जावा, हेरीस्टिक वर्टेक्स के पक्ष में है जो सबसे बड़े ग्राफ को प्रेरित करता है: 1825 1855 1873
नीचे दिया गया कोड 10 मिनट से कम समय में चलता है और निम्न मार्ग को पाता है:
[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]
मूल विचार
सबसे लंबे समय तक निर्देशित रास्तों और साइकिलों के लिए , बोजर्कलंड, हसफेल्ट, और खन्ना, कंप्यूटर विज्ञान में व्याख्यान नोट्स (2004), 222-233, लेखकों प्रस्ताव में विरल विस्तारक एक लंबे पथ को आरेखित करता एक लालची खोज द्वारा पाया जा सकता है जो प्रत्येक में चयन पथ की वर्तमान पूंछ के पड़ोसी को चरणबद्ध करें जो G 'में सबसे बड़ा सबग्राफ फैलाता है, जहां G' वर्तमान ग्राफ़ में वर्तमान ग्राफ़ को हटाए गए मार्ग के साथ मूल ग्राफ़ है। मुझे यह परखने का कोई अच्छा तरीका नहीं है कि एक ग्राफ एक विस्तारक ग्राफ है, लेकिन हम निश्चित रूप से एक विरल ग्राफ के साथ काम कर रहे हैं, और चूंकि इसका कोर लगभग 20000 कोने है और इसमें केवल 15 का व्यास है, यह अच्छा होना चाहिए विस्तार गुण। इसलिए मैं इस लालची विधर्मी को अपनाता हूं।
एक ग्राफ को देखते हुए G(V, E), हम पा सकते हैं कि कितने कोने का उपयोग कर प्रत्येक शिखर से पहुंचा जा सकता है फ्लोयड-Warshall में Theta(V^3)समय, या का उपयोग करते हुए जॉनसन एल्गोरिथ्म में Theta(V^2 lg V + VE)समय। हालांकि, मुझे पता है कि हम एक ग्राफ के साथ काम कर रहे हैं जिसमें एक बहुत बड़ा दृढ़ता से जुड़ा घटक (एससीसी) है, इसलिए मैं एक अलग दृष्टिकोण लेता हूं। यदि हम टार्जन के एल्गोरिथ्म का उपयोग करते हुए SCCs की पहचान करते हैं तो हमें संपीड़ित ग्राफ के लिए एक सामयिक प्रकार भी मिलता है G_c(V_c, E_c), जो O(E)समय में बहुत छोटा होगा । चूंकि G_cएक डीएजी है, हम समय G_cमें पुनरावृत्ति की गणना कर सकते हैं O(V_c^2 + E_c)। (मुझे बाद में पता चला है कि यह CLR के 26-2.8 अभ्यास में संकेत दिया गया है )।
चूंकि चल रहे समय में प्रमुख कारक है E, इसलिए मैं उपसर्गों / प्रत्ययों के लिए डमी नोड्स सम्मिलित करके इसे अनुकूलित करता हूं। तो न खत्म होने वाली शब्द के बजाय 151 * 64 = 9664 किनारों -res शब्द शुरू res- मैं न खत्म होने वाली शब्दों से 151 किनारों है -res को # रेस # और से 64 किनारों # रेस # शब्द शुरू res- ।
और अंत में, चूंकि प्रत्येक खोज में मेरे पुराने पीसी पर लगभग 4 मिनट लगते हैं, इसलिए मैं पिछले लंबे रास्तों के साथ परिणामों को संयोजित करने का प्रयास करता हूं। यह बहुत तेज है, और मेरे वर्तमान सबसे अच्छे समाधान को बदल दिया।
कोड
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");
}
}
}
