Minimum Operations to Make Character Frequencies Equal

Problem Description

You are given a string s. A string t is called good if all characters of t occur the same number of times. You can perform the following operations any number of times:

• Delete a character from s.
• Insert a character in s.
• Change a character in s to its next letter in the alphabet.

Return the minimum number of operations required to make s good.

Key Insights

• The objective is to ensure that all characters in the string have equal frequencies.
• Operations allowed include insertion, deletion, and character transformation.
• The problem can be approached by analyzing character frequencies and determining the optimal target frequency for the characters.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1) (since the number of distinct characters is fixed at 26)

Solution

To solve this problem, we can use a frequency count of each character in the string. By counting how many times each character appears, we can identify the unique frequencies and determine the minimum number of operations needed to make all frequencies equal.

1. Count the frequency of each character in the string.
2. Create a frequency map to determine how many characters have each frequency.
3. For each possible target frequency (from 1 to the maximum frequency), calculate the total operations needed to adjust all character frequencies to this target.
4. Return the minimum number of operations found.

This approach ensures that we explore the fewest possible operations needed to equalize character frequencies.

Code Solutions