Interactive heap sort. Build a max-heap, then repeatedly swap the root (max) to the end and sift the new root down.
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First build a max-heap (parent ≥ children), then pull the max off the top n−1 times.
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build max-heap (bottom-up)
heapify each non-leaf down
repeat n-1 times:
swap root (max) to the end
shrink heap by one
sift-down the new root
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