206 lines
24 KiB
Markdown
206 lines
24 KiB
Markdown
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---
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id: 5900f3cf1000cf542c50fee1
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title: 'Problem 98: Anagramic squares'
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challengeType: 5
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forumTopicId: 302215
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dashedName: problem-98-anagramic-squares
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---
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# --description--
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By replacing each of the letters in the word CARE with 1, 2, 9, and 6 respectively, we form a square number: $1296 = 36^2$. What is remarkable is that, by using the same digital substitutions, the anagram, RACE, also forms a square number: $9216 = 96^2$. We shall call CARE (and RACE) a square anagram word pair and specify further that leading zeroes are not permitted, neither may a different letter have the same digital value as another letter.
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Using the `words` array, find all the square anagram word pairs (a palindromic word is NOT considered to be an anagram of itself).
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What is the largest square number formed by any member of such a pair?
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**Note:** All anagrams formed must be contained in the given `words` array.
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# --hints--
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`anagramicSquares(['CARE', 'RACE'])` should return a number.
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```js
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assert(typeof anagramicSquares(['CARE', 'RACE']) === 'number');
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```
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`anagramicSquares(['CARE', 'RACE'])` should return `9216`.
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```js
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assert.strictEqual(anagramicSquares(['CARE', 'RACE']), 9216);
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```
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`anagramicSquares(testWords1)` should return `4761`.
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```js
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assert.strictEqual(anagramicSquares(_testWords1), 4761);
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```
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`anagramicSquares(testWords2)` should return `18769`.
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```js
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assert.strictEqual(anagramicSquares(_testWords2), 18769);
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```
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# --seed--
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## --after-user-code--
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```js
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const _testWords1 = [
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"DAMAGE","DANGER","DANGEROUS","DARK","DATA","DATE","DAUGHTER","DAY","DEAD","DEAL","DEATH","DEBATE","DEBT","DECADE","DECIDE","DECISION","DECLARE","DEEP","DEFENCE","DEFENDANT","DEFINE","DEFINITION","DEGREE","DELIVER","DEMAND","DEMOCRATIC","DEMONSTRATE","DENY","DEPARTMENT","DEPEND","DEPUTY","DERIVE","DESCRIBE","DESCRIPTION","DESIGN","DESIRE","DESK","DESPITE","DESTROY","DETAIL","DETAILED","DETERMINE","DEVELOP","DEVELOPMENT","DEVICE","DIE","DIFFERENCE","DIFFERENT","DIFFICULT","DIFFICULTY","DINNER","DIRECT","DIRECTION","DIRECTLY","DIRECTOR","DISAPPEAR","DISCIPLINE","DISCOVER","DISCUSS","DISCUSSION","DISEASE","DISPLAY","DISTANCE","DISTINCTION","DISTRIBUTION","DISTRICT","DIVIDE","DIVISION","DO","DOCTOR","DOCUMENT","DOG","DOMESTIC","DOOR","DOUBLE","DOUBT","DOWN","DRAW","DRAWING","DREAM","DRESS","DRINK","DRIVE","DRIVER","DROP","DRUG","DRY","DUE","DURING","DUTY","LABOUR","LACK","LADY","LAND","LANGUAGE","LARGE","LARGELY","LAST","LATE","LATER","LATTER","LAUGH","LAUNCH","LAW","LAWYER","LAY","LEAD","LEADER","LEADERSHIP","LEADING","LEAF","LEAGUE","LEAN","LEARN","LEAST","LEAVE","LEFT","LEG","LEGAL","LEGISLATION","LENGTH","LESS","LET","LETTER","LEVEL","LIABILITY","LIBERAL","LIBRARY","LIE","LIFE","LIFT","LIGHT","LIKE","LIKELY","LIMIT","LIMITED","LINE","LINK","LIP","LIST","LISTEN","LITERATURE","LITTLE","LIVE","LIVING","LOAN","LOCAL","LOCATION","LONG","LOOK","LORD","LOSE","LOSS","LOT","LOVE","LOVELY","LOW","LUNCH"
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];
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const _testWords2 = [
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"A","ABILITY","ABLE","ABOUT","ABOVE","ABSENCE","ABSOLUTELY","ACADEMIC","ACCEPT","ACCESS","ACCIDENT","ACCOMPANY","ACCORDING","ACCOUNT","ACHIEVE","ACHIEVEMENT","ACID","ACQUIRE","ACROSS","ACT","ACTION","ACTIVE","ACTIVITY","ACTUAL","ACTUALLY","ADD","ADDITION","ADDITIONAL","ADDRESS","ADMINISTRATION","ADMIT","ADOPT","ADULT","ADVANCE","ADVANTAGE","ADVICE","ADVISE","AFFAIR","AFFECT","AFFORD","AFRAID","AFTER","AFTERNOON","AFTERWARDS","AGAIN","AGAINST","AGE","AGENCY","AGENT","AGO","AGREE","AGREEMENT","AHEAD","AID","AIM","AIR","AIRCRAFT","ALL","ALLOW","ALMOST","ALONE","ALONG","ALREADY","ALRIGHT","ALSO","ALTERNATIVE","ALTHOUGH","ALWAYS","AMONG","AMONGST","AMOUNT","AN","ANALYSIS","ANCIENT","AND","ANIMAL","ANNOUNCE","ANNUAL","ANOTHER","ANSWER","ANY","ANYBODY","ANYONE","ANYTHING","ANYWAY","APART","APPARENT","APPARENTLY","APPEAL","APPEAR","APPEARANCE","APPLICATION","APPLY","APPOINT","APPOINTMENT","APPROACH","APPROPRIATE","APPROVE","AREA","ARGUE","ARGUMENT","ARISE","ARM","ARMY","AROUND","ARRANGE","ARRANGEMENT","ARRIVE","ART","ARTICLE","ARTIST","AS","ASK","ASPECT","ASSEMBLY","ASSESS","ASSESSMENT","ASSET","ASSOCIATE","ASSOCIATION","ASSUME","ASSUMPTION","AT","ATMOSPHERE","ATTACH","ATTACK","ATTEMPT","ATTEND","ATTENTION","ATTITUDE","ATTRACT","ATTRACTIVE","AUDIENCE","AUTHOR","AUTHORITY","AVAILABLE","AVERAGE","AVOID","AWARD","AWARE","AWAY","AYE","BABY","BACK","BACKGROUND","BAD","BAG","BALANCE","BALL","BAND","BANK","BAR","BASE","BASIC","BASIS","BATTLE","BE","BEAR","BEAT","BEAUTIFUL","BECAUSE","BECOME","BED","BEDROOM","BEFORE","BEGIN","BEGINNING","BEHAVIOUR","BEHIND","BELIEF","BELIEVE","BELONG","BELOW","BENEATH","BENEFIT","BESIDE","BEST","BETTER","BETWEEN","BEYOND","BIG","BILL","BIND","BIRD","BIRTH","BIT","BLACK","BLOCK","BLOOD","BLOODY","BLOW","BLUE","BOARD","BOAT","BODY","BONE","BOOK","BORDER","BOTH","BOTTLE","BOTTOM","BOX","BOY","BRAIN","BRANCH","BREAK","BREATH","BRIDGE","BRIEF","BRIGHT","BRING","BROAD","BROTHER","BUDGET","BUILD","BUILDING","BURN","BUS","BUSINESS","BUSY","BUT","BUY","BY","CABINET","CALL","CAMPAIGN","CAN","CANDIDATE","CAPABLE","CAPACITY","CAPITAL","CAR","CARD","CARE","CAREER","CAREFUL","CAREFULLY","CARRY","CASE","CASH","CAT","CATCH","CATEGORY","CAUSE","CELL","CENTRAL","CENTRE","CENTURY","CERTAIN","CERTAINLY","CHAIN","CHAIR","CHAIRMAN","CHALLENGE","CHANCE","CHANGE","CHANNEL","CHAPTER","CHARACTER","CHARACTERISTIC","CHARGE","CHEAP","CHECK","CHEMICAL","CHIEF","CHILD","CHOICE","CHOOSE","CHURCH","CIRCLE","CIRCUMSTANCE","CITIZEN","CITY","CIVIL","CLAIM","CLASS","CLEAN","CLEAR","CLEARLY","CLIENT","CLIMB","CLOSE","CLOSELY","CLOTHES","CLUB","COAL","CODE","COFFEE","COLD","COLLEAGUE","COLLECT","COLLECTION","COLLEGE","COLOUR","COMBINATION","COMBINE","COME","COMMENT","COMMERCIAL","COMMISSION","COMMIT","COMMITMENT","COMMITTEE","COMMON","COMMUNICATION","COMMUNITY","COMPANY","COMPARE","COMPARISON","COMPETITION","COMPLETE","COMPLETELY","COMPLEX","COMPONENT","COMPUTER","CONCENTRATE","CONCENTRATION","CONCEPT","CONCERN","CONCERNED","CONCLUDE","CONCLUSION","CONDITION","CONDUCT","CONFERENCE","CONFIDENCE","CONFIRM","CONFLICT","CONGRESS","CONNECT","CONNECTION","CONSEQUENCE","CONSERVATIVE","CONSIDER","CONSIDERABLE","CONSIDERATION","CONSIST","CONSTANT","CONSTRUCTION","CONSUMER","CONTACT","CONTAIN","CONTENT","CONTEXT","CONTINUE","CONTRACT","CONTRAST","CONTRIBUTE","CONTRIBUTION","CONTROL","CONVENTION","CONVERSATION","COPY","CORNER","CORPORATE","CORRECT","COS","COST","COULD","COUNCIL","COUNT","COUNTRY","COUNTY","COUPLE","COURSE","COURT","COVER","CREATE","CREATION","CREDIT","CRIME","CRIMINAL","CRISIS","CRITERION","CRITICAL","CRITICISM","CROSS","CROWD","CRY","CULTURAL","CULTURE","CUP","CURRENT","CURRENTLY","CURRICULUM","CUSTOMER","CUT","DAMAGE","DANGER","DANGEROUS","DARK","DATA","DATE","DAUGHTER","DAY","DEAD","DEAL","DEATH","DEBATE","DEBT","DECADE","DECIDE","DECISION","DECLARE","DEEP","DEFENCE","DEFENDANT","DEFINE","DEFINITION","DEGREE","DELIVER","DEMAND","DEMOCRATIC","DEMONSTRATE","DENY","DEPARTMENT","DEPEND","DEPUTY","DERIVE","DESCRIBE","DESCRIPTION","DESIGN","DESIRE","DESK","DESPITE","DESTROY","DETAIL","DETAILED","DETERMINE","DEVELOP","DEVELOPMENT","DEVI
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];
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```
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## --seed-contents--
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```js
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function anagramicSquares(words) {
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return true;
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}
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// Only change code above this line
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const testWords1 = [
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"DAMAGE","DANGER","DANGEROUS","DARK","DATA","DATE","DAUGHTER","DAY","DEAD","DEAL","DEATH","DEBATE","DEBT","DECADE","DECIDE","DECISION","DECLARE","DEEP","DEFENCE","DEFENDANT","DEFINE","DEFINITION","DEGREE","DELIVER","DEMAND","DEMOCRATIC","DEMONSTRATE","DENY","DEPARTMENT","DEPEND","DEPUTY","DERIVE","DESCRIBE","DESCRIPTION","DESIGN","DESIRE","DESK","DESPITE","DESTROY","DETAIL","DETAILED","DETERMINE","DEVELOP","DEVELOPMENT","DEVICE","DIE","DIFFERENCE","DIFFERENT","DIFFICULT","DIFFICULTY","DINNER","DIRECT","DIRECTION","DIRECTLY","DIRECTOR","DISAPPEAR","DISCIPLINE","DISCOVER","DISCUSS","DISCUSSION","DISEASE","DISPLAY","DISTANCE","DISTINCTION","DISTRIBUTION","DISTRICT","DIVIDE","DIVISION","DO","DOCTOR","DOCUMENT","DOG","DOMESTIC","DOOR","DOUBLE","DOUBT","DOWN","DRAW","DRAWING","DREAM","DRESS","DRINK","DRIVE","DRIVER","DROP","DRUG","DRY","DUE","DURING","DUTY","LABOUR","LACK","LADY","LAND","LANGUAGE","LARGE","LARGELY","LAST","LATE","LATER","LATTER","LAUGH","LAUNCH","LAW","LAWYER","LAY","LEAD","LEADER","LEADERSHIP","LEADING","LEAF","LEAGUE","LEAN","LEARN","LEAST","LEAVE","LEFT","LEG","LEGAL","LEGISLATION","LENGTH","LESS","LET","LETTER","LEVEL","LIABILITY","LIBERAL","LIBRARY","LIE","LIFE","LIFT","LIGHT","LIKE","LIKELY","LIMIT","LIMITED","LINE","LINK","LIP","LIST","LISTEN","LITERATURE","LITTLE","LIVE","LIVING","LOAN","LOCAL","LOCATION","LONG","LOOK","LORD","LOSE","LOSS","LOT","LOVE","LOVELY","LOW","LUNCH"
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];
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anagramicSquares(testWords1);
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```
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# --solutions--
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```js
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function anagramicSquares(words) {
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// Based on https://www.mathblog.dk/project-euler-98-anagrams-square-numbers/
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function findMaximumSquare(squares, word1, word2) {
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let maximumSquare = 0;
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for (let i = 0; i < squares.length; i++) {
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const length = squares[i].toString().length;
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if (length < word1.length) {
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continue;
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}
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if (length > word1.length) {
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break;
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}
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const word1Square = squares[i];
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const letterToDigit = mapLettersToDigits(word1, word1Square);
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const noProperMappingExist = Object.keys(letterToDigit).length === 0;
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if (noProperMappingExist) {
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continue;
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}
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const word2Square = getNumberFromMapping(word2, letterToDigit);
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if (word2Square === 0) {
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continue;
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}
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const doesWord2SquareExist = squares.indexOf(word2Square) !== -1;
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if (doesWord2SquareExist) {
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const pairMaximum = Math.max(word1Square, word2Square);
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maximumSquare = Math.max(maximumSquare, pairMaximum);
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}
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}
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return maximumSquare;
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}
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function getNumberFromMapping(word, letterToDigit) {
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const wouldNumberHaveLeadingZero = letterToDigit[word[0]] === 0;
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if (wouldNumberHaveLeadingZero) {
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return 0;
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}
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let number = 0;
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for (let i = 0; i < word.length; i++) {
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number = number * 10 + letterToDigit[word[i]];
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}
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return number;
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}
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function mapLettersToDigits(word, square) {
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const letterToDigit = {};
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for (let j = word.length - 1; j >= 0; j--) {
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const curDigit = square % 10;
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square = Math.floor(square / 10);
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const curLetter = word[j];
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const isLetterRepeated = letterToDigit.hasOwnProperty(curLetter);
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if (isLetterRepeated) {
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const isLetterUsedForTheSameDigit =
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letterToDigit[curLetter] === curDigit;
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if (isLetterUsedForTheSameDigit) {
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continue;
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}
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return {};
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}
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const isDigitUsed = Object.values(letterToDigit).indexOf(curDigit) !== -1;
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if (isDigitUsed) {
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return {};
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}
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letterToDigit[curLetter] = curDigit;
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}
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return letterToDigit;
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}
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function groupWordsWithSameLetters(words) {
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const lettersToWords = {};
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for (let i = 0; i < words.length; i++) {
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const word = words[i];
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const sortedLetters = word.split('').sort().join('');
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if (!lettersToWords.hasOwnProperty(sortedLetters)) {
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lettersToWords[sortedLetters] = [];
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}
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lettersToWords[sortedLetters].push(word);
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}
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return lettersToWords;
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}
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const lettersToWords = groupWordsWithSameLetters(words);
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const anagrams = Object.keys(lettersToWords).filter(
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letters => lettersToWords[letters].length > 1
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);
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const lengthOfLongestAnagram = anagrams
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.map(anagram => anagram.length)
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.sort((a, b) => b - a)[0];
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const squares = [];
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const numberLimit = (10 ** lengthOfLongestAnagram) ** 0.5;
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for (let number = 2; number < numberLimit; number++) {
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const square = number ** 2;
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squares.push(square);
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}
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let largestSquare = 0;
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for (let i = 0; i < anagrams.length; i++) {
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const curWords = lettersToWords[anagrams[i]];
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for (let j = 0; j < curWords.length; j++) {
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for (let k = j + 1; k < curWords.length; k++) {
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const squareValue = findMaximumSquare(
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squares,
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curWords[j],
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curWords[k]
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);
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if (squareValue > largestSquare) {
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largestSquare = squareValue;
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}
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}
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}
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}
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return largestSquare;
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}
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```
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