Java, heurística a favor do vértice que induz o maior gráfico: 1825 1855 1873
O código abaixo é executado em menos de 10 minutos e encontra o seguinte caminho:
[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]
Idéias principais
Em Aproximando caminhos e ciclos diretos mais longos , Bjorklund, Husfeldt e Khanna, Lecture Notes in Computer Science (2004), 222-233, os autores propõem que, em gráficos esparsos de expansores, um caminho longo pode ser encontrado por uma pesquisa ambiciosa que seleciona a cada pise o vizinho da cauda atual do caminho que se estende pelo maior subgrafo em G ', onde G' é o gráfico original com os vértices no caminho atual excluídos. Não tenho certeza de uma boa maneira de testar se um gráfico é um gráfico expansor, mas certamente estamos lidando com um gráfico esparso, e como seu núcleo é de cerca de 20.000 vértices e tem um diâmetro de apenas 15, deve ter uma boa propriedades de expansão. Então, eu adoto essa heurística gananciosa.
Dado um gráfico G(V, E) , podemos encontrar quantos vértices são alcançáveis de cada vértice usando Floyd-Warshall no Theta(V^3)tempo ou usando o algoritmo de Johnson no Theta(V^2 lg V + VE)tempo. No entanto, eu sei que estamos lidando com um gráfico que tem um componente fortemente conectado (SCC) muito grande, por isso adoto uma abordagem diferente. Se identificarmos SCCs usando o algoritmo de Tarjan , também obteremos uma classificação topológica para o gráfico compactado G_c(V_c, E_c), que será muito menor com o O(E)tempo. Como G_cé um DAG, podemos calcular a acessibilidade G_cno O(V_c^2 + E_c)tempo. (Descobri subseqüentemente que isso é sugerido no exercício 26-2.8 do CLR ).
Como o fator dominante no tempo de execução é E, eu o otimizo inserindo nós fictícios para os prefixos / sufixos. Então, em vez de 151 * 64 = 9664 arestas das palavras que terminam -res em palavras que começam com res- Eu tenho 151 arestas das palavras que terminam -res para # res # e 64 arestas de # res # para palavras que começam com res- .
E, finalmente, como cada pesquisa leva cerca de 4 minutos no meu PC antigo, tento combinar os resultados com caminhos longos anteriores. Isso é muito mais rápido e apareceu minha melhor solução atual.
Código
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");
}
}
}
