Remove Letter To Equalize Frequency

Problem Description

You are given a 0-indexed string word, consisting of lowercase English letters. You need to select one index and remove the letter at that index from word so that the frequency of every letter present in word is equal. Return true if it is possible to remove one letter so that the frequency of all letters in word are equal, and false otherwise.

Key Insights

• The frequency of each character in the string must be analyzed.
• Removing a character may result in all remaining characters having the same frequency.
• There are specific frequency patterns that can lead to a valid solution, such as:
  • All characters have the same frequency.
  • All but one character have the same frequency, and one character occurs exactly once more than the others.

Space and Time Complexity

Time Complexity: O(n) - We traverse the string to count frequencies and then analyze the frequency counts. Space Complexity: O(1) - The frequency count array has a fixed size of 26 for the lowercase English letters.

Solution

To solve this problem, we will use a hash table (or a frequency array) to count the occurrences of each character in the string. After counting, we will analyze the frequency of those counts. The algorithm checks for the possible configurations of frequencies that allow for the removal of a single character to equalize the rest.

1. Count the frequency of each character in the string.
2. Count how many times each frequency occurs.
3. Analyze the frequency counts:
   • If there is only one unique frequency, return true (removing any character will maintain equal frequency).
   • If there are two unique frequencies:
     • Check if one frequency occurs once and is either one greater than the other or is exactly one (i.e., removing this character balances the frequencies).

Code Solutions