Algorithms / Heap Frontier Top K
Least You Need to Know: K-Way Merge, Top-K, and Heap Frontier Ideas
Heaps are useful when many sorted or partially ordered sources expose only a few promising next candidates. The heap stores the current frontier so you can pop the next best item without materializing every unseen option.
Least you need to know
- In k-way merge, the heap usually stores one frontier item from each still-active list.
- After popping one item, push only the next item from the same source that produced it.
- For top-k tasks, a heap can avoid fully sorting every element when only a small frontier matters.
- Heap size often reflects the number of active sources, not the total number of items.
- The key idea is frontier management, not total order over the whole dataset.
Key notation
- frontier — current best visible candidates from all sources
- k-way merge — merge multiple sorted streams into one order
- top-k — only the k best items are required
Worked example
- Suppose you have k sorted log streams and need the global next event each time.
- Put the first item from each stream into a min-heap.
- Pop the smallest visible item.
- Then push only the next item from that same stream.
- The heap never needs to hold every unseen item at once.
Common mistakes
- Students often push all items into the heap immediately, losing the frontier advantage.
- Students often forget to push the successor from the same list after popping.
- Students often use full sorting when the task only asks for a small top-k result.
How to recognize it
- You have multiple sorted sources or a large pool but only need a small frontier.
- Each step reveals only a few new candidates after one extraction.
- Heap size should stay tied to active sources or k, not total input size.
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