Tracking Maximum Frequency

Track the maximum frequency while counts mutate: maintain best and update in O(1) when a single key increments—avoid scanning all keys each time when possible.

Why this shows up in the real world

Leaderboards keep top score; rate limiters track hottest keys in a time bucket.

Core idea (explained for students)

On cnt[x]+=1: if new count > best, update. On decrement affecting the current champion, re-scan or maintain a reverse index freq_to_keys for O(1) amortized advanced structures.

Try this in Python

from collections import Counter


def max_freq(nums: list[int]) -> int:
    return max(Counter(nums).values()) if nums else 0


print(max_freq([1, 2, 2, 3, 3, 3]))

Common mistakes

• Assuming max is unique—ties may matter.
• Forgetting to drop keys at count 0 from auxiliary structures.

Key takeaways

• For static counts, max(counter.values()) is simplest.
• For streaming, evaluate whether lazy recompute of max every k steps is acceptable.