices) {
            this.filteredVertices = new HashSet<String>(filteredVertices);
        }

        @Override
        public Set<String> getAdjacent(String node) {
            if (filteredVertices.contains(node)) return Collections.emptySet();

            Set<String> adj = new HashSet<String>(fullGraph.getAdjacent(node));
            adj.removeAll(filteredVertices);
            return adj;
        }

        @Override
        public double getWeight(String from, String to) {
            throw new RuntimeException("Not used");
        }
    }
}

Rubis, 1701

"Del" -> "ersatz's"( séquence complète )

Essayer de trouver la solution optimale s'est avéré trop coûteux en temps. Alors pourquoi ne pas choisir des échantillons aléatoires, mettre en cache ce que nous pouvons et espérer le meilleur?

Un premier Hashest construit qui mappe les préfixes aux mondes complets en commençant par ce préfixe (par exemple "the" => ["the", "them", "their", ...]). Ensuite, pour chaque mot de la liste, la méthode sequenceest appelée. Il obtient les mots qui pourraient éventuellement découler du Hash, en prend un échantillon 100et s'appelle récursivement. Le plus long est pris et affiché fièrement. Le germe du RNG ( Random::DEFAULT) et la longueur de la séquence sont également affichés.

J'ai dû exécuter le programme plusieurs fois pour obtenir un bon résultat. Ce résultat particulier a été généré avec des graines 328678850348335483228838046308296635426328678850348335483228838046308296635426.

Scénario

require "json"

def prefix(word); word[0, 3];  end
def suffix(word); word[-3, 3]; end

def sequence(word, prefixes, skip)
  if SUBS.key?(word) && (SUBS[word] - skip) == SUBS[word]
    return SUBS[word]
  end

  skip         += [word] 
  suffix        = suffix(word)
  possibilities = (prefixes[suffix] ||= []) - skip

  if possibilities.empty?
    return [word]
  else
    sequences = possibilities.sample(100).map do |possibility|
      sequence(possibility, prefixes, skip)
    end

    return SUBS[word] = [word] + sequences.max_by(&:size)
  end
end

def correct?(sequence)
  once_only = sequence.all? { |y| sequence.count(y) == 1 }
  following = sequence.each_cons(2).all? { |a,b| a[-3,3] == b[0,3] }

  return once_only && following
end

words = open("words.txt", "r", &:read).split.select { |word| word.size >= 3 }

SUBS     = {}
PREFIXES = {}

# Built a Hash that maps prefixes to an Array of words starting with the prefix.
words.each do |word|
  prefix = prefix(word)

  PREFIXES[prefix] ||= []
  PREFIXES[prefix] << word
end

longest = [1]

words.each do |word|
  PREFIXES[prefix(word)].delete(word)

  sequence = sequence(word, PREFIXES, [word])

  if sequence.size > longest.size
    longest = sequence
  end
end

puts longest.inspect
puts 
puts "Generated with seed: #{Random::DEFAULT.seed}"
puts "Length: #{longest.size}"
puts "Correct: #{correct?(longest)}"

Résultat: 1631 1662 mots

['Aachen', 'hen', 'henceforward', 'ardor', 'dorsal', 'salmon', 'monolog', 'log', 'logjam', 
'jam', 'jamb', 'ambassador', 'dormouse', 'useable', 'bleeding', 'ingenious', 'ouster', 
'terminable', 'bleakness', 'essay', 'say', 'saying', 'ingress', 'essences', 'cession', 
....
....
'ionosphere', 'ere', 'erecting', 'ingratiating', 'ingrate', 'ate', 'ateliers', "ersatz's"]

Vous pouvez retrouver toute la séquence ici: http://pastebin.com/TfAvhP9X

Je n'ai pas le code source complet. J'essayais différentes approches. Mais voici quelques extraits de code, qui devraient pouvoir générer une séquence d'environ la même longueur. Désolé, ce n'est pas très beau.

Code (Python):

D'abord un prétraitement des données.

from collections import defaultdict

with open('words') as f:
    words = [line.strip() for line in f]
words = [word for word in words if len(word)>=3 and word[-2:]!="'s"]

word_connections = defaultdict(list)
for word in words:
    word_connections[word[:3]].append(word)

J'ai ensuite défini une fonction récursive (Depth first search).

global m
m=0
def find_chain(chain):
    s = set(word_connections[chain[-1][-3:]])-set(chain)
    if len(s)== 0:
        global m
        if len(chain) > m:
            m=len(chain)
            print(len(chain), chain)
    else:
        for w in s:
            if w not in chain:
                find_chain(chain + [w])

for word in words:
    find_chain([word])

Bien sûr, cela prend trop de temps. Mais après un certain temps, il a trouvé une séquence de 1090 éléments, et je me suis arrêté.

La prochaine chose à faire est une recherche locale. Pour chacun des deux voisins n1, n2 dans la séquence, j'essaie de trouver une séquence commençant à n1 et se terminant à n2. Si une telle séquence existe, je l'insère.

def tryimpove(chain, length, startvalue=0):
    s=set(chain)
    for i in range(startvalue,len(chain)-1):
        print(i)
        for sub in sorted(short_sequences([chain[i]],length,chain[i+1]),key=len,reverse=True):

            if len(s & set(sub))==1:
                chain[i:i+1]=sub
                print(i,'improved:',len(chain))
                return tryimpove(chain,length,i)
    return chain

def short_sequences(chain,length,end):
    if 2 <= len(chain):
        if chain[-1][-3:]==end[:3]:
            yield chain
    if len(chain) < length:
        s = set(word_connections[chain[-1][-3:]])-set(chain)
        for w in s:
            for i in short_sequences(chain + [w],length,end):
                yield i

for m in range(5, 100):
    seq = tryimpove(seq,m)

Bien sûr, j'ai également dû arrêter le programme manuellement.

PHP, 1742 1795

J'ai dérangé avec PHP à ce sujet. L'astuce consiste à éliminer la liste aux environ 20k qui sont réellement valides, et à jeter le reste. Mon programme le fait de manière itérative (certains mots qu'il jette lors de la première itération signifient que d'autres ne sont plus valides) au début.

Mon code est horrible, il utilise un certain nombre de variables globales, il utilise beaucoup trop de mémoire (il conserve une copie de la table de préfixes entière pour chaque itération) et il a fallu littéralement des jours pour trouver mon meilleur actuel, mais il gère toujours gagner - pour l'instant. Cela commence assez rapidement mais devient plus lent et plus lent au fil du temps.

<?php

  function show_list($list)
  {
      $st="";
      foreach ($list as $item => $blah)
      $st.="$item ";
      return rtrim($st);
  }

  function mysort($a,$b)
  {
      global $parts;
      $a_count=isset($parts[substr($a,-3,3)])?count($parts[substr($a,-3,3)]):0;
      $b_count=isset($parts[substr($b,-3,3)])?count($parts[substr($b,-3,3)]):0;
      return $b_count-$a_count;
  }  

  function recurse($line,$list,$parts)
  {
    global $lines; 
    global $max;
    global $finished;
    global $best;
    $end=substr($line,-3,3);
    $count=0;
    if ($finished)
        return;
    if (isset($parts[$end]))
    {
        $maxp=count($parts[$end])-1;
        if ($maxp<0)
            return;
        $randa=array();
        for ($a=1;$a<3;$a++)
        {
            $randa[mt_rand(0,$maxp)]=1;
        }
        $n=mt_rand(0,$maxp);

        foreach ($parts[$end] as $key => $endpart)
        {

            if (!isset($list[$endpart]))
            {
                $this_part=$parts[$end];
                unset($this_part[$key]);
                $new_parts=$parts;
                unset($new_parts[$end][$key]);
                $list[$endpart]=1;
                recurse($endpart,$list,$new_parts);
                unset($list[$endpart]);
            }
        }

    }
    $count=count($list);
    if ($count>$max)
    {
        //echo "current best: $count\n";
        file_put_contents('best.txt',show_list($list) . "\n",FILE_APPEND);
        $max=$count;
        $best=$list;
    }
  }

  function cull_lines(&$lines)
  {
      global $parts;
      do 
      {    
          $wordcount=count($lines);
          $parts=array();$end_parts=array();
          foreach ($lines as $line)
          {
              if (strlen($line)<3)
                continue;
              $parts[substr($line,0,3)][]=$line;
              if (strlen($line)>3)
                $end_parts[substr($line,-3,3)][]=$line;
          }
          foreach ($lines as $key => $line)
          {
              $end=substr($line,-3,3);
              if (strlen($line)<3 || !isset($parts[$end]) || !isset($end_parts[substr($line,0,3)] ) )
                unset($lines[$key]);
          }
          foreach ($parts as $part)
          {
            if (count($part)==1)
            {
                $source_part=mt_rand(0,count($part)-1);
                $this_part = substr($part[0],0,3);
                $this_min = 10000;
                $this_key = 0;
                if (strlen($part[$source_part])==3)
                {
                    foreach ($lines as $key => $line)
                    if ($line == $part[$source_part])
                    {
                            unset($lines[$key]);
                            break;
                    }
                }
                elseif (isset($end_parts[$this_part]))
                {
                    foreach ($end_parts[$this_part] as $key => $end_part)
                    {
                        if (isset($parts[substr($end_part,0,3)]))
                        {
                            $n=count($parts[substr($end_part,0,3)]);
                            if ($n<$this_min)
                            {
                                $this_min=$n;
                                $this_key=$key;    
                            }
                        }
                    }

                    foreach ($lines as $key => $line)
                    if ($line == $part[$source_part])
                    {
                            unset($lines[$key]);

                    }
                    elseif ($line == $end_parts[$this_part][$this_key])
                    {
                        $lines[$key].=' ' . $part[$source_part];
                    }
                }

            }
          }
          echo "$wordcount words left\n";
      }
      while ($wordcount!=count($lines));
  }

  ini_set('xdebug.max_nesting_level',10000);
  ini_set('memory_limit','1024M');
  $lines = explode("\n",file_get_contents('words.txt'));
  cull_lines($lines);
  $max=0;
  foreach ($parts as $key=>$part)
    usort($parts[$key],'mysort');    

  $n=count($lines);
  foreach ($lines as $rand => $blah)
  {
      if (mt_rand(0,$n)==1)
        break;
  }
  $rand=$lines[$rand];
  $line[$rand]=1;
  echo "Starting with $rand...\n";
  recurse($rand,$line,$parts);
  unset($line[$rand]);

?>

Une amélioration évidente consisterait à utiliser un mot orphelin pour le début et la fin.

Quoi qu'il en soit, je ne sais vraiment pas pourquoi ma liste pastebin a été déplacée dans un commentaire ici, elle est de retour sous forme de lien vers pastebin car j'ai maintenant inclus mon code.

http://pastebin.com/Mzs0XwjV

Python: 1702 - 1704 - 1733 mots

J'ai utilisé un dict pour mapper tous les préfixes à tous les mots, comme

{
    "AOL" : [
        "AOL", "AOL's"
    ],...
    "oct" : [
         "octet","octets","octette's"
    ],...
}

Modifier une petite amélioration: supprimer tous les uselessmots au début, si leurs suffixes ne sont pas dans la liste des préfixes (ce serait évidemment un mot de fin)

Ensuite, prenez un mot dans la liste et parcourez la carte de préfixe comme un arbre Node

import sys, fileinput
def p(w):return w[:3]

class Computing:
    def __init__(_):
        _.wordData = []; _.prefixes = {}
        _.seq = []; _.bestAttempt = []
        _.stop = False
        for l in fileinput.input():
            word = l.strip()
            if len(word) > 2:_.wordData.append(_.addPfx(word, p(word)))
        _.rmUseless();_.rmUseless()
        _.fromI = 0; _.toI = len(_.wordData)

    def rmUseless(_):
        for w in _.wordData:
            if not w[-3:] in _.prefixes: _.wordData.remove(_.rmPfx(w,p(w)))

    def addPfx(_, w, px):
        if not px in _.prefixes:_.prefixes[px] = []
        _.prefixes[px].append(w)
        return w
    def rmPfx(_,w,px):
        _.prefixes[px].remove(w)
        if len(_.prefixes[px]) == 0:del _.prefixes[px];
        return w

    def findBestSequence(_):
        def pickItem():
            r = None
            if _.fromI < _.toI:r = _.wordData[_.toI-1];_.toI -= 1;
            return r
        while not _.stop:
            w = pickItem()
            if not w:break;
            _.seq = [_.rmPfx(w,p(w))]
            _.checkForNextWord()
            _.addPfx(w, p(w))

        print " ".join(_.bestAttempt)

    def checkForNextWord(_):
        _.stop = len(_.seq) >= 1733
        cw = _.seq[-1]
        if not _.stop:
            if cw[-3:] in _.prefixes:
                lW = []
                for word in _.prefixes[cw[-3:]]:
                    if not word[-3:] in lW:
                        _.seq.append(_.rmPfx(word,p(word)))
                        _.checkForNextWord()
                        if _.stop :break;
                        _.addPfx(_.seq.pop(), p(word))
                        lW.append(word[-3:])
                    if _.stop :break;
        if len(_.bestAttempt) < len(_.seq):_.bestAttempt = _.seq[:];

sys.setrecursionlimit(6000)
Computing().findBestSequence()

Le programme a besoin d'un certain nombre de mots pour savoir quand s'arrêter, peut être trouvé comme 1733dans la méthodecheckForNextWord̀

Le programme a besoin du chemin du fichier comme argument

Pas très pythonique mais j'ai essayé.

Il a fallu moins de 2 minutes pour calculer cette séquence: sortie complète :

études desalinate ate ateliers ... blest estimating ingénues évincés

Score: 249 500 1001

Aix-la-Chapelle -> poule -> désormais -> ardent -> entraînent -> ail -> ailed -> led -> ledger -> gerbil -> bilatéral -> rallye -> ingénieux - -> évincé -> fastidieux -> éviction -> térabit -> mors -> garce -> hérisson -> porc -> hogan -> jars -> déraillement -> ailerons -> début -> ensemble -> retrait -> acquittement -> entraîné -> registres -> ersatzes -> zeste -> établi -> haie -> rangée -> chaloupe -> avoine - -> avoine -> dix -> tenable -> eau de Javel -> mal -> cheapen -> stylo -> pénalise -> zestful -> fulcra -> crabe -> rabbinique -> calebasse -> frêne -> honte -> médaille -> dale -> ale -> alerté -> fastidieusement -> sournois ->slyest -> établit -> hes -> hésitant -> fourmi -> antiacide -> cidre -> déraillé -> corniches -> gestationnel -> ennui -> essai -> dis - -> dire -> ingénieusement -> ruse -> essayer -> ingénu -> évincer -> ingénu -> essayiste -> isthme -> muscat -> chat -> cataclysmique -> souris -> glace -> iceberg -> erg -> ergonomique -> micra -> crabe -> lit -> éblouissements -> lesbiennes -> réponse -> étaient -> avant - -> érection -> ingestion -> établissement -> ingestion -> ingestion -> ion -> ionisation -> ioniseur -> zéro -> érode -> ode -> odes -> dessale -> test -> établissement - -> entraînant -> lingot -> obtenu -> obtenu ->locataire -> antagoniste -> isthme -> sésame -> amebas -> basal -> salaamed -> médaillon -> ionisant -> enracinement -> enracinement -> ins -> fou - -> anecdotique -> talc -> alcool -> hold -> old -> olden -> den -> denature -> urea -> reach -> endolori -> haies -> gestates -> testables -> blanchis -> couverture -> ingrédients -> testament -> enchevêtrement -> brillant -> médaillons -> onshore -> minerai -> origan -> anodes - -> dessalement -> ingrats -> testates -> testeur -> térabits -> son -> lui-même -> elfe -> elfin -> fin -> finagle -> brillant -> ingrat -> ingrat - - glycérine -> croûte -> endettement -> essences ->césariennes -> responsables -> gradins -> elle -> héraut -> aulne -> déraillement -> ingrédient -> enchevêtrement -> enchevêtrements -> lésion -> ionosphère -> érection - -> ionosphères -> revente -> alerte -> entrées -> sésames -> mes -> mesas -> ceinture -> ashcan -> can -> canard -> ardour -> dorkiest -> domaines -> testicules -> testicule -> nettoyant -> nerdiest -> estimé -> immixtions -> locataire -> voir -> ensemencé -> dédiés -> testicules - -> diminuer -> sénats -> testicules -> estimant -> incarné -> propre -> propriétaire -> nerfs -> vésicule -> plus propre -> ester -> téraoctets -> testicules -> tissus -> sue -> suède -> œdème -> émaciés ->testostérone -> un -> ceux -> nid -> esthètes -> testicules -> sty -> orgelets -> oui -> yeshivas -> vasculaires -> mélèzes -> avec hésitation - -> glycérine -> non comestible -> agents de blanchiment -> hésite -> témoignant -> ingrat -> mangé -> ateliers

Voici mon code:

import sys
sys.setrecursionlimit(10000)
w=[i for i in open("words.txt").read().split("\n") if len(i)>=3 and "'" not in i]
b=[i[:3] for i in w]
e=[i[-3:] for i in w]
a=[i for i in zip(*(w,b,e))]
def pathfrom(i,a,l):
    longpath=[]
    for j in a:
        if j[1]==i[2]:
            r=pathfrom(j,[m for m in a if m!=j],l+1)
            path=[i]+r[0]
            if r[1]:
                return path,r[1]
            if len(path)>len(longpath):
                longpath=path
    if l>=250:
        return longpath,True
        sys.exit()
    return longpath,False
for i in a[:2]:
    print i
    p=pathfrom(i,[j for j in a if i!=j],1)
    if len(p)>len(chain_):
        chain_=p
        print p
    print p

Modifier: 1001:

http://pastebin.com/yN0eXKZm

Modifier: 500:

Aix-la-Chapelle -> poule -> désormais -> ardent -> entraînent -> ail -> ailed -> led -> ledger -> gerbil -> bilatéral -> rallye -> ingénieux - -> évincé -> fastidieux -> éviction -> térabit -> mors -> garce -> hérisson -> porc -> hogan -> jars -> déraillement -> ailerons -> début -> ensemble -> retrait -> acquittement -> entraîné -> registres -> ersatzes -> zeste -> établi -> haie -> rangée -> chaloupe -> avoine - -> avoine -> dix -> tenable -> eau de Javel -> mal -> cheapen -> stylo -> pénalise -> zestful -> fulcra -> crabe -> rabbinique -> calebasse -> frêne -> honte -> médaille -> dale -> ale -> alerté -> fastidieusement -> sournois ->slyest -> établit -> hes -> hésitant -> fourmi -> antiacide -> cidre -> déraillé -> corniches -> gestationnel -> ennui -> essai -> dis - -> dire -> ingénieusement -> ruse -> essayer -> ingénu -> évincer -> ingénu -> essayiste -> isthme -> muscat -> chat -> cataclysmique -> souris -> glace -> iceberg -> erg -> ergonomique -> micra -> crabe -> lit -> éblouissements -> lesbiennes -> réponse -> étaient -> avant - -> érection -> ingestion -> établissement -> ingestion -> ingestion -> ion -> ionisation -> ioniseur -> zéro -> érode -> ode -> odes -> dessale -> test -> établissement - -> entraînant -> lingot -> obtenu -> obtenu ->locataire -> antagoniste -> isthme -> sésame -> amebas -> basal -> salaamed -> médaillon -> ionisant -> enracinement -> enracinement -> ins -> fou - -> anecdotique -> talc -> alcool -> hold -> old -> olden -> den -> denature -> urea -> reach -> endolori -> haies -> gestates -> testables -> blanchis -> couverture -> ingrédients -> testament -> enchevêtrement -> brillant -> médaillons -> onshore -> minerai -> origan -> anodes - -> dessalement -> ingrédients -> testates -> testeur -> térabits -> son -> lui-même -> elfe -> elfin -> fin -> finagle -> brillant -> ingrat -> ingrat - - glycérine -> croûte -> endettement -> essences ->césariennes -> responsables -> gradins -> elle -> héraut -> aulne -> déraillement -> ingrédient -> enchevêtrement -> enchevêtrements -> lésion -> ionosphère -> érection - -> ionosphères -> revente -> alerte -> entrées -> sésames -> mes -> mesas -> ceinture -> ashcan -> can -> canard -> ardour -> dorkiest -> domaines -> testicules -> testicule -> nettoyant -> nerdiest -> estimé -> immixtions -> locataire -> voir -> ensemencé -> dédiés -> testicules - -> diminuer -> sénats -> testicules -> estimant -> incarné -> propre -> propriétaire -> nerfs -> vésicule -> plus propre -> ester -> téraoctets -> testicules -> tissus -> sue -> suède -> œdème -> émaciés ->testostérone -> un -> ceux -> nid -> esthètes -> testicules -> sty -> orgelets -> oui -> yeshivas -> vasculaires -> mélèzes -> avec hésitation - -> glycérine -> non comestible -> plus sombre -> kératine -> étain -> teinture -> urethras -> coquin -> calamine -> inéducable -> plus sombre -> esthétique -> tic -> tick -> ickiest -> estimable -> bleariest -> estimator -> tor -> flambé -> hedonistic -> ticker -> kerchieves -> vesicles -> lessens - -> installé -> cèdre -> osez -> êtes -> zone -> accessible -> bêlé -> mangez -> mangeable -> saignez -> déraillez -> entrez -> terme -> hermine -> ineffable -> bleep -> pedagog - - goggle -> gleans ->répondu -> rouge -> rouge-poitrine -> aster -> termagant -> antagoniste -> ticket -> kettledrum -> rhum -> rumbas -> basalte -> autel -> tar - -> tarentules -> lasagne -> noueux -> éloignement -> entré -> redcap -> cap -> capable -> bips -> epsilon -> solitaire -> estranges -> gestured -> redcaps -> abside -> pseudonym -> nymphomania -> niacin -> cinchonas -> nasal -> vendable -> blend -> end -> endanger -> geriatric - -> riz -> glace -> undeceives -> vesper -> per -> perambulator -> tore -> minerais -> reventes -> moindre -> sera -> era -> époques -> éruption cutanée -> cendre -> homme de main -> homme -> manacle -> plus propre ->œstrogène -> gendarmes -> mescal -> calcine -> inefficace -> divertissant -> glycérol -> rôle -> laurier-rose -> dérangement -> divertissement -> divertit -> insatiable - -> mélangé -> déduit -> cèdres -> arsenic -> gentil -> glacière -> boîte -> wagon couvert -> voiture -> caracul -> cullender -> deranges -> gestes -> reprogrammations -> leçon -> fils -> sonar -> narc -> arc -> arcade -> adénoïde -> dales -> bailleur -> sorbet -> pari - -> betaken -> ken -> kens -> ensemble -> blender -> deride -> idea -> diacre -> con -> concave -> avenger -> germane -> anémie -> miaowed -> mer -> marié -> déductible -> blent - -> enthrall ->all -> allay -> lay -> layaway -> way -> wayfarer -> reran -> ran -> rancher -> heralded -> déductible -> blessed -> sedan - -> dansé -> cedes -> descendant -> fourmilier -> appelé -> intrus - - omégas -> gaz -> entaille -> ashram -> bélier -> bélier -> soufflé -> lewder -> derides -> descend - - en voie de disparition -> redcoat -> serment -> athérosclérose -> sis -> sisal - -> salad -> lad -> ladder - -> dérivés -> vaisseau -> rarement -> domaines -> inscrits -> punaise de lit -> bug -> bugaboo -> boo -> boobed -> bedder -> dérive -> vestiges -> gesundheit -> soit -> héraldique -> dés -> brise-glace -> kérosène -> lavement -> email ->maladie -> intronisation -> enthuse -> utilisation -> utilisé -> sédatif -> terminateur -> toréador -> dormant -> antebellum - -> lumbago -> il y a -> angoissant - -> glycogène -> sexe -> derme -> mésaventures -> annulation -> indécent -> enthousiaste -> sédatifs -> vêtement -> enthousiaste -> astir -> tirades -> descendant -> antécédent -> séduire -> calotte glaciaire -> condensateur -> tourment -> séduit -> cédille -> lama -> amalgame -> gambit -> chiennes -> hésite - -> témoignant -> ingrat -> mangé -> atelierssexe -> derme -> mésaventures -> annulation -> indécent -> enthousiaste -> sédatifs -> vêtement -> passionné -> astir -> tirades -> descendant -> antécédent - -> séduire -> calotte glaciaire -> condensateur -> tourment -> séduit -> cédille -> lama -> amalgame -> gambit -> chiennes -> hésite -> témoigner -> ingrate -> mangé -> atelierssexe -> derme -> mésaventures -> annulation -> indécent -> enthousiaste -> sédatifs -> vêtement -> passionné -> astir -> tirades -> descendant -> antécédent - -> séduire -> calotte glaciaire -> condensateur -> tourment -> séduit -> cédille -> lama -> amalgame -> gambit -> chiennes -> hésite -> témoigner -> ingrate -> mangé -> ateliers

Mathematica 1482 1655

Quelque chose pour commencer ...

dict=Import["words.txt"];
words=Union@Select[StringSplit[dict],(StringFreeQ[#,"'s"])\[And]StringLength[#]>2
  \[And]LowerCaseQ@StringTake[#,1]&]

Les liens sont les préfixes et suffixes d'intersection des mots.

prefixes=Union[StringTake[#,3]&/@words];
suffixes=Union[StringTake[#,-3]&/@words];
links=Intersection[prefixes,suffixes];
linkableWords=(wds=RandomSample@Select[words,MemberQ[links,StringTake[#,3]]\[And]MemberQ[links,StringTake[#,-3]]& ])/.
w_String:> {w,StringTake[w,3],StringTake[w,-3]}

Les bords sont tous les liens dirigés d'un mot à d'autres mots:

edges[{w_,fr_,fin_}]:= Cases[linkableWords,{w1_,fin,_}:> (w\[DirectedEdge]w1)]
allEdges=Flatten[edges/@linkableWords];
g=Graph@allEdges;

Trouvez un chemin entre "raccommoder" et "zeste".

FindPath[g, "begin", "end", {1480, 3000}, 1][[1]]

Résultat (1655 mots)

{"mend", "endorser", "server", "vertebral", "rallying", "ingrains", 
"insurrectionist", "isthmus", "mussels", "elsewhere", "erection", 
"ionizes", "zestful", "fullness", "essaying", "ingeniously", 
"slyest", "estimator", "tornados", "doses", "sesame", "amebic", 
"bicycled", "ledges", "gestation", "ionizing", "ingratiates", 
"testifying", "ingesting", "inglorious", "ouster", "terminated", 
"tediousness", "essayist", "isthmuses", "session", "ion", 
"ionization", "ionospheres", "resubmitted", "tedious", "ousting", 
"ingest", "ester", "terminates", "testicle", "cleanliness", "essay", 
"say", "saying", "ingratiating", "ingratiatingly", "glycerine", 
"inefficient", "entrances", "cesarians", "answering", "ingenious", 
"ousted", "tediously", "sly", "slyness", "essences", "cesareans", 
"answer", "were", "erecting", "ingredient", "enterprises", 
"sessions", "onshore", "oregano", "anorak", "raking", "ingraining", 
"ingrown", "owner", "nerdiest", "estranging", "ingot", "gotten", 
"tendonitis", "tissue", "suede", "edelweiss", "issuing", "ingestion", 
"ionosphere", "erections", "onset", "settles", "lesion", "ionizer", 
"zeroing", "ingresses", "sesames", "mesmerizing", "ingrates", 
"testes", "testiest", "estrangement", "entail", "ail", "ailment", 
"entice", "icecap", "captivates", "testy", "sty", "stylistic", 
"tickles", "lessee", "seeded", "deductibles", "lesser", 
"servicewoman", "many", "anymore", "ores", "resourceful", "fullback", 
"acknowledgment", "entertainer", "nerves", "vest", "esteemed", 
"mediates", "testament", "entered", "redbreast", "astonishes", 
"hesitatingly", "glycogen", "genera", "eras", "rashes", "hesitates", 
"testicles", "lest", "establishment", "entwines", "nest", "estates", 
"testates", "testosterone", "oneself", "elf", "elfin", "fingered", 
"redcaps", "apse", "pseudonym", "nymphomania", "niacin", "cinemas", 
"masochistic", "tickled", "led", "ledger", "geriatric", "rice", 
"icebreaker", "kerosine", "inexperienced", "ceded", "deductible", 
"blew", "lewder", "derivable", "blemished", "hedgerow", "rowel", 
"welfare", "arena", "enamel", "melded", "dedicates", "tester", 
"terabit", "bitmap", "mapped", "pedicures", "restored", "redeemer", 
"merchantman", "manipulator", "torpedos", "dosed", "seduced", 
"cedilla", "llano", "another", "heretic", "tic", "ticker", "keratin", 
"tinctures", "restaurateur", "euros", "rosettes", "testable", 
"bleaker", "kerosene", "energizer", "zero", "eroded", "deduced", 
"cedar", "dare", "ares", "respondent", "entranced", "cedillas", 
"lasagnas", "nastiest", "esthetic", "ticket", "ketches", "hes", 
"hesitant", "antipasto", "stoppered", "redounded", "deducible", 
"bleeped", "pedant", "antimatter", "terminable", "blent", "enthuse", 
"user", "serenade", "adenoidal", "dales", "lessen", "sentimental", 
"talker", "kerchieves", "vestry", "try", "tryout", "outdone", "ones", 
"nestles", "lesson", "songwriter", "terrapin", "pinched", 
"hedonistic", "tick", "ickiest", "established", "hedgehog", "hogan", 
"gander", "derringer", "gerbil", "billboard", "ardor", "dorkiest", 
"estrogen", "gent", "entirety", "etymological", "calk", "alkalis", 
"lissome", "omegas", "gasolene", "enema", "emaciates", "test", 
"estranges", "gestured", "redeemed", "medic", "diced", "cedars", 
"arsenic", "nice", "iceberg", "erg", "ergonomic", "microcomputer", 
"terser", "sergeant", "antipastos", "tost", "osteopathy", "thy", 
"thymus", "mussiest", "estimable", "blend", "endeavored", "redound", 
"undercover", "verbal", "balk", "alkali", "alibi", "ibis", "bison", 
"sonar", "narcosis", "sister", "terraced", "cede", "edema", 
"emancipator", "torpor", "portraiture", "urea", "reassign", 
"ignoble", "blenched", "hedges", "gesture", "urethras", "raspy", 
"spyglass", "ass", "assailant", "antiquarians", "answered", 
"reduced", "cedes", "despair", "airfares", "resumed", "medicine", 
"ineffable", "bleacher", "herdsmen", "menhaden", "dent", 
"entitlement", "enticement", "entangle", "gleamed", "medullas", 
"lassie", "sieve", "even", "vender", "derivatives", "vessel", 
"selectmen", "mentor", "toreador", "dormer", "meringue", "guerrilla", 
"llanos", "nosedove", "overact", "actionable", "bleeps", "epsilon", 
"longhorn", "ornament", "entreaty", "atypical", "calendar", "dares", 
"resurgent", "entreat", "eater", "term", "ermine", "inedible", 
"bleeder", "derrières", "resentful", "fulcra", "crabbed", 
"bedevilment", "entwine", "inelegant", "antitoxins", "inspired", 
"redder", "derides", "descendant", "antihistamine", "inequitable", 
"bleat", "eaten", "tenured", "redcap", "capstans", "answerable", 
"blender", "deranges", "gestures", "restart", "arteriosclerosis", 
"sis", "sisal", "saltpeter", "terrifyingly", "glycerin", "rink", 
"inkwell", "ellipsis", "sisterhood", "oodles", "lessor", "sorrowed", 
"wedges", "gesundheit", "either", "hereafter", "termite", "iterator", 
"tornado", "adobes", "bespoken", "ken", "kens", "ensnare", "area", 
"rear", "earful", "fulfil", "fillet", "letdown", "ownership", 
"hipped", "pediatric", "richer", "heretical", "calculus", "lusher", 
"heraldic", "dice", "icebound", "underscored", "redskins", "instant", 
"antiperspirant", "anthropomorphic", "hiccup", "cup", "cups", 
"upstage", "agendas", "dashingly", "glycerol", "role", "oleo", 
"leonine", "ineluctable", "blessed", "sedatives", "vesicles", 
"lessens", "ensured", "redefine", "inextinguishable", "bleach", 
"achoo", "hooch", "ocher", "hero", "erode", "ode", "odes", "desktop", 
"topple", "pleasured", "redeveloped", "pediment", "entrapped", 
"pederasty", "stylus", "lush", "usher", "hermaphrodite", "item", 
"tempos", "postpaid", "aide", "ideogram", "rampart", "artisan", 
"sandhog", "hog", "hogwash", "ash", "ashram", "rammed", "mediocre", 
"crestfallen", "lend", "endow", "downcast", "astronomer", 
"merriment", "entrant", "antiwar", "warden", "dentures", "restful", 
"fulfillment", "entrapment", "enthrall", "allay", "layout", 
"outbound", "underclassman", "manhole", "oleander", "dermis", 
"misused", "sedater", "terrific", "fiche", "cheapens", "ensnares", 
"restrains", "insolent", "entombed", "bedraggle", "gleeful", 
"fulfilment", "entrenchment", "entrap", "rapper", "persistent", 
"enthronement", "enthusiast", "astute", "uterus", "rustproofed", 
"fedora", "orangeades", "despised", "seducer", "ceramic", 
"microscopic", "picnic", "nicotine", "inexpedient", "entomb", 
"ombudsman", "mantel", "teletypewriter", "terminological", "calif", 
"lifetimes", "mescaline", "inertia", "tiaras", "raster", "terrace", 
"acetaminophen", "henchmen", "menhadens", "enslaves", "vesper", 
"peroxide", "ideograph", "aphid", "hides", "desideratum", "tumor", 
"mortgagee", "geegaw", "gawk", "awkward", "ardent", "enthused", 
"sediment", "enter", "termed", "mediaeval", "valentine", "inexact", 
"actives", "vestment", "entourage", "agent", "entryway", "wayside", 
"idea", "dear", "earache", "checkups", "upsides", "descent", 
"entertainment", "entomological", "calicos", "cosign", "ignored", 
"redcoat", "oaten", "tensed", "sedan", "dank", "anklet", "lettered", 
"redskin", "kingpin", "pinups", "ups", "upshot", "hotbed", 
"bedtimes", "mes", "messenger", "germicides", "destitute", "utensil", 
"silencer", "cervix", "vixens", "ensign", "ignorant", "antipasti", 
"stimulus", "lusty", "stymie", "miens", "enslave", "averred", 
"redrew", "rewritten", "tenpins", "instructor", "torrent", 
"entertains", "insult", "ultrasound", "undersides", "despoil", 
"oilcloth", "other", "hereupon", "pondered", "redundant", "anthill", 
"ill", "illicit", "citizens", "ensnared", "rediscovered", "redesign", 
"ignoramus", "muskmelon", "longer", "gerrymander", "deride", "ideas", 
"easy", "asylum", "lumbermen", "mendicant", "antlered", "redevelop", 
"lopes", "pester", "terrapins", "instil", "tildes", "deserves", 
"vesicle", "cleave", "avenger", "germane", "anemia", "miasmas", 
"mash", "ashy", "shy", "shyster", "termagant", "antiaircraft", 
"afterglow", "lowland", "and", "androgen", "genitalia", "liars", 
"arson", "sonatas", "taste", "stepsister", "termini", "initiator", 
"tor", "torn", "ornamental", "tallow", "lowered", "red", "redraft", 
"aft", "aftertaste", "stereotypes", "pesky", "skyrocket", 
"kettledrum", "rummer", "merciful", "fulsome", "omens", "ensures", 
"resultant", "antennas", "nasal", "saleswoman", "mane", "anemometer", 
"terrains", "insightful", "fulcrum", "rumbas", "baseman", 
"mannikins", "insures", "resound", "underpass", "assassins", "inset", 
"settee", "teethe", "theological", "calf", "alfresco", "scornful", 
"fulfill", "illustrator", "torpid", "pidgin", "gins", "instal", 
"talc", "alcove", "overtakes", "kestrel", "relabel", "beleaguered", 
"redraw", "rawhide", "identical", "caliber", "beret", "retrace", 
"acetylene", "enemas", "massacred", "redeploys", "oyster", 
"terminator", "tortillas", "last", "astronomical", "calliope", 
"operator", "tort", "orthographic", "hiccups", "upstart", 
"artificer", "cervical", "callus", "lustre", "trend", "endeavor", 
"vortex", "textures", "researcher", "heroins", "instill", "illegal", 
"galloped", "pedagogical", "callipered", "rediscover", "vertebra", 
"brasher", "herbicides", "descry", "cryptogram", "ramrod", "rodeo", 
"deodorizer", "zeros", "rosebush", "ushered", "redden", "denatures", 
"reset", "setups", "upside", "ides", "describes", "besides", 
"desperado", "adores", "reshuffle", "flea", "leaflet", "lethal", 
"halibut", "but", "button", "tonic", "niche", "cherubim", "bimbos", 
"bosun", "sunk", "unkind", "indentures", "resend", "endures", 
"restorer", "reran", "rang", "anger", "germicide", "ideological", 
"calabash", "ashamed", "medical", "caloric", "rickshas", "hasten", 
"tendon", "donkey", "keyword", "ordains", "insecticides", "desires", 
"resin", "sins", "inspector", "torrid", "rid", "rides", "despot", 
"potpie", "piebald", "aldermen", "menace", "ace", "acerbic", "bicep", 
"cephalic", "lichen", "hennas", "nasty", "styes", "yesterday", "day", 
"daybed", "bedridden", "dental", "talisman", "mankind", "indignant", 
"antique", "questionnaires", "resubmit", "mitten", "tenfold", "old", 
"olden", "denudes", "design", "ignores", "resumes", "mesdames", 
"mesas", "sass", "assemblywoman", "mangle", "glee", "leeway", 
"waylay", "laywomen", "menswear", "ear", "earldom", "domains", "ins", 
"instrumental", "tall", "all", "allegorical", "calm", "almanac", 
"nacre", "credit", "dittos", "tossup", "superman", "mandolin", 
"linesman", "manacle", "cleverer", "rerun", "runaway", "way", 
"wayfarer", "reruns", "unshaven", "ventures", "resell", "elliptical", 
"calmer", "mercuric", "ricochet", "heterodoxy", "oxymora", 
"orangutang", "angina", "inapt", "apt", "aptitudes", "descend", 
"endear", "earlobes", "bestowal", "walleyes", "yes", "yeshivas", 
"vassal", "saltcellar", "larval", "valiant", "anthropological", 
"calfskin", "kind", "inductee", "tee", "teenager", "gerund", 
"underclass", "assemblyman", "manservant", "antelopes", "peso", 
"esoteric", "rickshaw", "hawser", "servicewomen", "mental", 
"tallyhos", "hospital", "talon", "longshoremen", "men", "menthol", 
"holography", "phylum", "lumberman", "manikin", "kingpins", 
"install", "allures", "resuscitator", "tortilla", "llamas", 
"massacres", "resistor", "tormentor", "torque", "queasy", 
"asymmetric", "ricksha", "sharped", "pedlar", "largos", "gossamer", 
"merganser", "service", "icebox", "boxer", "xerography", "physical", 
"calculator", "tortures", "resonant", "anticlimax", "maxima", "imam", 
"mammon", "monograph", "aphelia", "liaison", "sonic", "nicknamed", 
"media", "diametrical", "calliper", "performed", "medulla", "llama", 
"amalgam", "gamins", "insulin", "lineman", "mantra", "transplant", 
"antigen", "genres", "respires", "resold", "oldie", "diesel", 
"seldom", "domed", "medieval", "valor", "lordship", "hipper", "per", 
"perspires", "restores", "restructures", "resort", "orthodoxy", 
"oxygen", "gentlemen", "menopausal", "saltpetre", "treacle", 
"cleaver", "verdigris", "risen", "send", "end", "endemic", 
"microfiche", "checkout", "outclass", "assault", "ultraviolet", 
"let", "letterbox", "boxcar", "carom", "roman", "manifesto", 
"stovepipes", "pesticides", "described", "bedsides", "descant", 
"anthem", "hempen", "penguins", "insignificant", "antebellum", 
"lumbar", "barracudas", "dash", "ashcan", "cannonball", "allover", 
"verbena", "enamor", "morgue", "guerrillas", "lash", "ashen", 
"henchman", "mandolins", "inspires", "resistant", "antechamber", 
"bereave", "aver", "vermin", "minim", "nimbus", "bus", "businessman", 
"mantras", "rasp", "asphalt", "altogether", "her", "hereabout", 
"outcast", "astrological", "calisthenic", "nicknames", "mescal", 
"calliopes", "pesetas", "tassel", "selectman", "mannikin", 
"kinswoman", "man", "manic", "nicer", "cerebra", "bravado", "adobe", 
"obeisant", "antiparticle", "clever", "versus", "sushi", "shirr", 
"irrelevant", "antelope", "open", "pentagon", "gonad", "nadir", 
"directorship", "hippopotami", "amid", "midwifed", "fedoras", 
"rasher", "herbal", "ball", "allot", "lot", "lotus", "tussle", 
"sledgehammer", "merchant", "ant", "antidepressant", "anther", 
"heraldry", "drywall", "allegros", "rosebud", "budgerigar", 
"garbageman", "manikins", "inscribes", "bestow", "townsmen", "menu", 
"enures", "restaurant", "antithetical", "calico", "icon", "confound", 
"underbid", "bidden", "denser", "seraphic", "hiccuped", "pedigree", 
"reeve", "ever", "vertical", "caliper", "perusal", "salami", "amir", 
"mires", "restraint", "interstellar", "larkspur", "puritanical", 
"calligrapher", "herdsman", "manatee", "teepee", "peeve", "everyday", 
"daydreamer", "meres", "result", "ultimatum", "tumbril", "rill", 
"illogical", "calligraphy", "physic", "sickbed", "bedsores", 
"resolver", "vertebras", "rascal", "call", "allergenic", "nickname", 
"amebas", "baste", "stepson", "son", "sonnet", "net", "nether", 
"heros", "rosins", "insular", "larvas", "vast", "astrakhan", 
"handyman", "manicures", "resins", "instep", "tepid", "pidgins", 
"inscribed", "bedbug", "bug", "bugbear", "earwax", "waxen", 
"xenophobia", "biathlon", "longhair", "airstrip", "ripple", "pleas", 
"eastbound", "underachiever", "verbatim", "timbre", "brew", 
"rewound", "underplay", "laywoman", "mandarins", "insofar", "farm", 
"armpit", "pitcher", "herald", "alderman", "mangos", "gossip", 
"sipped", "pedagogue", "guerillas", "laser", "serape", "aped", 
"pederast", "astound", "underground", "underpins", "insane", 
"anemic", "micra", "crane", "anew", "new", "newscast", "astir", 
"tiro", "ironware", "are", "areas", "east", "astronomic", 
"microchip", "hippopotamus", "mustache", "chervil", "villas", "lass", 
"assassin", "sinew", "newsman", "mangrove", "overtax", "taxicab", 
"cabana", "anathemas", "mast", "astronaut", "author", "horoscope", 
"opera", "eraser", "serfdom", "dominos", "nostrum", "rumpus", "pus", 
"pushcart", "arthropod", "podia", "diatom", "tomboy", "boycott", 
"ottoman", "manhunt", "untidy", "idyllic", "licensee", "seethe", 
"thereabout", "outplay", "layoff", "officer", "cerebrum", "rum", 
"rumple", "plethora", "oracle", "clergyman", "maneuver", "verandas", 
"dashikis", "kisser", "serum", "rumor", "morbid", "bidet", "detach", 
"achiever", "vertex", "text", "extremer", "merino", "inopportune", 
"uneaten", "tensor", "sort", "orthopedic", "dickie", "kielbasas", 
"sashay", "hayloft", "often", "ten", "tenpin", "pinkeye", "eyeball", 
"allegro", "grout", "outfox", "fox", "foxtrot", "rot", "rotund", 
"underwear", "earshot", "hot", "hotshot", "hotel", "telex", 
"lexicon", "congresswoman", "manor", "northbound", "undertow", 
"township", "hippos", "possessor", "sorbet", "betcha", "chart", 
"art", "article", "clear", "earwig", "wigwam", "wampum", "pummel", 
"melodic", "dictum", "tumbrel", "relic", "licit", "citadel", "delay", 
"lay", "laypeople", "plectra", "traumas", "mascot", "cotyledon", 
"donor", "nor", "normal", "malt", "altar", "tart", "artiste", 
"stencil", "cilantro", "trouper", "pericardia", "diadem", "democrat", 
"rattan", "tang", "angstrom", "romper", "perturb", "urban", "bang", 
"angel", "gelatin", "tint", "intros", "rostra", "trapper", 
"persimmon", "monsignori", "origin", "ginkgos", "gospel", "pelvis", 
"visor", "sorghum", "humid", "midair", "air", "airfoil", "oil", 
"oilskin", "kin", "kindergarten", "tentacle", "cleanser", "sermon", 
"monolog", "logarithmic", "microbes", "bestir", "tiros", "rosin", 
"sin", "singleton", "tonsil", "silicon", "con", "constraint", 
"intagli", "glint", "interwove", "overshadow", "downtrodden", 
"dentin", "tin", "tinsel", "sellout", "out", "output", "put", 
"putsch", "schoolmarm", "arm", "armor", "moribund", "underpin", 
"pint", "interloper", "periwig", "wig", "wigwag", "wagon", 
"gonorrhea", "hearten", "tenon", "nonverbal", "balsam", "samovar", 
"varmint", "interviewee", "weeper", "perturbed", "bed", "bedpan", 
"panache", "chestnut", "nut", "nutmeg", "meg", "megalopolis", 
"lissom", "somersault", "ultra", "tram", "ramp", "amputee", "teeth", 
"ethos", "hos", "hostel", "telescopic", "picayune", "uneven", 
"vendor", "dorsal", "salad", "ladybug", "bugaboo", "boomerang", 
"angora", "orangutan", "tandem", "demagogry", "gryphon", 
"honeycombed", "bedlam", "lamb", "ambergris", "risky", "sky", 
"skycap", "capstan", "tannin", "ninepin", "pinpoint", "interpret", 
"retiree", "reefer", "fer", "ferret", "returnee", "needlepoint", 
"interurban", "bantam", "tamp", "ampul", "pullout", "outrun", 
"runabout", "outstrip", "rip", "ripen", "pennon", "nonfat", "fathom", 
"homespun", "puns", "unsubscribes", "besom", "sombre", "breathe", 
"theatre", "tremor", "mortar", "tarpaulin", "lintel", "telethon", 
"honeydew", "dewlap", "lap", "lapel", "pelvic", "victim", "timpani", 
"animus", "muscat", "cat", "catsup", "sup", "superstar", "taro", 
"arousal", "salamis", "misprint", "interwoven", "venom", "nomad", 
"madam", "dam", "dampen", "penicillin", "lint", "intercom", 
"compound", "underpay", "pay", "payoff", "off", "offal", "fallout", 
"outwit", "withal", "halt", "altho", "tho", "thou", "housebound", 
"undergrad", "radio", "diocesan", "sanserif", "riffraff", 
"affidavit", "vitamin", "minicam", "campus", "pussycat", "catamaran", 
"rancor", "cornucopia", "piano", "anon", "non", "nonpartisan", 
"sandbar", "bar", "barren", "renewal", "walkout", "outruns", 
"unsnap", "naphtha", "thalamus", "musky", "skydove", "overrun", 
"run", "runs", "unsheathe", "the", "theorem", "remove", "overreach", 
"ache", "cherub", "rubes", "beseech", "echo", "chosen", "sensor", 
"sorrel", "relay", "layman", "mantillas", "lasagna", "gnat", 
"natures", "resonator", "torus", "russet", "set", "setback", 
"acknowledgement", "entanglement", "entombment", "entourages", 
"gestates", "testing", "ingratiate", "ate", "ateliers", "ersatzes", 
"zest"}

Python, 90

franchises renversées locataire balancé mer épousé déduit césariennes bénédictions sésames mailles hésitation ionosphère érection ioniseur zéro érode ode odes désertions terminaisons terrestres minerais terrestres idéaliser tic chatouilles leçon chanson chanson en cours inculquer le rassemblement illibéral ingérer estranges gestes réponses sésame modifier endives vêtement artiste du spectacle nerveusement sesterestesters esters reconnaît les éruptions cutanées de l'urètre hésitant anticlimax maxima imaginer les ivrognes testés fastidieusement la ruse essences césariennes réponse estimé les loups-garous gilet estimé médiocre omelette laitues cession ionisation ionisation ingestion ionosphères ionosphères sauvetage cueing incarné propriété hanche hippie piété étymologiste isthmuses sessions début des registres établis

Je nettoie d'abord la liste manuellement en supprimant tout

• mots avec une majuscule
• mots avec apostrophe
• mots avec éêèáâàö
• Mots à 1 et 2 lettres

cela me coûte au plus 2 points car ces mots ne peuvent être qu'au début ou à la fin de la chaîne, mais cela réduit la liste de mots de 1/3 et je n'ai pas à gérer unicode.

Ensuite, je construis une liste de tous les pré- et suffixes, trouve le chevauchement et jette tous les mots à moins que le pré- et le suffixe ne soient dans l'ensemble de chevauchement. Encore une fois, cela réduit au maximum 2 points de mon score maximal réalisable, mais cela réduit la liste de mots à un tiers de la taille d'origine (essayez d'exécuter votre algorithme sur la liste courte pour une accélération possible) et les mots restants sont hautement connectés (sauf 3 -les mots lettres qui ne sont liés qu’à eux-mêmes). En fait, presque n'importe quel mot peut être atteint à partir de n'importe quel autre mot par un chemin avec une moyenne de 4 bords.

Je stocke le nombre de liens dans une matrice d'adjacence qui simplifie toutes les opérations et me permet de faire des trucs sympas comme regarder n étapes en avant ou compter des cycles ... au moins en théorie, car il faut environ 15 secondes pour cadrer la matrice que je ne fais pas réellement ceci pendant la recherche. Au lieu de cela, je commence par un préfixe aléatoire et je me promène au hasard, soit en choisissant une fin uniformément, en favorisant ceux qui se produisent souvent (comme «-ing») ou ceux qui se produisent moins souvent.
Les trois variantes sont nulles et produisent des chaînes de 20 à 40, mais au moins c'est rapide. Je suppose que je dois ajouter une récursivité après tout.

from numpy import *
f = open('words_short.txt')
words = f.read().split() # 62896
f.close()

prefix = [w[:3] for w in words]     # 2292
suffix = [w[-3:] for w in words]    # 2262
common = set(prefix) & set(suffix)  # 1265

PSW = [(p,s,w) for (p,s,w) in zip(prefix, suffix, words) if p in common and s in common] # 28673
common = list(common)
mapping = dict(zip(common, range(len(common)))) # enumerate trigrams

M = zeros((len(common), len(common)), dtype=int) # for fast processing
W = [[[] for i in range(len(common))] for j in range(len(common))] # for reconstruction
for p,s,w in PSW: # build adjacency matrix
    M[mapping[p], mapping[s]] += 1
    W[mapping[p]][mapping[s]].append(w)

def chain(A, rho=0):
    B = array(A)
    links = []
    start = random.randint(len(B))
    links.append(start)
    while 1:
        nextpos = where(B[links[-1],:]>0)[0]
        if len(nextpos)==0: return links
        nextnum = B[links[-1],nextpos]

        p = ones(len(nextnum))/len(nextnum) # pick uniformly
        if rho>0: p = nextnum*1./sum(nextnum) # prioritize many links
        if rho>1: p = 1/p; p = p/sum(p) # prioritize few links

        chosen = random.choice(nextpos, p=p)
        B[links[-1], chosen] -= 1
        links.append(chosen)

def chain2words(L):
    # can only be used once because of .pop()
    z = zip(L[:-1],L[1:])
    res = []
    for p,s in z:
        res.append(W[p][s].pop())
    return res

chains = [chain(M) for i in range(100)]
bestchain = chains[argmax(map(len, chains))]
print ' '.join(chain2words(bestchain))

Au départ , je voulais essayer quelque chose de similaire à ce mais puisque c'est un graphe orienté avec des cycles, aucun des algorithmes standards pour topologiques tri, chemin le plus long, le plus grand chemin Eulerian ou de travail chinois Postman problème sans modifications lourdes.

Et juste parce que ça a l'air bien, voici une image de la matrice d'adjacence M, M ^ 2 et M ^ infini (infini = 32, ça ne change pas par la suite) avec blanc = entrées non nulles