Quick Sort
Recognize the pattern
Brute force idea
If you approach Quick Sort in the most literal way possible, you get this: Not applicable — quicksort IS a sorting algorithm. It is a fair place to begin because it matches the surface of the question, yet it does not capture the deeper structure that makes the problem simpler.
Better approach
The deeper shift in Quick Sort is this: Choose pivot, partition: elements < pivot go left, > pivot go right. Recursively sort both sides. Average, worst with bad pivots. space for recursion stack. Once you hold onto the right piece of information from moment to moment, the problem feels less like trial and error and more like following a shape that was there all along.
Key invariant
At the center of Quick Sort is one steady idea: After partitioning, the pivot is in its final sorted position. All elements left of it are smaller; all right are larger. Recursion handles the sub-arrays. When you keep that truth intact, each local choice supports the larger solution instead of fighting it.
Watch out for
The trap in Quick Sort usually looks like this: Always choosing the first or last element as pivot — this gives on already-sorted input. Use random pivot or median-of-three for better average performance. When the code becomes mechanical before the idea is clear, small edge cases start breaking the whole story.