Find the Most Frequent Character with a Tie-Breaker

Problem Statement

Given a string s consisting of lowercase English letters, find the character that appears most frequently. If there is a tie between multiple characters with the same maximum frequency, return the character that comes first in alphabetical order (lexicographically smallest).

Your solution should be efficient enough to process strings containing millions of characters.

Function Signature

def most_frequent_char(s: str) -> str:
    pass

Input & Output Format

• Input: A non-empty string s containing only lowercase English letters ('a' through 'z').
• Output: A single lowercase English character representing the most frequent character with tie-breaking applied.

Constraints

• 1 <= len(s) <= 10^7
• s contains only lowercase English letters ('a' - 'z').
• Target time complexity: O(n) where n = len(s).
• Target space complexity: O(1) auxiliary space beyond the input string.

Examples

Example 1

Input: s = "abacaba"
Output: "a"
Explanation: 'a' appears 4 times, 'b' appears 2 times, and 'c' appears 1 time. The highest frequency is 4, belonging to 'a'.

Example 2

Input: s = "dcbaabcd"
Output: "a"
Explanation:
Frequencies:
- 'a': 2
- 'b': 2
- 'c': 2
- 'd': 2
All characters tie with a frequency of 2. Alphabetically, 'a'  `"z"`).
- String where all characters are distinct (tie among all present characters; return the alphabetically smallest).
- Very large strings (`~10^7` characters) where avoiding unnecessary object allocations is critical.