Java, heuristic ủng hộ đỉnh tạo ra đồ thị lớn nhất: 1825 1855 1873
Mã dưới đây chạy trong dưới 10 phút và tìm thấy đường dẫn sau:
[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]
Ý tưởng cốt lõi
Trong xấp xỉ các đường dẫn và chu trình dài nhất , Bjorklund, Husfeldt và Khanna, Ghi chú bài giảng trong Khoa học máy tính (2004), 222-233, các tác giả đề xuất rằng trong các biểu đồ giãn nở thưa thớt có thể tìm thấy một con đường dài bước hàng xóm của đuôi hiện tại của đường dẫn kéo dài sơ đồ con lớn nhất trong G ', trong đó G' là đồ thị ban đầu với các đỉnh trong đường dẫn hiện tại bị xóa. Tôi không chắc chắn về cách tốt để kiểm tra xem đồ thị có phải là đồ thị giãn nở hay không, nhưng chúng tôi chắc chắn đang xử lý một đồ thị thưa thớt, và vì lõi của nó có khoảng 20000 đỉnh và nó có đường kính chỉ 15 nên nó phải tốt tính chất mở rộng. Vì vậy, tôi chấp nhận heuristic tham lam này.
Cho một đồ thị G(V, E), chúng ta có thể tìm thấy bao nhiêu đỉnh có thể truy cập từ mỗi đỉnh bằng Floyd-Warshall trong Theta(V^3)thời gian, hoặc sử dụng thuật toán Johnson trong Theta(V^2 lg V + VE)thời gian. Tuy nhiên, tôi biết rằng chúng ta đang xử lý một biểu đồ có thành phần được kết nối rất lớn (SCC), vì vậy tôi có một cách tiếp cận khác. Nếu chúng tôi xác định SCC bằng thuật toán Tarjan thì chúng tôi cũng sẽ nhận được một loại cấu trúc liên kết cho biểu đồ nén G_c(V_c, E_c), sẽ nhỏ hơn nhiều, theo O(E)thời gian. Kể từ khi G_clà một DAG, chúng ta có thể tính toán reachability trong G_ctrong O(V_c^2 + E_c)thời gian. (Sau đó tôi đã phát hiện ra rằng điều này được gợi ý trong bài tập 26-2.8 của CLR ).
Vì yếu tố chi phối trong thời gian chạy là E, tôi tối ưu hóa nó bằng cách chèn các nút giả cho các tiền tố / hậu tố. Vì vậy, chứ không phải là 151 * 64 = 9664 cạnh từ từ kết thúc -res đến từ bắt đầu res- Tôi có 151 cạnh từ từ kết thúc -res để # res # và 64 cạnh từ # res # để từ bắt đầu res- .
Và cuối cùng, vì mỗi tìm kiếm mất khoảng 4 phút trên PC cũ của tôi, tôi cố gắng kết hợp các kết quả với các đường dẫn dài trước đó. Điều này nhanh hơn nhiều, và bật lên giải pháp tốt nhất hiện tại của tôi.
Mã
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");
}
}
}
