Stack Overflow
Stack Overflow

Questions tagged [median-of-medians]

The median-of-medians algorithm is a deterministic, worst-case O(n)-time algorithm for the selection problem (given a list of values, find the kth largest value). The constant factor in the O(n) is large, and the algorithm is not commonly used in practice.

62 questions
63
votes
2 answers

Understanding "median of medians" algorithm

I want to understand "median of medians" algorithm on the following example: We have 45 distinct numbers divided into 9 group with 5 elements each. 48 43 38 33 28 23 18 13 8 49 44 39 34 29 24 19 14 9 50 45 40 35 30 25 20 15 10 51 46 41 36 31 26…
simon
  • 1,335
  • 1
  • 12
  • 23
19
votes
2 answers

Why is the median-of-medians algorithm described as using O(1) auxiliary space?

Wikipedia lists the median-of-medians algorithm as requiring O(1) auxiliary space. However, in the middle of the algorithm, we make a recursive call on a subarray of size n/5 to find the median of medians. When this recursive call returns, we use…
John Kurlak
  • 6,070
  • 7
  • 38
  • 56
13
votes
1 answer

Explanation of the Median of Medians algorithm

The Median of medians approach is very popular in quicksort type partitioning algorithms to yield a fairly good pivot, such that it partitions the array uniformly. Its logic is given in Wikipedia as: The chosen pivot is both less than and greater…
SexyBeast
  • 8,635
  • 25
  • 92
  • 179
10
votes
3 answers

Find a median of N^2 numbers having memory for N of them

I was trying to learn about distributed computing and came across a problem of finding median of a large set of numbers: Assume that we have a large set of numbers (lets say number of elements is N*K) that cannot fit into memory (size N). How do we…
Akshya11235
  • 771
  • 3
  • 9
  • 22
7
votes
2 answers

Not understanding median of medians algorithm to find k-th element

Below is my code for trying to understand the median of medians algorithm (using blocks of size 5). I understand how to get medians of the input, but I'm not sure how to code the block to keep recursing the input until I just have the median. Then…
Emmanuel Mudiay
  • 123
  • 6
5
votes
4 answers

Worst-case O(n) algorithm for doing k-selection

Apart from the median-of-medians algorithm, is there any other way to do k-selection in worst-case O(n) time? Does implementing median-of-medians make sense; I mean, is the performance advantage good enough for practical purposes ?
Harman
  • 1,531
  • 1
  • 18
  • 31
5
votes
3 answers

Dividing the elements of an array in 3 groups

I have to divide the elements of an array into 3 groups. This needs to be done without sorting the array. Consider the example we have 120 unsorted values thus the smallest 40 values need to be in the first group and next 40 in the second and the…
nishant mehta
  • 109
  • 1
  • 10
4
votes
2 answers

Median of median algorithms understanding

I've searched around the web and visited the wiki page for the Median of median algorithm. But can't seem to find an explicit statement to my question: If one has a very very large list of integers (TBs in size) and wants to find the median of this…
Jared Krumsie
  • 387
  • 1
  • 8
  • 17
4
votes
2 answers

Median of Medians algorithm misunderstanding?

What I understand already I understand that median of medians algorithm(I will denote as MoM) is a high constant factor O(N) algorithm. It finds the medians of k-groups(usually 5) and uses them as the next iteration's sets to find medians of. The…
OneRaynyDay
  • 2,990
  • 1
  • 14
  • 39
4
votes
1 answer

Where does the constant 5 come from in the median-of-medians algorithm?

I've been trying to understand where the "5" comes from in the Median of Medians algorithm, but can't seem to find a simple description of how it is derived and why it is optimal. For example, why isn't say 7 a viable option? The only advantage I…
Rikardo Koder
  • 652
  • 9
  • 16
3
votes
2 answers

Something I dont understand about median of medians algorithm

There is something I don't understand about the algorithm of median of medians. One key step about this algorithm is to find an approximate median, and according to Wikipedia, we have the guarantee that this approximate median is greater than 30%…
Truc Truca
  • 69
  • 6
3
votes
2 answers

Stack overflow error with Quicksort and median implementation

First of all I'm just going to state that this is a homework question which I have made an extensive amount of attempts on. I've been asked to modify quicksort in Java to set the pivot as the psuedo median of 9 values in the array using the formula…
Habitat
  • 709
  • 10
  • 21
3
votes
1 answer

Median of Medians space complexity

I implemented an nth_number selection algorithm using Medians of Medians. On wikipedia, it states that it's space complexity is O(1) I had to store the medians in a temporary array in order to find the median amongst those medians. How would you be…
Kamran224
  • 1,384
  • 7
  • 19
  • 31
2
votes
1 answer

Multiple Count and Median Values from a Dataframe

I am trying to perform several operations in one program at same time. I have a data-frame that has Dates of which I have no clue of start and end and I want to find: Total number of days the data-set has Total number of hours Median of the…
Sitz Blogz
  • 927
  • 5
  • 23
  • 46
2
votes
1 answer

Find median of N 8-bit numbers

Given an array of N 8-bit numbers ( value 0-255)? How to find the median? I have tried radix sort and median of medians algorithms. Is there a better way given the values of the numbers are between 0 and 255?
Idan
  • 160
  • 1
  • 14
1
2 3 4 5