## What is the running time of quicksort?

To sort an array of n distinct elements, **quicksort** takes O(n log n) **time** in expectation, averaged over all n! permutations of n elements with equal probability. We list here three common proofs to this claim providing different insights into **quicksort’s** workings.

## What would be the running time of quicksort to sort an array of n elements if the largest item is chosen as the pivot?

Choice of **Pivot** in **Quicksort**

In that case, choosing the last **element** every **time will** result in partition of sizes **n**-1 and 0 and thus, **will** give us a quadratic **running time** i.e., Θ(**n**2) Θ ( **n** 2 ). This **will** also happen when we **will** always choose the first **element** of the **array** as the **pivot**.

## How do you calculate time complexity of quicksort?

Lemma 2.14 (Textbook): The worst-case **time complexity of quicksort** is Ω(n2). Proof. The partitioning step: at least, n − 1 comparisons. one less, so that T(n) = T(n − 1) + (n − 1); T(1) = 0.

## Does quicksort work with duplicates?

When the list of items to be sorted contains a lot of **duplicate** values, we can improve **QuickSort** by grouping all the values that are equal to the pivot to the middle and then we recursively **QuickSort** those values on the left and those values on the right.

## What is the fastest sorting algorithm?

But because it has the best performance in the average **case** for most inputs, **Quicksort** is generally considered the “fastest” sorting algorithm.

## Why is quicksort faster than heapsort?

A good reason why **Quicksort** is so **fast** in practice compared to most other O(nlogn) algorithms such as **Heapsort**, is because it is relatively cache-efficient. Its running time is actually O(nBlog(nB)), where B is the block size.

## What is quick sort example?

In simple QuickSort algorithm, we select an element as pivot, partition the **array** around pivot and recur for subarrays on left and right of pivot. Consider an **array** which has many redundant elements. For example, {1, 4, 2, 4, 2, 4, 1, 2, 4, 1, 2, 2, 2, 2, 4, 1, 4, 4, 4}.

## Why QuickSort is the best sorting method?

**Quick sort** is an in-place **sorting algorithm**. In-place **sorting** means no additional storage space is needed to perform **sorting**. Merge **sort** requires a temporary array to merge the **sorted** arrays and hence it is not in-place giving **Quick sort** the advantage of space.

## What is the big O of QuickSort?

**Quicksort** is a logarithmic-time algorithm, in other words, it has a **Big O** notation of **O**(log n)-(more about **Big O** Notation)- and depending on the way you implement it, it can be up to 2x or even 3x faster than Merge Sort or Heap Sort.

## Which is better merge or quick sort?

**Merge sort** is more efficient and works **faster** than **quick sort** in case of larger array size or datasets. **Quick sort** is more efficient and works **faster** than **merge sort** in case of smaller array size or datasets. **Sorting** method: The **quick sort** is internal **sorting** method where the data is **sorted** in main memory.

## Which parts need to be sorted in the quick sort algorithm after applying the 3 way partition?

**3 way quick sort** basically **partitions** the array in **3 parts**. First **part** is lesser than the pivot, Second **part** is equal to pivot and third **part** is greater than pivot.It is linear-time **partition algorithm**.