Quick Sort vs Heap Sort
Quick Sort vs Heap Sort pits average-case speed against worst-case reliability. Both are in-place comparison sorts, but they behave very differently under pressure. Understanding the trade-off explains why production libraries combine them in Introsort.
The core trade-off
Quick Sort is faster on average (O(n log n)) thanks to cache-friendly partitioning, but its worst case is O(n²). Heap Sort is slower on average due to scattered memory access, but guarantees O(n log n) on every input. Both use roughly O(1)-O(log n) extra space and neither is stable.
When to choose each
Choose Quick Sort for general-purpose speed where average performance matters most. Choose Heap Sort when you need a hard worst-case guarantee — real-time systems, security-sensitive code, or anywhere an adversary might craft inputs to trigger Quick Sort's O(n²) blow-up.
The best of both: Introsort
You do not always have to choose. Introsort runs Quick Sort but falls back to Heap Sort when recursion gets too deep, capturing Quick Sort's speed and Heap Sort's guarantee. This hybrid is what C++ std::sort uses.
Frequently asked questions
Is Heap Sort better than Quick Sort? +
Why is Quick Sort faster than Heap Sort? +
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