# Questions tagged [quicksort]

Sorting algorithm based on recursive partitioning devised by Hoare (ACM Algorithm 63) with fast average case running time.

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### Hoare partition scheme may cause infinite recursion

Wiki states: "...partitioning algorithm guarantees lo ≤ p < hi which implies both resulting partitions are non-empty, hence there's no risk of infinite recursion." What prevents Hoare ...
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### Runtime of sorting algorithms given a particular input

say that we have {2,3,5,4,6} as input that we want to sort in ascending order. Then, we know that we can use any of the sorting algorithms: bubble, insertion, selection, quick, merge, heap or counting....
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### Understanding the upper bound proof for quick sort

I'm trying to understand the average run time of quicksort which is $O(n \log n)$. I understand the intuition behind it: if we partition array $A$ to e.g. $\alpha n$ and $(1-\alpha)n$ then we ...
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### Is there a way to find the correct element in the array for the given index x?

In quick sort, in each iteration we are able to find correct index for an element (i.e. pivot element). Is there any algorithm to find correct element for a given index ? Here, correct index of an ...
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### How to arrange a sub-array for Quick sorting algorithm?

Alghorithm : Quick sort . idea : devide and conqure . steps : 1- find the pivot point from array like first element . 2- partiotioning the array so that elements are smaller than pivot point are in ...
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### Number of comparisons in Quicksort

So would it be correct to say that the number of comparisons from level 1 to level 2 would be $2(n/2-1)$? Or would it be more correct to say that the number of comparisons is $2^i(n/2^i-1)$?
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### Quicksort: Probability of an element being compared to fewer than $k$ pivot elements

Assume we want to use quicksort on some array $s$ with length $n$ consisting of only $n$ distinct elements. Let $S_{(1)},S_{(2)},\dots,S_{(n)}$ be the sorted order of the elements in $S$. Furthermore, ...
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### How does size of list in merge-sort, quick-sort, insertion-sort, matter?

We have been taught that: Insertion-sort will best work if we have a small list. Quick-sort will best work if we have a long list. Merge-sort will best work if we have a huge list. It is not ...
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### TAoCP on quicksort: What are the differences between printings/editions?

In a footnote to the preface of "The Art of Computer Programming - Sorting and Searching", D. E. Knuth writes in a copy copyrighted 1973: In this second printing […] The section on ...
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### Quickly determine if insertion sort or quick sort is better

I'm in a scenario where ~30% of the time, my array is almost completely sorted, and the other 70% of the time, it is basically completely random. I want to quickly determine if my list is almost ...
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### How to known which algorithm is the best for what situation, when sorting numbers?

Is there some kind of "universal list" of performance of different algorithms in different situations? I have different databases that save user input (numbers). However some of these sets ...
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### Average case running time of quick sort

How to show that the quick-sort algorithm runs in $O(n^2)$ time on average ? Because on average, the expected running time is in $O(n\log n)$. The algorithm should not be in exponential time.
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### QuickSort when the range of data is known

In QuickSort Algorithm, the pivot is chosen as the first element or a randomised element. However, if the range of data to be sorted is known, For example, from 1 to 100, and they are mostly equally ...
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### Isn't linear time O(n)?

In the question in this video about quicksort luckily picking the median in each recursive call. Tim Roughgarden, the presenter, says at 11:22 Partition needs really linear time, not just $O(n)$ time....
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### Solving the recursive equation $T(n)=T(k)+T(n-k-1)+O(n)$

The question is clear in the title. I am trying to solve this recursion as a part of showing that the worst case of quicksort algorithm occurs when $k=0$, but can't do it. I could do the following ...
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### Running time of random pivot quicksort on random and sorted arrays

I don't understand why I am getting the following execution times for the quicksort with a random pivot. Times are in microseconds they are the average of five executions. Random array: ...
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### Time complexity of a machine which combines Insertion Sort and Quicksort

Given a machine that sorts an array of length $n$ with the following algorithm: Sort first $2\sqrt{n} + 1$ elements of array with Insertion Sort.(Check Insertion Sort) Select the median of the whole ...
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### How does quicksort handle case when we choose the first number as pivot and all the remaining elements after the pivot is greater

For example, we have an array [4,7,6,13] and I choose the first item 4 as the pivot. Now I have a pointer i that goes through the array from index 1 to index 3; and I have another pointer j that ...
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### Calculating the running time of Quicksort's PARTITION procedure

I am confused about calculating the PARTITION procedure's running time. PARTITION procedure is used in the Quicksort Algorithm to partition the array $A[p...r]$ I analyzed the PARTITION procedure ...
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### Clarification of the analysis of the worst case situation of quicksort as dealt with in CLRS

I was going through the text Introduction to Algorithms by Cormen et. al. and I came across their analysis of the worst case of the quicksort algorithm. I could not quite understand a few specific ...
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### Average number of exchanges during first partition stage in Quicksort

I am trying to understand average no of exchanges in Quicksort. Here is the code to partition the array - ...
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### Quicksort Time Complexity

I am learning the Quicksort algorithm and I am struggling with understanding the time complexity. Here is the JavaScript ES6 code for the partition function that is used in the algorithm: ...
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### How to predict the number of comparisons done by QuickSort if you know the percentage to which the array is pre-sorted?

I've noticed that correlating the number of comparisons done by a naive implementation of QuickSort with the percentage of elements that were already sorted gives you a curly-brace-shaped-curve if you ...
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### Quick Sort Equal to or Less Than

For my course I have to memorise a number of algorithms and to know how to perform them by hand. The steps of the quick sort are given as the following in the text book I am using: Choose the item at ...
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### What is the worst case for C++ “sort” function?

So, what is the worst case for C++ "sort" function, when does it go to O(n^2) time? I know it's QuickSort, therefore, it's very fast in most cases, but it gets to O(n^2) in special cases. I've tried ...
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### What is the probability of comparision between smallest and greatest element in array when quick sort randomly choose the pivot element?

Consider the recursive quick sort with random pivoting i.e. each time a random pivot element is chosen uniformly. When this ...
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### Algorithm Design: Efficient O(n) algorithm to get the ith to jth largest elements in an array

I am trying to design an efficient algorithm that retrieves the ith to jth largest elements in an array. For example, if the following array is the input: ...
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### Average Case Running Time of Quicksort Algorithm

From this website, it states that the average case of Quicksort algorithm is T(n) = T(n/9) + T(9n/10) + θ(n) Im a bit confused. Is it supposed to be ? ...
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### Is finding Kth largest element using selection algorithm taking O(n) only if K is fixed?

Wikipedia here https://en.m.wikipedia.org/wiki/Selection_algorithm shows an algorithm using sort of quicksort.. in order to find Kth largest or smallest element taking O(n) time only on average. The ...
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### Quicksort Algorithm with Pivot element as Median

I have read that when pivot element is choosen as Median, then QS Algorithm gets nearly balanced splits and have time complexity of O(nlogn), but my doubt is what if all the elements of the input are ...
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### Quicksort where element comparison outcome is random. Probability of element being in a certain position

So we have this block of pseudocode: Monsters = [M1,M2,M3,M4,M5,M6,M7,M8]; qsort(Monsters,rand_compare); qsort() sorts the ...
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### Quick sort worst case complexity improvement [closed]

Can the worst case time complexity of quick sort be changed from $O(n^2)$ to $O(n\log n)$ by modifying it?
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### Worst Case Scenario for Quicksort algorithm with pivot element n/2

What would the worst case array look like if I decide to always take the element on the position $\frac{n}{2}$ as the pivot element? I know that if I choose the left or rightmost element as pivot ,the ...
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### Big O: Analyzing the time complexity of an $O(n \log n)$-algorithm

For homework, the task is to verify the time complexity of quicksort. User Nick suggested on quora that one could check the number of comparisons made when doubling the input size. If the comparisons ...
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### Is there a sorting algorithm of order $n + k \log{k}$?

I'm given an integer vector which is said to contain many duplicate values (total of k distinct integers), for example ...