package Question20_13;
import java.util.LinkedList;
public class Question {
private int maxWordLength;
private WordGroup[] groupList ;
private Trie trieList[];
public Question(String[] list) {
groupList = WordGroup.createWordGroups(list);
maxWordLength = groupList.length;
// Initialize trieList to store trie of groupList[i] at ith position.
trieList = new Trie[maxWordLength];
}
/* This function finds a rectangle of letters of the largest
* possible area (length x breadth) such that every row forms a
* word (reading left to right) from the list and every column
* forms a word (reading top to bottom) from the list.
*/
public Rectangle maxRectangle() {
// The dimensions of the largest possible rectangle.
int maxSize = maxWordLength * maxWordLength;
for (int z = maxSize; z > 0; z--) {
// Find out all pairs i,j less than maxWordLength
// such that i * j = z
for (int i = 1; i <= maxWordLength; i ++ ) {
if (z % i == 0) {
int j = z / i;
if (j <= maxWordLength) {
// Check if a Rectangle of length i and height
// j can be created.
Rectangle rectangle = makeRectangle(i,j);
if (rectangle != null) {
return rectangle;
}
}
}
}
}
return null;
}
/* This function takes the length and height of a rectangle as
* arguments. It tries to form a rectangle of the given length and
* height using words of the specified length as its rows, in which
* words whose length is the specified height form the columns. It
* returns the rectangle so formed, and null if such a rectangle
* cannot be formed.
*/
private Rectangle makeRectangle(int length, int height) {
if (groupList[length - 1] == null || groupList[height - 1] == null) {
return null;
}
if (trieList[height - 1] == null) {
LinkedList<String> words = groupList[height - 1].getWords();
trieList[height - 1] = new Trie(words);
}
return makePartialRectangle(length, height, new Rectangle(length));
}
/* This function recursively tries to form a rectangle with words
* of length l from the dictionary as rows and words of length h
* from the dictionary as columns. To do so, we start with an empty
* rectangle and add in a word with length l as the first row. We
* then check the trie of words of length h to see if each partial
* column is a prefix of a word with length h. If so we branch
* recursively and check the next word till we've formed a complete
* rectangle. When we have a complete rectangle check if every
* column is a word in the dictionary.
*/
private Rectangle makePartialRectangle(int l, int h, Rectangle rectangle) {
// Check if we have formed a complete rectangle by seeing if each column
// is in the dictionary
if (rectangle.height == h) {
if (rectangle.isComplete(l, h, groupList[h - 1])) {
return rectangle;
} else {
return null;
}
}
// If the rectangle is not empty, validate that each column is a
// substring of a word of length h in the dictionary using the
// trie of words of length h.
if (!rectangle.isPartialOK(l, trieList[h - 1])) {
return null;
}
// For each word of length l, try to make a new rectangle by adding
// the word to the existing rectangle.
for (int i = 0; i < groupList[l-1].length(); i++) {
Rectangle org_plus = rectangle.append(groupList[l-1].getWord(i));
Rectangle rect = makePartialRectangle(l, h, org_plus);
if (rect != null) {
return rect;
}
}
return null;
}
// Test harness.
public static void main(String[] args) {
Question dict = new Question(wordList);
Rectangle rect = dict.maxRectangle();
if (rect != null) {
rect.print();
} else {
System.out.println ("No rectangle exists");
}
}
//Words in the dictionary.
static String[] wordList = {
"the",
"of",
"and",
"a",
"to",
"in",
"is",
"be",
"that",
"was",
"he",
"for",
"it",
"with",
"as",
"his",
"I",
"on",
"have",
"at",
"by",
"not",
"they",
"this",
"had",
"are",
"but",
"from",
"or",
"she",
"an",
"which",
"you",
"one",
"we",
"all",
"were",
"her",
"would",
"there",
"their",
"will",
"when",
"who",
"him",
"been",
"has",
"more",
"if",
"no",
"out",
"do",
"so",
"can",
"what",
"up",
"said",
"about",
"other",
"into",
"than",
"its",
"time",
"only",
"could",
"new",
"them",
"man",
"some",
"these",
"then",
"two",
"first",
"May",
"any",
"like",
"now",
"my",
"such",
"make",
"over",
"our",
"even",
"most",
"me",
"state",
"after",
"also",
"made",
"many",
"did",
"must",
"before",
"back",
"see",
"through",
"way",
"where",
"get",
"much",
"go",
"well",
"your",
"know",
"should",
"down",
"work",
"year",
"because",
"come",
"people",
"just",
"say",
"each",
"those",
"take",
"day",
"good",
"how",
"long",
"Mr",
"own",
"too",
"little",
"use",
"US",
"very",
"great",
"still",
"men",
"here",
"life",
"both",
"between",
"old",
"under",
"last",
"never",
"place",
"same",
"another",
"think",
"house",
"while",
"high",
"right",
"might",
"came",
"off",
"find",
"states",
"since",
"used",
"give",
"against",
"three",
"himself",
"look",
"few",
"general",
"hand",
"school",
"part",
"small",
"American",
"home",
"during",
"number",
"again",
"Mrs",
"around",
"thought",
"went",
"without",
"however",
"govern",
"don't",
"does",
"got",
"public",
"United",
"point",
"end",
"become",
"head",
"once",
"course",
"fact",
"upon",
"need",
"system",
"set",
"every",
"war",
"put",
"form",
"water",
"took",
"program",
"present",
"government",
"thing",
"told",
"possible",
"group",
"large",
"until",
"always",
"city",
"didn't",
"order",
"away",
"called",
"want",
"eyes",
"something",
"unite",
"going",
"face",
"far",
"asked",
"interest",
"later",
"show",
"knew",
"though",
"less",
"night",
"early",
"almost",
"let",
"open",
"enough",
"side",
"case",
"days",
"yet",
"better",
"nothing",
"tell",
"problem",
"toward",
"given",
"why",
"national",
"room",
"young",
"social",
"light",
"business",
"president",
"help",
"power",
"country",
"next",
"things",
"word",
"looked",
"real",
"John",
"line",
"second",
"church",
"seem",
"certain",
"big",
"Four",
"felt",
"several",
"children",
"service",
"feel",
"important",
"rather",
"name",
"per",
"among",
"often",
"turn",
"development",
"keep",
"family",
"seemed",
"white",
"company",
"mind",
"members",
"others",
"within",
"done",
"along",
"turned",
"god",
"sense",
"week",
"best",
"change",
"kind",
"began",
"child",
"ever",
"law",
"matter",
"least",
"means",
"question",
"act",
"close",
"mean",
"leave",
"itself",
"force",
"study",
"York",
"action",
"it's",
"door",
"experience",
"human",
"result",
"times",
"run",
"different",
"car",
"example",
"hands",
"whole",
"center",
"although",
"call",
"Five",
"inform",
"gave",
"plan",
"woman",
"boy",
"feet",
"provide",
"taken",
"thus",
"body",
"play",
"seen",
"today",
"having",
"cost",
"perhaps",
"field",
"local",
"really",
"am",
"increase",
"reason",
"themselves",
"clear",
"I'm",
"information",
"figure",
"late",
"above",
"history",
"love",
"girl",
"held",
"special",
"move",
"person",
"whether",
"college",
"sure",
"probably",
"either",
"seems",
"cannot",
"art",
"free",
"across",
"death",
"quite",
"street",
"value",
"anything",
"making",
"past",
"brought",
"moment",
"control",
"office",
"heard",
"problems",
"became",
"full",
"near",
"half",
"nature",
"hold",
"live",
"available",
"known",
"board",
"effect",
"already",
"Economic",
"money",
"position",
"believe",
"age",
"together",
"shall",
"TRUE",
"political",
"court",
"report",
"level",
"rate",
"air",
"pay",
"community",
"complete",
"music",
"necessary",
"society",
"behind",
"type",
"read",
"idea",
"wanted",
"land",
"party",
"class",
"organize",
"return",
"department",
"education",
"following",
"mother",
"sound",
"ago",
"nation",
"voice",
"six",
"bring",
"wife",
"common",
"south",
"strong",
"town",
"book",
"students",
"hear",
"hope",
"able",
"industry",
"stand",
"tax",
"west",
"meet",
"particular",
"cut",
"short",
"stood",
"university",
"spirit",
"start",
"total",
"future",
"front",
"low",
"century",
"Washington",
"usually",
"care",
"recent",
"evidence",
"further",
"million",
"simple",
"road",
"sometimes",
"support",
"view",
"fire",
"says",
"hard",
"morning",
"table",
"left",
"situation",
"try",
"outside",
"lines",
"surface",
"ask",
"modern",
"top",
"peace",
"personal",
"member",
"minutes",
"lead",
"schools",
"talk",
"consider",
"gone",
"soon",
"father",
"ground",
"living",
"months",
"therefore",
"America",
"started",
"longer",
"Dr",
"dark",
"various",
"finally",
"hour",
"north",
"third",
"fall",
"greater",
"pressure",
"stage",
"expected",
"secretary",
"needed",
"That's",
"kept",
"eye",
"values",
"union",
"private",
"alone",
"black",
"required",
"space",
"subject",
"english",
"month",
"understand",
"I'll",
"nor",
"answer",
"moved",
"amount",
"conditions",
"direct",
"red",
"student",
"rest",
"nations",
"heart",
"costs",
"record",
"picture",
"taking",
"couldn't",
"hours",
"deal",
"forces",
"everything",
"write",
"coming",
"effort",
"market",
"island",
"wall",
"purpose",
"basis",
"east",
"lost",
"St",
"except",
"letter",
"looking",
"property",
"Miles",
"difference",
"entire",
"else",
"color",
"followed",
"feeling",
"son",
"makes",
"friend",
"basic",
"cold",
"including",
"single",
"attention",
"note",
"cause",
"hundred",
"step",
"paper",
"developed",
"tried",
"simply",
"can't",
"story",
"committee",
"inside",
"reached",
"easy",
"appear",
"include",
"accord",
"Actually",
"remember",
"beyond",
"dead",
"shown",
"fine",
"religious",
"continue",
"ten",
"defense",
"getting",
"Central",
"beginning",
"instead",
"river",
"received",
"doing",
"employ",
"trade",
"terms",
"trying",
"friends",
"sort",
"administration",
"higher",
"cent",
"expect",
"food",
"building",
"religion",
"meeting",
"ready",
"walked",
"follow",
"earth",
"speak",
"passed",
"foreign",
"NATURAL",
"medical",
"training",
"County",
"list",
"floor",
"piece",
"especially",
"indeed",
"stop",
"wasn't",
"England",
"difficult",
"likely",
"Suddenly",
"moral",
"plant",
"bad",
"club",
"needs",
"international",
"working",
"countries",
"develop",
"drive",
"reach",
"police",
"sat",
"charge",
"farm",
"fear",
"test",
"determine",
"hair",
"results",
"stock",
"trouble",
"happened",
"growth",
"square",
"William",
"cases",
"effective",
"serve",
"miss",
"involved",
"doctor",
"earlier",
"increased",
"being",
"blue",
"hall",
"particularly",
"boys",
"paid",
"sent",
"production",
"district",
"using",
"thinking",
"concern",
"Christian",
"press",
"girls",
"wide",
"usual",
"direction",
"feed",
"trial",
"walk",
"begin",
"weeks",
"points",
"respect",
"certainly",
"ideas",
"industrial",
"methods",
"operation",
"addition",
"association",
"combine",
"knowledge",
"decided",
"temperature",
"statement",
"Yes",
"below",
"game",
"nearly",
"science",
"directly",
"horse",
"influence",
"size",
"showed",
"build",
"throughout",
"questions",
"character",
"foot",
"Kennedy",
"firm",
"reading",
"husband",
"doubt",
"services",
"according",
"lay",
"stay",
"programs",
"anyone",
"average",
"French",
"spring",
"former",
"summer",
"bill",
"lot",
"chance",
"due",
"comes",
"army",
"actual",
"Southern",
"neither",
"relate",
"rise",
"evening",
"normal",
"wish",
"visit",
"population",
"remain",
"measure",
"merely",
"arrange",
"condition",
"decision",
"account",
"opportunity",
"pass",
"demand",
"strength",
"window",
"active",
"deep",
"degree",
"ran",
"western",
"E",
"sales",
"continued",
"fight",
"heavy",
"arm",
"standard",
"generally",
"carry",
"hot",
"provided",
"serious",
"led",
"wait",
"hotel",
"opened",
"performance",
"maybe",
"station",
"changes",
"literature",
"marry",
"claim",
"works",
"bed",
"wrong",
"main",
"unit",
"George",
"hit",
"planning",
"supply",
"systems",
"add",
"chief",
"officer",
"Soviet",
"pattern",
"stopped",
"price",
"success",
"lack",
"myself",
"truth",
"freedom",
"manner",
"quality",
"gun",
"manufacture",
"clearly",
"share",
"movement",
"length",
"ways",
"burn",
"forms",
"Organization",
"break",
"somewhat",
"efforts",
"cover",
"meaning",
"progress",
"treatment",
"beautiful",
"placed",
"happy",
"attack",
"apparently",
"blood",
"groups",
"carried",
"sign",
"radio",
"dance",
"I've",
"regard",
"man's",
"train",
"herself",
"numbers",
"corner",
"REACTION",
"immediately",
"language",
"running",
"recently",
"shake",
"larger",
"lower",
"machine",
"attempt",
"learn",
"couple",
"race",
"audience",
"Oh",
"middle",
"brown",
"date",
"health",
"persons",
"understanding",
"arms",
"daily",
"suppose",
"additional",
"hospital",
"pool",
"technical",
"served",
"declare",
"described",
"current",
"poor",
"steps",
"reported",
"sun",
"based",
"produce",
"determined",
"receive",
"park",
"staff",
"faith",
"responsibility",
"Europe",
"latter",
"British",
"season",
"equal",
"learned",
"practice",
"green",
"writing",
"ones",
"choice",
"fiscal",
"term",
"watch",
"scene",
"activity",
"product",
"types",
"ball",
"heat",
"clothe",
"lived",
"distance",
"parent",
"letters",
"returned",
"forward",
"obtained",
"offer",
"specific",
"straight",
"fix",
"division",
"slowly",
"shot",
"poet",
"seven",
"moving",
"mass",
"plane",
"proper",
"propose",
"drink",
"obviously",
"plans",
"whatever",
"afternoon",
"figures",
"parts",
"approve",
"saying",
"born",
"immediate",
"fame",
"gives",
"extent",
"justice",
"cars",
"mark",
"pretty",
"opinion",
"ahead",
"glass",
"refuse",
"enter",
"completely",
"send",
"desire",
"judge",
"none",
"waiting",
"popular",
"Democratic",
"film",
"mouth",
"Corps",
"importance",
"touch",
"director",
"ship",
"there's",
"council",
"EFFECTS",
"event",
"worth",
"existence",
"designed",
"hardly",
"indicated",
"analysis",
"established",
"products",
"growing",
"patient",
"rule",
"bridge",
"pain",
"base",
"check",
"cities",
"elements",
"leaders",
"discussion",
"limited",
"sit",
"Thomas",
"agreement",
"gas",
"factors",
"marriage",
"easily",
"closed",
"excite",
"accept",
"applied",
"allow",
"bit",
"married",
"oil",
"Rhode",
"shape",
"interested",
"strange",
"compose",
"professional",
"remained",
"news",
"Despite",
"beauty",
"responsible",
"wonder",
"spent",
"tear",
"unless",
"eight",
"permit",
"covered",
"Negro",
"played",
"I'd",
"vote",
"balance",
"Charles",
"loss",
"Commission",
"original",
"fair",
"reasons",
"studies",
"exactly",
"built",
"behavior",
"enemy",
"teeth",
"bank",
"die",
"James",
"relations",
"weight",
"prepared",
"related",
"sea",
"bar",
"warn",
"post",
"trees",
"official",
"separate",
"clay",
"Sunday",
"raised",
"events",
"thin",
"dropped",
"cattle",
"invite",
"playing",
"prevent",
"detail",
"standing",
"grow",
"places",
"someone",
"bright",
"Talking",
"meant",
"print",
"capital",
"happen",
"sides",
"everyone",
"facilities",
"filled",
"lip",
"essential",
"techniques",
"June",
"knows",
"stain",
"hadn't",
"dinner",
"dog",
"dollars",
"caught",
"shout",
"buy",
"divide",
"entered",
"Chicago",
"speed",
"jazz",
"appoint",
"governor",
"institutions",
"fit",
"materials",
"sight",
"store",
"dependence",
"explain",
"gain",
"he'd",
"leadership",
"quiet",
"realize",
"parents",
"Communist",
"neighbor",
"round",
"included",
"kitchen",
"thousand",
"Christ",
"isn't",
"radiation",
"broad",
"failure",
"retire",
"election",
"primary",
"king",
"books",
"command",
"edge",
"March",
"sitting",
"conference",
"bottom",
"lady",
"advise",
"churches",
"model",
"battle",
"giving",
"sport",
"address",
"considerable",
"spread",
"funds",
"trip",
"youth",
"CONSTRUCTION",
"rock",
"regular",
"changed",
"boat",
"memory",
"successful",
"captain",
"hell",
"brother",
"murder",
"quick",
"moreover",
"highly",
"difficulty",
"inch",
"saw",
"clean",
"collect",
"camp",
"experiment",
"shows",
"Authority",
"older",
"lord",
"variety",
"material",
"frame",
"distinguish",
"scientific",
"introduce",
"principal",
"Jack",
"kill",
"collection",
"fell",
"entertain",
"pieces",
"management",
"otherwise",
"security",
"danger",
"entirely",
"civil",
"frequently",
"advertise",
"records",
"secret",
"title",
"impossible",
"yesterday",
"fast",
"Mike",
"produced",
"favor",
"noted",
"caused",
"lose",
"purposes",
"solid",
"song",
"corporation",
"lie",
"winter",
"dress",
"electric",
"key",
"dry",
"reduce",
"fresh",
"goes",
"hill",
"names",
"slow",
"quickly",
"telephone",
"threaten",
"oppose",
"deliver",
"officers",
"expression",
"published",
"famous",
"pray",
"adopt",
"London",
"clothes",
"laws",
"citizens",
"announced",
"minute",
"master",
"sharp",
"advantage",
"greatest",
"relation",
"Mary",
"leaving",
"gray",
"manager",
"animal",
"object",
"bottle",
"draw",
"honor",
"recognize",
"drop",
"intend",
"relationship",
"opposite",
"sources",
"poetry",
"ability",
"assistance",
"operating",
"bear",
"join",
"climb",
"companies",
"exist",
"fixed",
"gradual",
"possibility",
"hunt",
"spoke",
"satisfy",
"units",
"neck",
"sleep",
"doesn't",
"finished",
"carefully",
"facts",
"nice",
"practical",
"save",
"takes",
"allowed",
"wine",
"remind",
"rich",
"financial",
"dream",
"knife",
"stations",
"civilize",
"Rose",
"cool",
"died",
"thick",
"imagine",
"literary",
"bind",
"inches",
"earn",
"familiar",
"seeing",
"distribution",
"marked",
"coffee",
"rules",
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};
}