Compare Strings by Frequency of the Smallest Character

Problem Description

Let the function f(s) be the frequency of the lexicographically smallest character in a non-empty string s. You are given an array of strings words and another array of query strings queries. For each query queries[i], count the number of words in words such that f(queries[i]) < f(W) for each W in words. Return an integer array answer, where each answer[i] is the answer to the i-th query.

Key Insights

• The function f(s) requires identifying the smallest character in the string and counting its occurrences.
• Each query must be compared against all words, making an efficient approach essential due to potential input size.
• Sorting the words based on their f(W) values allows for quick comparisons using binary search.

Space and Time Complexity

Time Complexity: O(n * m + q * log(n)), where n is the number of words, m is the average length of words, and q is the number of queries. Space Complexity: O(n), for storing the frequencies of the smallest characters of each word.

Solution

To solve the problem, we can follow these steps:

1. Create a helper function that calculates f(s), which finds the smallest character in the string and counts its occurrences.
2. For each word in the words array, compute f(W) and store these values alongside the words.
3. Sort the computed values.
4. For each query, compute f(queries[i]) and use binary search to find the count of words where f(queries[i]) < f(W).
5. Return the results as an array.

This approach efficiently reduces the number of comparisons needed for each query by leveraging sorting and binary search.

Code Solutions