Question

1255. Maximum Score Words Formed by Letters

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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 1: Binary Enumeration

Given the small data range in the problem, we can use binary enumeration to enumerate all word combinations for the given word list. Then, we check whether each word combination meets the requirements of the problem. If it does, we calculate its score and finally take the word combination with the highest score.

First, we use a hash table or array $cnt$ to record the number of occurrences of each letter in the alphabet $letters$.

Next, we use binary enumeration to enumerate all word combinations. Each bit in the binary represents whether each word in the word list is selected. If the $i$th bit is $1$, it means the $i$th word is selected; otherwise, the $i$th word is not selected.

Then, we count the number of occurrences of each letter in the current word combination and record it in the hash table or array $cur$. If the number of occurrences of each letter in $cur$ is not greater than the corresponding letter in $cnt$, it means the current word combination meets the requirements of the problem. We calculate the score of the current word combination and take the word combination with the highest score.

The time complexity is $(2^n \times n \times M)$, and the space complexity is $O(C)$. Where $n$ and $M$ are the number of words in the word set and the maximum length of the word, respectively; and $C$ is the number of letters in the alphabet, in this problem, $C=26$.

class Solution:
  def maxScoreWords(
    self, words: List[str], letters: List[str], score: List[int]
  ) -> int:
    cnt = Counter(letters)
    n = len(words)
    ans = 0
    for i in range(1 << n):
      cur = Counter(''.join([words[j] for j in range(n) if i >> j & 1]))
      if all(v <= cnt[c] for c, v in cur.items()):
        t = sum(v * score[ord(c) - ord('a')] for c, v in cur.items())
        ans = max(ans, t)
    return ans

class Solution {
  public int maxScoreWords(String[] words, char[] letters, int[] score) {
    int[] cnt = new int[26];
    for (int i = 0; i < letters.length; ++i) {
      cnt[letters[i] - 'a']++;
    }
    int n = words.length;
    int ans = 0;
    for (int i = 0; i < 1 << n; ++i) {
      int[] cur = new int[26];
      for (int j = 0; j < n; ++j) {
        if (((i >> j) & 1) == 1) {
          for (int k = 0; k < words[j].length(); ++k) {
            cur[words[j].charAt(k) - 'a']++;
          }
        }
      }
      boolean ok = true;
      int t = 0;
      for (int j = 0; j < 26; ++j) {
        if (cur[j] > cnt[j]) {
          ok = false;
          break;
        }
        t += cur[j] * score[j];
      }
      if (ok && ans < t) {
        ans = t;
      }
    }
    return ans;
  }
}

class Solution {
public:
  int maxScoreWords(vector<string>& words, vector<char>& letters, vector<int>& score) {
    int cnt[26]{};
    for (char& c : letters) {
      cnt[c - 'a']++;
    }
    int n = words.size();
    int ans = 0;
    for (int i = 0; i < 1 << n; ++i) {
      int cur[26]{};
      for (int j = 0; j < n; ++j) {
        if (i >> j & 1) {
          for (char& c : words[j]) {
            cur[c - 'a']++;
          }
        }
      }
      bool ok = true;
      int t = 0;
      for (int j = 0; j < 26; ++j) {
        if (cur[j] > cnt[j]) {
          ok = false;
          break;
        }
        t += cur[j] * score[j];
      }
      if (ok && ans < t) {
        ans = t;
      }
    }
    return ans;
  }
};

func maxScoreWords(words []string, letters []byte, score []int) (ans int) {
  cnt := [26]int{}
  for _, c := range letters {
    cnt[c-'a']++
  }
  n := len(words)
  for i := 0; i < 1<<n; i++ {
    cur := [26]int{}
    for j := 0; j < n; j++ {
      if i>>j&1 == 1 {
        for _, c := range words[j] {
          cur[c-'a']++
        }
      }
    }
    ok := true
    t := 0
    for i, v := range cur {
      if v > cnt[i] {
        ok = false
        break
      }
      t += v * score[i]
    }
    if ok && ans < t {
      ans = t
    }
  }
  return
}