Minimum Length of Anagram Concatenation

Problem Description

You are given a string s, which is known to be a concatenation of anagrams of some string t. Return the minimum possible length of the string t. An anagram is formed by rearranging the letters of a string.

Key Insights

• Anagrams consist of the same characters with the same frequency.
• The minimum length of t is determined by the highest frequency of any character in s.
• If a character appears k times in s, it contributes at least ceil(k / m) to the length of t, where m is the number of anagrams of t present in s.
• The solution requires counting the frequency of characters in s and utilizing these counts to deduce the minimum length of t.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the string s.
Space Complexity: O(1), as the frequency count is limited to a fixed size (26 for lowercase English letters).

Solution

To solve the problem, we will:

1. Count the frequency of each character in the string s using a hash table (or dictionary).
2. Identify the maximum frequency among the characters.
3. The minimum length of t will be the maximum frequency found, as each character must appear at least once in t to form the anagrams.

Code Solutions