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2135. Count Words Obtained After Adding a Letter

Description

You are given two 0-indexed arrays of strings startWords and targetWords. Each string consists of lowercase English letters only.

For each string in targetWords, check if it is possible to choose a string from startWords and perform a conversion operation on it to be equal to that from targetWords.

The conversion operation is described in the following two steps:

  1. Append any lowercase letter that is not present in the string to its end.
    • For example, if the string is "abc", the letters 'd', 'e', or 'y' can be added to it, but not 'a'. If 'd' is added, the resulting string will be "abcd".
  2. Rearrange the letters of the new string in any arbitrary order.
    • For example, "abcd" can be rearranged to "acbd", "bacd", "cbda", and so on. Note that it can also be rearranged to "abcd" itself.

Return the number of strings in targetWords that can be obtained by performing the operations on any string of startWords.

Note that you will only be verifying if the string in targetWords can be obtained from a string in startWords by performing the operations. The strings in startWords do not actually change during this process.

 

Example 1:

Input: startWords = ["ant","act","tack"], targetWords = ["tack","act","acti"]
Output: 2
Explanation:
- In order to form targetWords[0] = "tack", we use startWords[1] = "act", append 'k' to it, and rearrange "actk" to "tack".
- There is no string in startWords that can be used to obtain targetWords[1] = "act".
  Note that "act" does exist in startWords, but we must append one letter to the string before rearranging it.
- In order to form targetWords[2] = "acti", we use startWords[1] = "act", append 'i' to it, and rearrange "acti" to "acti" itself.

Example 2:

Input: startWords = ["ab","a"], targetWords = ["abc","abcd"]
Output: 1
Explanation:
- In order to form targetWords[0] = "abc", we use startWords[0] = "ab", add 'c' to it, and rearrange it to "abc".
- There is no string in startWords that can be used to obtain targetWords[1] = "abcd".

 

Constraints:

  • 1 <= startWords.length, targetWords.length <= 5 * 104
  • 1 <= startWords[i].length, targetWords[j].length <= 26
  • Each string of startWords and targetWords consists of lowercase English letters only.
  • No letter occurs more than once in any string of startWords or targetWords.

Solutions

Solution 1: Hash Table + Bit Manipulation

We notice that the given strings only contain lowercase letters, and each letter in a string appears at most once. Therefore, we can represent a string with a binary number of length $26$, where the $i$-th bit being $1$ indicates that the string contains the $i$-th lowercase letter, and $0$ indicates the absence of the $i$-th lowercase letter.

We can convert each string in the array $\textit{startWords}$ into a binary number and store these binary numbers in a set $\textit{s}$. For each string in the array $\textit{targetWords}$, we first convert it into a binary number, then enumerate each letter in this string, remove this letter from the binary number, and check if there exists a binary number in the set $\textit{s}$ such that the XOR result of this binary number with the removed letter's binary number is in the set $\textit{s}$. If such a binary number exists, then this string can be obtained by performing a transformation operation on some string in $\textit{startWords}$, and we increment the answer by one. Then, we skip this string and continue processing the next string.

The time complexity is $O(n \times |\Sigma|)$, and the space complexity is $O(n)$. Here, $n$ is the length of the string array $\textit{targetWords}$, and $|\Sigma|$ is the size of the character set in the string, which is $26$ in this problem.

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class Solution:
    def wordCount(self, startWords: List[str], targetWords: List[str]) -> int:
        s = {sum(1 << (ord(c) - 97) for c in w) for w in startWords}
        ans = 0
        for w in targetWords:
            x = sum(1 << (ord(c) - 97) for c in w)
            for c in w:
                if x ^ (1 << (ord(c) - 97)) in s:
                    ans += 1
                    break
        return ans

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class Solution {
    public int wordCount(String[] startWords, String[] targetWords) {
        Set<Integer> s = new HashSet<>();
        for (var w : startWords) {
            int x = 0;
            for (var c : w.toCharArray()) {
                x |= 1 << (c - 'a');
            }
            s.add(x);
        }
        int ans = 0;
        for (var w : targetWords) {
            int x = 0;
            for (var c : w.toCharArray()) {
                x |= 1 << (c - 'a');
            }
            for (var c : w.toCharArray()) {
                if (s.contains(x ^ (1 << (c - 'a')))) {
                    ++ans;
                    break;
                }
            }
        }
        return ans;
    }
}

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class Solution {
public:
    int wordCount(vector<string>& startWords, vector<string>& targetWords) {
        unordered_set<int> s;
        for (auto& w : startWords) {
            int x = 0;
            for (char c : w) {
                x |= 1 << (c - 'a');
            }
            s.insert(x);
        }
        int ans = 0;
        for (auto& w : targetWords) {
            int x = 0;
            for (char c : w) {
                x |= 1 << (c - 'a');
            }
            for (char c : w) {
                if (s.contains(x ^ (1 << (c - 'a')))) {
                    ++ans;
                    break;
                }
            }
        }
        return ans;
    }
};

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func wordCount(startWords []string, targetWords []string) (ans int) {
    s := map[int]bool{}
    for _, w := range startWords {
        x := 0
        for _, c := range w {
            x |= 1 << (c - 'a')
        }
        s[x] = true
    }
    for _, w := range targetWords {
        x := 0
        for _, c := range w {
            x |= 1 << (c - 'a')
        }
        for _, c := range w {
            if s[x^(1<<(c-'a'))] {
                ans++
                break
            }
        }
    }
    return
}

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function wordCount(startWords: string[], targetWords: string[]): number {
    const s = new Set<number>();
    for (const w of startWords) {
        let x = 0;
        for (const c of w) {
            x ^= 1 << (c.charCodeAt(0) - 97);
        }
        s.add(x);
    }
    let ans = 0;
    for (const w of targetWords) {
        let x = 0;
        for (const c of w) {
            x ^= 1 << (c.charCodeAt(0) - 97);
        }
        for (const c of w) {
            if (s.has(x ^ (1 << (c.charCodeAt(0) - 97)))) {
                ++ans;
                break;
            }
        }
    }
    return ans;
}

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