Frequency Bucket Logic (Grouping Elements by Frequency for Efficient Processing)

Bucket by frequency groups all values that appear the same number of times—classic for “top k frequent”, deletion scheduling, or building inverse indexes from counts.

Why this shows up in the real world

CDN cache eviction sometimes approximates frequency tiers; batch jobs bucket SKUs by popularity for different SLA tiers.

Core idea (explained for students)

After counting, invert the map: bucket[count] = list of values. Iterate counts from high to low to stream answers without sorting all elements.

Try this in Python

from collections import Counter, defaultdict


def bucket_by_freq(nums: list[int]) -> dict[int, list[int]]:
    c = Counter(nums)
    buckets: dict[int, list[int]] = defaultdict(list)
    for v, k in c.items():
        buckets[k].append(v)
    return dict(buckets)


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

Common mistakes

• Buckets with empty lists when a frequency never occurs—skip gracefully.
• Stable tie-breaking: problem may require lexicographic order among ties.

Key takeaways

• Time is often O(n) for count + O(U log U) for unique keys—still linear when U ≤ n.
• Use defaultdict(list) to append values per frequency.