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Heap sort works by transforming the list into a max heap and then swapping the largest element with the last one.

Heap sort is a comparison-based sorting algorithm that uses a binary heap data structure. The algorithm begins by transforming the list into a max heap, a specialised tree-based data structure that satisfies the heap property. In a max heap, for any given node i, the value of i is greater than or equal to the values of its children. This means that the largest element in the heap is the root node.

The next step in the heap sort algorithm is to swap the root node (the largest element) with the last element of the heap. This effectively removes the largest element from the heap and places it in its correct position in the sorted list. The heap size is reduced by one and the heap property is restored by 'heapifying' the root node again. This process is repeated until the heap is empty, resulting in a sorted list.

Heap sort is an in-place algorithm, meaning it does not require additional space and instead sorts the list by manipulating the original data. This makes it a space-efficient sorting algorithm. However, it is not a stable sort, meaning that equal elements may not retain their original order in the sorted list.

The time complexity of heap sort is O(n log n) for both the best and worst case scenarios, making it an efficient sorting algorithm for large data sets. However, it is worth noting that heap sort is typically slower in practice than other O(n log n) algorithms such as quicksort and mergesort due to its high overhead.

In summary, heap sort is a powerful sorting algorithm that works by transforming the list into a max heap and then repeatedly swapping the largest element with the last one. It is an in-place, comparison-based algorithm with a time complexity of O(n log n). Despite its efficiency, it is often overshadowed by quicker algorithms for practical use.

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