freeCodeCamp/curriculum/challenges/portuguese/10-coding-interview-prep/project-euler/problem-98-anagramic-squares.md

---
id: 5900f3cf1000cf542c50fee1
title: 'Problema 98: Quadrados anagrâmicos'
challengeType: 5
forumTopicId: 302215
dashedName: problem-98-anagramic-squares
---

# --description--

Ao substituir cada uma das letras na palavra CARE por 1, 2, 9 e 6, respectivamente, formamos um número quadrado: $1296 = 36^2$. O que é notável é que, usando as mesmas substituições digitais, o anagrama, RACE, também formamos um número quadrado: $9216 = 96^2$. Vamos chamar CARE (e RACE) de um par de palavras de anagrama quadrado. Especificaremos mais adiante que zeros à frente do número não são permitidos, nem uma outra letra pode ter o mesmo valor numérico que outra.

Usando o array `words`, encontre todos os pares de palavras que são anagramas quadrados (uma palavra palindrômica NÃO é considerada um anagrama de si mesmo).

Qual é o maior número quadrado formado por algum membro de um par desse tipo?

**Observação:** todos os anagramas formados devem estar contidos no array dado `words`.

# --hints--

`anagramicSquares(['CARE', 'RACE'])` deve retornar um número.

```js
assert(typeof anagramicSquares(['CARE', 'RACE']) === 'number');
```

`anagramicSquares(['CARE', 'RACE'])` deve retornar `9216`.

```js
assert.strictEqual(anagramicSquares(['CARE', 'RACE']), 9216);
```

`anagramicSquares(testWords1)` deve retornar `4761`.

```js
assert.strictEqual(anagramicSquares(_testWords1), 4761);
```

`anagramicSquares(testWords2)` deve retornar `18769`.

```js
assert.strictEqual(anagramicSquares(_testWords2), 18769);
```

# --seed--

## --after-user-code--

```js
const _testWords1 = [
  "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"
];
const _testWords2 = [
  "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
];
```

## --seed-contents--

```js
function anagramicSquares(words) {

  return true;
}

// Only change code above this line
const testWords1 = [
"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"
];

anagramicSquares(testWords1);
```

# --solutions--

```js
function anagramicSquares(words) {
  // Based on https://www.mathblog.dk/project-euler-98-anagrams-square-numbers/
  function findMaximumSquare(squares, word1, word2) {
    let maximumSquare = 0;

    for (let i = 0; i < squares.length; i++) {
      const length = squares[i].toString().length;

      if (length < word1.length) {
        continue;
      }
      if (length > word1.length) {
        break;
      }

      const word1Square = squares[i];
      const letterToDigit = mapLettersToDigits(word1, word1Square);

      const noProperMappingExist = Object.keys(letterToDigit).length === 0;
      if (noProperMappingExist) {
        continue;
      }

      const word2Square = getNumberFromMapping(word2, letterToDigit);
      if (word2Square === 0) {
        continue;
      }

      const doesWord2SquareExist = squares.indexOf(word2Square) !== -1;
      if (doesWord2SquareExist) {
        const pairMaximum = Math.max(word1Square, word2Square);
        maximumSquare = Math.max(maximumSquare, pairMaximum);
      }
    }
    return maximumSquare;
  }

  function getNumberFromMapping(word, letterToDigit) {
    const wouldNumberHaveLeadingZero = letterToDigit[word[0]] === 0;
    if (wouldNumberHaveLeadingZero) {
      return 0;
    }

    let number = 0;
    for (let i = 0; i < word.length; i++) {
      number = number * 10 + letterToDigit[word[i]];
    }
    return number;
  }

  function mapLettersToDigits(word, square) {
    const letterToDigit = {};
    for (let j = word.length - 1; j >= 0; j--) {
      const curDigit = square % 10;
      square = Math.floor(square / 10);

      const curLetter = word[j];

      const isLetterRepeated = letterToDigit.hasOwnProperty(curLetter);
      if (isLetterRepeated) {
        const isLetterUsedForTheSameDigit =
          letterToDigit[curLetter] === curDigit;
        if (isLetterUsedForTheSameDigit) {
          continue;
        }

        return {};
      }

      const isDigitUsed = Object.values(letterToDigit).indexOf(curDigit) !== -1;
      if (isDigitUsed) {
        return {};
      }

      letterToDigit[curLetter] = curDigit;
    }
    return letterToDigit;
  }

  function groupWordsWithSameLetters(words) {
    const lettersToWords = {};
    for (let i = 0; i < words.length; i++) {
      const word = words[i];
      const sortedLetters = word.split('').sort().join('');
      if (!lettersToWords.hasOwnProperty(sortedLetters)) {
        lettersToWords[sortedLetters] = [];
      }
      lettersToWords[sortedLetters].push(word);
    }
    return lettersToWords;
  }

  const lettersToWords = groupWordsWithSameLetters(words);

  const anagrams = Object.keys(lettersToWords).filter(
    letters => lettersToWords[letters].length > 1
  );
  const lengthOfLongestAnagram = anagrams
    .map(anagram => anagram.length)
    .sort((a, b) => b - a)[0];

  const squares = [];
  const numberLimit = (10 ** lengthOfLongestAnagram) ** 0.5;
  for (let number = 2; number < numberLimit; number++) {
    const square = number ** 2;
    squares.push(square);
  }

  let largestSquare = 0;
  for (let i = 0; i < anagrams.length; i++) {
    const curWords = lettersToWords[anagrams[i]];

    for (let j = 0; j < curWords.length; j++) {
      for (let k = j + 1; k < curWords.length; k++) {
        const squareValue = findMaximumSquare(
          squares,
          curWords[j],
          curWords[k]
        );
        if (squareValue > largestSquare) {
          largestSquare = squareValue;
        }
      }
    }
  }

  return largestSquare;
}
```