Java, heuristik mendukung vertex yang menginduksi grafik terbesar: 1825 1855 1873
Kode di bawah ini berjalan dalam waktu kurang dari 10 menit dan menemukan jalur berikut:
[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]
Ide inti
Dalam Perkiraan jalur dan siklus terarah terpanjang , Bjorklund, Husfeldt, dan Khanna, Lecture Notes in Computer Science (2004), 222-233, penulis mengusulkan bahwa dalam grafik expander yang jarang, jalur panjang dapat ditemukan oleh pencarian serakah yang memilih masing-masing langkah tetangga dari ekor saat ini dari jalur yang membentang subgraf terbesar di G ', di mana G' adalah grafik asli dengan simpul di jalur saat ini dihapus. Saya tidak yakin dengan cara yang baik untuk menguji apakah suatu grafik adalah grafik expander, tapi kami jelas berhadapan dengan grafik yang jarang, dan karena intinya adalah sekitar 20.000 simpul dan memiliki diameter hanya 15, ia harus memiliki yang baik properti ekspansi. Jadi saya mengadopsi heuristik serakah ini.
Diberikan grafik G(V, E), kita dapat menemukan berapa banyak simpul yang bisa dijangkau dari setiap simpul menggunakan Floyd-Warshall dalam Theta(V^3)waktu, atau menggunakan algoritma Johnson dalam Theta(V^2 lg V + VE)waktu. Namun, saya tahu bahwa kita sedang berhadapan dengan grafik yang memiliki komponen terhubung sangat besar (SCC), jadi saya mengambil pendekatan yang berbeda. Jika kami mengidentifikasi SCC menggunakan algoritma Tarjan maka kami juga mendapatkan semacam topologi untuk grafik terkompresi G_c(V_c, E_c), yang akan jauh lebih kecil, pada O(E)waktunya. Karena G_cini adalah DAG, kita dapat menghitung keterjangkauan G_cdalam O(V_c^2 + E_c)waktu. (Saya kemudian menemukan bahwa ini mengisyaratkan dalam latihan 26-2.8 dari CLR ).
Karena faktor dominan dalam waktu berjalan adalah E, saya mengoptimalkannya dengan menyisipkan simpul dummy untuk awalan / sufiks. Jadi, alih-alih 151 * 64 = 9664 tepi dari kata-kata yang berakhir -res ke kata-kata mulai res- Saya memiliki 151 tepi dari kata-kata yang berakhir -res ke # res # dan 64 tepi dari # res # untuk kata-kata yang dimulai res- .
Dan akhirnya, karena setiap pencarian memakan waktu sekitar 4 menit pada PC lama saya, saya mencoba untuk menggabungkan hasil dengan jalur panjang sebelumnya. Ini jauh lebih cepat, dan muncul solusi terbaik saya saat ini.
Kode
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");
}
}
}
