Introsort

Introsort is a hybrid sorting algorithm that combines the strengths of quicksort, heapsort, and insertion sort to provide efficient performance in a wide range of scenarios. It was designed by David Musser in 1997. The primary goal of introsort is to achieve the average-case speed of quicksort while guaranteeing worst-case O(n log n) performance, thus avoiding the quadratic time complexity that quicksort can exhibit in certain situations.

The algorithm begins with quicksort. However, it tracks the recursion depth. If the depth exceeds a certain limit, typically based on the logarithm of the number of elements being sorted, introsort switches to heapsort. This limit is designed to prevent quicksort from degenerating into its worst-case behavior due to pathological input data.

Heapsort guarantees O(n log n) performance but is generally slower than quicksort in the average case. Introsort utilizes heapsort only when quicksort is exhibiting signs of poor performance.

Finally, when the size of the partition being sorted becomes sufficiently small, introsort switches to insertion sort. Insertion sort is efficient for small datasets because of its low overhead. For small sub-arrays, the overhead of quicksort or heapsort can outweigh their advantages, making insertion sort the faster choice.

In summary, introsort's adaptive approach leverages the advantages of different sorting algorithms to provide a robust and efficient sorting solution. It combines the speed of quicksort with the worst-case guarantee of heapsort and the efficiency of insertion sort for small partitions.