Comparison Summary: Time and Space

Having completed our detailed analysis of Quick Sort's performance characteristics, we now consolidate all five sorting algorithms into a single, comprehensive comparison.

The summary table below highlights the crucial trade-offs between the simple quadratic sorts ($O(n^2)$) and the efficient divide-and-conquer sorts ($O(n \log n)$).
$O(n^2)$ algorithms (Bubble, Selection, Insertion) are desirable for their simplicity and extremely low auxiliary space requirements ($O(1)$), making them ideal for small data sets or highly constrained memory environments.
Merge Sort and Quick Sort offer superior performance for large inputs, but they embody different trade-offs:
Merge Sort is inherently Stable but requires significant auxiliary space ($O(n)$).
Quick Sort is highly space-efficient ($O(\log n)$ average) but is generally Unstable. The possibility of a worst-case $O(n^2)$ performance must be managed through effective pivot selection.

Algorithm	Best Time	Average Time	Worst Time	Auxiliary Space	Stability
Bubble Sort	$O(n)$	$O(n^2)$	$O(n^2)$	$O(1)$	Stable
Selection Sort	$O(n^2)$	$O(n^2)$	$O(n^2)$	$O(1)$	Unstable
Insertion Sort	$O(n)$	$O(n^2)$	$O(n^2)$	$O(1)$	Stable
Merge Sort	$O(n \log n)$	$O(n \log n)$	$O(n \log n)$	$O(n)$	Stable
Quick Sort	$O(n \log n)$	$O(n \log n)$	$O(n^2)$	$O(\log n)$	Unstable