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For questions about dividing groups of objects based on their properties.

0 votes
2 answers
724 views

Linear algebra to find EV of sort algorithm

I am having a hard time figuring out how to use Markov chains to address a sorting method. It is for a PE problem (i.e. problems done for fun), if anyone's curious. I do not want spoilers but just ...
John Smith's user avatar
13 votes
2 answers
3k views

Median of distinct numbers

What is the least number of comparisons we need to find the median of 6 distinct numbers? I am able to find the answer to the median of 5 distinct numbers to be 6 comparisons, and it makes sense, ...
Sev's user avatar
  • 2,123
11 votes
5 answers
31k views

Worst case analysis of MAX-HEAPIFY procedure .

From CLRS book for MAX-HEAPIFY procedure : The children's subtrees each have size at most 2n/3 - the worst case occurs when the last row of the tree is exactly half full I fail to see this ...
Geek's user avatar
  • 2,349
11 votes
1 answer
4k views

Why is sorting pancakes NP hard?

An article posted yesterday (http://www.i-programmer.info/news/112-theory/3280-pancake-flipping-is-hard-np-hard.html) references a new study released on Arxiv (http://arxiv.org/abs/1111.0434v1) with ...
Fosco's user avatar
  • 212
5 votes
5 answers
35k views

Merge Sort time complexity analysis

How can I prove that $T(n) = 2T(n/2) + n$ is $O(n \log n)$ ?
Dan's user avatar
  • 53
5 votes
3 answers
2k views

expected number of shuffles to sort the cards

Initially the deck is randomly ordered. The aim is to sort the deck in order. Now in each turn the deck is shuffled randomly. If any of the initial or last cards are in sorted order then they are kept ...
Manoj R's user avatar
  • 561
3 votes
2 answers
3k views

How many rounds are required in a "Swiss tournament sorting algorithm"?

You're organizing a Swiss-style tournament with N players of a game. The game is a two-player game, and it results in one winner and one loser. The players are totally ordered by skill, and whenever ...
Tanner Swett's user avatar
  • 10.7k
3 votes
4 answers
2k views

Merge sort seems to take the same number of comparisons for best and worst case.

I am trying to clear up my conceptions of merge sort. What I cannot understand how merge sort takes less number of comparisons during best case. Let me explain, looking at the merge procedure given ...
ng.newbie's user avatar
  • 1,025
2 votes
1 answer
1k views

Sort vectors according to their distance between them

I have a collection of vectors, let`s say $n$ vectors. I am trying to find an easy way to SORT these vectors in that way that after sorting of vectors $(V_1,V_2,...,V_n)$ the first vector $V_1$ and ...
Drill's user avatar
  • 35
2 votes
3 answers
321 views

Equation to calculate best liked comments

In my website, users can either "like" or "dislike" a posted comment. I want to put a link to sort comments by liking such that the most liked ones becomes on top. Of course I cannot just sort by ...
user avatar
2 votes
2 answers
3k views

Probability of a sorted sequence

Now I tried tackling this question from different sizes and perspectives (and already asked a couple of questions here and there), but perhaps only now can I formulate it well and ask you (since I ...
wh1t3cat1k's user avatar
2 votes
1 answer
81 views

How to sort 4 (or more) values with non-piecewise functions?

This question was inspired by this: Finding a non-piece wise function that gives us the $i$'th largest number. My question is how to do this for four or more values. In other words, given 4 ...
marty cohen's user avatar
2 votes
2 answers
250 views

Arranging numbers in an array (Swedish Math Olympiad 1986)

Consider an $m\times n$ array of real numbers. Let $d>0$. Suppose that the difference between the maximum number and the minimum number in each row is at most $d$. We then sort the numbers in ...
moray eel's user avatar
  • 184
1 vote
1 answer
95 views

Sort rectangles by size, but with a tunable advantage favoring squareness

I want to sort some rectangles from biggest to smallest, but with a tunable advantage favoring squarer rectangles. I'm sure this is super easy but I'm not getting it. I think it's related to topics ...
Jason Kleban's user avatar
1 vote
1 answer
98 views

Can a comparison network obtain all the n! permutations of a vector?

I want to permute a vector using comparison networks. This is the only method I have at my disposal. My original idea is to use a sorting network like Batcher or Bitonic. Basically I place my vector ...
DaWNFoRCe's user avatar
  • 175

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