Finding all the inversions in a permutation
1a. Find all the inversions in the permutation (5, 3, 6, 2, 7, 8, 4, 1). Which are consecutive inversions? 1b. Now write a Python function find_inv(perm) that returns a list (in any order) of all the...
View ArticleCounting the number of inversions for the function $f(x+yp)=qx+y$
Let $ p,q$ be odd primes. Define the function $ f:\mathbb{Z}_{pq}\to \mathbb{Z}_{pq}$ by $ f(x+yp)=qx+y$ , where $ x\in \mathbb{Z}_{p}$ and $ y\in\mathbb{Z}_{q}$ . How does one calculate the number of...
View ArticleRelation between groups An, Bn, Dn and Sn or inversions of random elements in...
First of of all I’m trying to find a general interperetation to the following facts below. Let’s look at the property of Kendall-Mann numbers $ M(n)$ which are row maxima of Triangle of Mahonian...
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Merge Sort- Number Of Inversions Meaning
I am doing a practice question on sorting a list of numbers. Question: How many neighbour swaps are needed to sort (x,y,z). Please see the question (pic attached). I know how to sort via merge sort,...
View ArticleCounting inversions in an array of 1 to N
Is there a straightforward way to characterise the number of inversions in an array of length N having distinct elements, each element an integer from 1 to N? It’s for a constraint optimization...
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SplitSort — An adaptive algorithm to handle collections with few inversions
SplitSort SplitSort is a rather simple Inv-adaptive and Rem-adaptive sorting algorithm described in Splitsort — an adaptive sorting algorithm by Christos Levcopoulos and Ola Petersson. The paper...
View ArticleConcatenate multiple integer arrays such that number of inversions in...
Given N arrays of variable length. Find a way to concatenate the arrays in such a way that the number of inversions is minimum An inversion for an array Arr can be defined as, a pair of indices (i,j)...
View Articlenumber of permutation with k inversions
We are given two numbers N and K. N <= 10^9. K<=min{1000,(N*(N-1))/2} We need to find numbers of permutations of ( 1 to N ) such that inversions are exactly K. If N was <= 10^3. It would be a...
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