Problem Description

In this problem, we are given two arrays of strings: queries and dictionary. Each string consists only of lowercase English letters, and every string in both arrays is of the same length.

We need to perform edits on the words in queries. An edit is defined as changing any single letter in a word to any other letter. Our objective is to determine which words from queries can be transformed into any word from dictionary using at most two such edits.

The output should be a list of words from queries that can be matched with any word in dictionary after performing no more than two edits. The returned list must preserve the original order of words as they appear in queries.

Intuition

The intuition behind the solution is to iterate over each word in queries and each word in dictionary, comparing them letter by letter. For each pair of words, we count the number of letters that are different between them. This count is the number of edits needed to transform the query word into the dictionary word.

Since we are allowed up to two edits, we look for pairs of words where the number of differing letters is less than or equal to two. If such a pair is found, the query word qualifies as a match, and we add it to our answer list.

We proceed with this process until we have checked the word from queries against all words in dictionary, ensuring we do not exceed two edits. The crucial observation is that any query word can be transformed into any dictionary word by changing at most two letters - signifying that the edit distance between them is less than or equal to two.

This approach ensures that we examine all possible pairs of words, and when a match is found, we immediately move to the next word in queries to maintain efficiency. We exit the inner loop early using break once we append the query word to the answer list, as we do not need any more comparisons for that word.

Solution Approach

The given Python code defines a class Solution with a method twoEditWords, which takes two parameters: queries and dictionary. These parameters are lists of strings representing the words we will be working with. The method returns a list of strings.

1class Solution:
2    def twoEditWords(self, queries: List[str], dictionary: List[str]) -> List[str]:
3        ans = []
4        for s in queries:
5            for t in dictionary:
6                if sum(a != b for a, b in zip(s, t)) < 3:
7                    ans.append(s)
8                    break
9        return ans

The algorithm proceeds with the following steps:

1. Initialize an empty list ans to store the final matching words from queries.
2. Iterate over each word s from queries.
3. For each word s, iterate over each word t from dictionary.
4. Zip the two words s and t to compare their corresponding letters. The built-in zip function pairs up elements from two iterables, allowing us to iterate over them in parallel.
5. Use a generator expression inside the sum function to count the number of differing letters between s and t. We compare each pair of letters and count a difference whenever a pair does not match (a != b).
6. If the count is less than 3 (meaning we can turn s into t with at most two edits), we append s to our answer list. This is because we are only allowed a maximum of two edits.
7. Once a word from queries matches a word from dictionary, break out of the inner loop to avoid unnecessary comparisons and move to the next word in queries.
8. After going through all the words in queries, return the answer list ans.

This solution uses a brute-force approach and takes advantage of Python's concise syntax for list comprehension and the sum function. This approach works efficiently when the dataset is not prohibitively large since it explores all possible pairs of words from queries and dictionary and calculates the edit distance in a straightforward manner.

However, it's worth noting that this algorithm has a quadratic time complexity with respect to the number of words in queries and dictionary. Therefore, for very large datasets, the performance might be a concern, and more sophisticated algorithms could be required to optimize the search and comparison processes.

Example Walkthrough

Let's take a small example to illustrate the solution approach using the Python code provided.

Suppose we have the following arrays:

• queries = ["abc", "def", "ghi"]
• dictionary = ["abd", "def", "hij"]

The question tells us that we can make at most two edits on each word in queries to see if it can match any word in dictionary. Let's walk through each word:

1. Starting with the first word in queries, which is "abc":

   • When we compare "abc" to "abd" in dictionary, we notice that they differ by one character (c != d). Since only one edit is needed, "abc" can be transformed into "abd" with a single change. Therefore, "abc" satisfies the condition of two or fewer edits and is appended to our answer list.
   • We do not need to compare "abc" further with other words in dictionary because we found a match. We move to the next word in queries.

2. Now, look at the second word in queries, "def":

   • Comparing "def" with "abd" from dictionary, we find three different characters, meaning we need more than two edits, so we move to the next word in dictionary.
   • The next comparison is between "def" from queries and "def" from dictionary. They are identical, so zero edits are required, and "def" is added to our answer list. Then we exit the inner loop and proceed to the next query.

3. Finally, for the third word in queries, "ghi":

   • We compare "ghi" with "abd" from dictionary, and all three characters are different, requiring more than two edits. So we continue to the next word in dictionary.
   • We compare "ghi" with "def" from dictionary, but again all characters differ, so we move on to the last word.
   • The last comparison is between "ghi" from queries and "hij" from dictionary. Here we see that only one character differs (g != h), so we can make one edit to match them. "ghi" is then added to our answer list, and we finish reviewing queries.

The final returned list (ans) from the twoEditWords method is ["abc", "def", "ghi"], preserving the original order from queries. Each of these words can be transformed into a word in dictionary with no more than two edits.

Using this example, we can see how the solution approach successfully iterates over the queries and dictionary, compares the words, and keeps track of the number of edits necessary to determine if a word from queries can be turned into any word in dictionary within the allowed edits.

Solution Implementation

Time and Space Complexity

Time Complexity

The given code has two nested loops; the outer loop iterates through each string in queries, while the inner loop iterates through each string in dictionary. Within the inner loop, there's a comparison of corresponding characters in two strings (from queries and dictionary) made using a generator expression with a zip function and sum. This comparison runs in O(min(len(s), len(t))) time, where len(s) and len(t) represent the lengths of the individual strings being compared.

To determine the time complexity of the entire code, we have to consider the lengths of the queries and dictionary lists and the average lengths of the strings within them. Let n denote the number of strings in queries, m denote the number of strings in dictionary, and L be the average length of the strings in both lists. The total time complexity is thus:

O(n * m * L)

For every string in queries, every string in dictionary is checked, and for each comparison, an iteration over the length of the strings occurs.

Space Complexity

The space complexity of the code consists of the space needed to store the ans list and the temporary space for the comparison operation. The ans list, in the worst case, will store all strings from queries. Therefore, its space complexity depends on the length of the output list, which is at most n (where n is the number of strings in queries).

The generator expression with zip and sum does not create a list of differences but rather creates an iterator, which takes constant space.

Hence, the space complexity is:

O(n)

This represents the space needed to store the ans list. The rest of the operations use constant additional space (ignoring the overhead of the input and the internal working storage of Python's function calls).

Learn more about how to find time and space complexity quickly using problem constraints.