Description Link to heading

1255. Maximum Score Words Formed by Letters (Hard)

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.

Solution Link to heading

We can use a hash table letters_arr to keep track of the numbers of letters that can be used when backtracking.

Code Link to heading 

class Solution {
  public:
    int dfs(int st_idx, vector<int> &letters_arr, vector<string> &words, vector<int> &score) {
        if (st_idx >= words.size()) {
            return 0;
        }
        int maxnum = 0;
        for (int i = st_idx; i < words.size(); i++) {
            int total = 0;
            bool check = true;
            for (char &c : words[i]) {
                letters_arr[c - 'a']--;
                total += score[c - 'a'];
                if (letters_arr[c - 'a'] < 0) {
                    check = false;
                }
            }
            if (check) {
                maxnum = std::max(maxnum, total + dfs(i + 1, letters_arr, words, score));
            }
            for (char &c : words[i]) {
                letters_arr[c - 'a']++;
            }
        }
        return maxnum;
    }
    int maxScoreWords(vector<string> &words, vector<char> &letters, vector<int> &score) {
        vector<int> words_arr(26, 0);
        vector<int> letters_arr(26, 0);
        for (int i = 0; i < letters.size(); i++) {
            letters_arr[letters[i] - 'a']++;
        }
        // 回溯
        return dfs(0, letters_arr, words, score);
    }
};