highschool/Grade 10/Computer Science/ICS4U1/Sorting Methods/Quick Sort.md

# Quick Sort

## What exactly is quicksort
- take an element as a pivot, move all greater elements than pivot to one side and the lesser elements to the other side. Keep partioning until array is sorted. It is a divide and conquer algorithm
- Known as the queen of all sorts.

## What are the steps of the quicksort algorithm
- Pick a pivot point
- Partion the list by using the pivot point, move lesser elements to the left and greater elements to the right
- Repeat until list is sorted

## What is the partiion method?
- Given ana array and an element $`x`$, put elements $`\gt x`$  to the right and $`\le x`$ to the left. This should be done in linear time
- You can either pick the last, first, middle or random element as the pivot

## Pros and Cons
- Pros
    - Inplace $`O(1)`$ memory
    - Relative fast time complexity most of the time $`O(n \log n)`$
- Cons
    - Can result in $`O(n^2)`$ worst time complexity
    - Hard to implement