# Tag Info

Accepted

### Why does Randomized Quicksort have O(n log n) worst-case runtime cost

Both of your sources refer to the "worst-case expected running time" of $O(n \log n).$ I'm guessing this refers to the expected time requirement, which differs from the absolute worst case. Quicksort ...
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### Why don't we use quick sort on a linked list?

The memory access pattern in Quicksort is random, also the out-of-the-box implementation is in-place, so it uses many swaps if cells to achieve ordered result. At the same time the merge sort is ...
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### Finding k'th smallest element from a given sequence only with O(k) memory O(n) time

Create a buffer of size $2k$. Read in $2k$ elements from the array. Use a linear-time selection algorithm to partition the buffer so that the $k$ smallest elements are first; this takes $O(k)$ time. ...
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### Why is the optimal cut-off for switching from Quicksort to Insertion sort machine dependent?

Because the actual running time (in seconds) of real code on a real computer depends on how fast that computer runs the instructions and how fast it retrieves the relevant data from memory, how well ...
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### Trying to understand this Quicksort Correctness proof

We are indeed assuming $P(k)$ holds for all $k < n$. This is a generalization of the "From $P(n-1)$, we prove $P(n)$" style of proof you're familiar with. The proof you describe is known as the ...
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### Dual-pivot Quicksort reference implementation?

I tried to do exactly such a comparison in my master thesis, which thus naturally includes pseudo-code of “basic” versions of several dual-pivot Quicksorts (there is a list of them on page 9). Here ...

### Would using the mean as pivot speed up quicksort?

Using the mean for your partition does not prevent the $\Omega(n^2)$ worst-case behavior. It occurs when the input list is exponentially increasing. Consider the input: $1,n^2,n^3,\ldots,n^n$ The ...

### Quicksort Partitioning: Hoare vs. Lomuto

Some comments added to the excellent Sebastian answer. I'm going to talk about the partition rearrangements algorithm in general and not about its particular use for Quicksort. Stability Lomuto's ...
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### Hoare partitioning scheme in Quicksort

"The devil is in the details". Algorithms and programming, fortunately and unfortunately, needs the greatest attention to detail. The part of code that are critical here are the following ...
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### Isn't linear time O(n)?

Usually we call statement $A$ stronger than $B$ when $A$ implies $B$: $A \Rightarrow B$ (weaker-stronger). In other words, $B$ is weaker than $A$. When the presenter is speaking about linear time for ...
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### Stability of QuickSort Algorithm

One huge advantage of a stable sorting algorithm is that a user is able to first sort a table on one column, and then by another. Say that you have a website like Wikipedia with some tabular data, say ...

### Can anyone give an example for worst case of quick sort if we employ median of three pivot selection?

If we employ quicksort by selecting the pivot as the median of three elements viz., the first element, the middle element and the last element, then when will the algorithm hit worst case? and also ...

### Trying to understand this Quicksort Correctness proof

This proof uses the principle of complete induction: Suppose that: Base case: $P(1)$ Step: For every $n > 1$, if $P(1),\ldots,P(n-1)$ hold (induction hypothesis) then $P(n)$ also holds....

### Why does Randomized Quicksort have O(n log n) worst-case runtime cost

You were missing that these texts talk about "worst case expected run time", not "worst case runtime". They are discussing a Quicksort implementation that involves a random element. Normally you ...
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### Implementation of QuickSort to handle duplicates

The simple implementation idea is to separate the values into three groups: values less than the pivot, values equal to the pivot, and values greater than the pivot. In pseudocode, the algorithm ...

### Is there a sorting algorithm of order $n + k \log{k}$?

The short answer is no, in the worst-case comparison based algorithms, for reasons stated here. Using a counting technique will at least take $O(n \log n)$ worst case and $O(n \log k)$ if you use a ...
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### Why does quicksort work well with virtual memory?

The phrase in Cormen is a bit obscure (and does read a bit quaint). A 1978 paper by Sedgewick "Implementing Quicksort Programs" has a nutshell on this: The hardware feature on modern computers that ...