1255. Maximum Score Words Formed by Letters

Description

Given a list of words, list of  single letters (might be repeating) and score of every character.

Return the maximum score of any valid set of words formed by using the given letters (words[i] cannot be used two or more times).

It is not necessary to use all characters in letters and each letter can only be used once. Score of letters 'a', 'b', 'c', ... ,'z' is given by score[0], score[1], ... , score[25] respectively.

 

Example 1:

Input: words = ["dog","cat","dad","good"], letters = ["a","a","c","d","d","d","g","o","o"], score = [1,0,9,5,0,0,3,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0]
Output: 23
Explanation:
Score  a=1, c=9, d=5, g=3, o=2
Given letters, we can form the words "dad" (5+1+5) and "good" (3+2+2+5) with a score of 23.
Words "dad" and "dog" only get a score of 21.

Example 2:

Input: words = ["xxxz","ax","bx","cx"], letters = ["z","a","b","c","x","x","x"], score = [4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,10]
Output: 27
Explanation:
Score  a=4, b=4, c=4, x=5, z=10
Given letters, we can form the words "ax" (4+5), "bx" (4+5) and "cx" (4+5) with a score of 27.
Word "xxxz" only get a score of 25.

Example 3:

Input: words = ["leetcode"], letters = ["l","e","t","c","o","d"], score = [0,0,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0]
Output: 0
Explanation:
Letter "e" can only be used once.

 

Constraints:

• 1 <= words.length <= 14
• 1 <= words[i].length <= 15
• 1 <= letters.length <= 100
• letters[i].length == 1
• score.length == 26
• 0 <= score[i] <= 10
• words[i], letters[i] contains only lower case English letters.

 

Solutions

Solution: Backtracking

• Time complexity: O(n*2ⁿ*words[i].length)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {string[]} words
 * @param {character[]} letters
 * @param {number[]} score
 * @return {number}
 */
const maxScoreWords = function (words, letters, score) {
  const BASE_CODE = 'a'.charCodeAt(0);
  const n = words.length;

  const getCode = letter => letter.charCodeAt(0) - BASE_CODE;

  const wordScores = words.map(word => {
    let result = 0;

    for (const letter of word) {
      result += score[getCode(letter)];
    }
    return result;
  });
  const letterCounts = Array.from({ length: 26 }, () => 0);

  for (const letter of letters) {
    letterCounts[getCode(letter)] += 1;
  }

  const useOrUnuseWord = (word, count) => {
    let isValid = true;

    for (const letter of word) {
      const code = getCode(letter);

      if (!letterCounts[code]) {
        isValid = false;
      }
      letterCounts[code] += count;
    }
    return isValid;
  };

  const getScore = start => {
    if (start >= n) return 0;
    let result = 0;

    for (let index = start; index < n; index++) {
      const word = words[index];
      const isValid = useOrUnuseWord(word, -1);

      if (isValid) {
        const nextScore = wordScores[index] + getScore(index + 1);

        result = Math.max(nextScore, result);
      }
      useOrUnuseWord(word, 1);
    }
    return result;
  };

  return getScore(0);
};