# Questions tagged [permutations]

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### Distance-preserving permutations

In the scope of my scheduling research, the question has been raised on whether distance-preserving permutations can be constructed easily. Suppose that our domain is the set of natural numbers up ...
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### Mathematically determine if two strings are permutations of each other

I've come across many coding exercises that require me to determine whether or not two strings are permutations of each other and I've repeatedly wondered if it would be possible to convert each ...
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### Algorithm to generate integer sets fulfills restrictions

I'm trying to solve the following problem. Input positive integers $v$, $b$ and $\ell$. ($\ell\leq v\leq b\ell$.) Output A list $S_1, \dots, S_k$ of all possible integer multisets (a ...
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### Gray-like code with maximum value <= maximum value of original symbol

I want to iterate through the numbers $0,1,2,\dots,n-1$ in some order, where each number in the sequence differs by only one bit from the previous bit. I'm going to be using each number as an index ...
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### Finding longest balanced parentheses using $n$ smaller strings

Given $n$ strings consisting only of '$($' and '$)$', how one can compute the length of the longest string that can be built by concatenating a subset of these strings in some order such that the ...
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### Counting permutations whose elements are not exactly their index ± M

I was recently asked this problem in an algorithmic interview and failed to solve it. Given two values N and M, you have to count the number of permutations of length N (using numbers from 1 to N) ...
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### Sort array with minimum swaps

Given an array, I need to sort the array (if not already sorted) in either decreasing or increasing order so that number of swaps are minimized. I was thinking of first determining whether it is ...
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### Optimization problem where penalty is sensitive to permutation

Say, I have the situation where I am looking into all the possibilities to obtain a value of e.g. 20 (exactly) by taking all possible combinations of sums using values from 1 to 5. While doing this, I ...
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### Most Efficient Way to List All $n$-bit Permutations

Suppose we are tasked with expressing a randomized list of all numbers up to but excluding $2^n$ (ie. a random list of all n-bit numbers). What are some efficient ways to do such a listing using as ...
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### Optimal permutation of matrix rows and columns

Let $M$ be a square matrix and $S(M) = \sum_{i<j} m_{i,j}$ the sum of the elements in the upper triangular part of $M$. Is there an efficient algorithm to find a permutation matrix $A$ that ...
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### permuting points for range compression between subsets

For $k = 0,\ldots, K - 1$, $M_k$ is a subset of $\{0, \ldots, N - 1\}$, and the subsets $M_k$ are not necessarily disjoint. I want to find a permutation on $\{0, \ldots, N - 1\}$ such that the range ...
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### Enumerating the List of nPr (n Permute r) objects [closed]

I have been using MATLAB for a particular project, and have seemed to find a function that may or may not exist. This question isn't MATLAB specific, more algorithm specific. I have a list of 12 ...
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### Finding Permutations with Exclusions

Recently, I was given a puzzle by a friend of mine, which has 6 pieces. Giddy to try it out, I took it apart without batting an eye to follow what I was removing or moving or sliding. I've been ...
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### Correctness proof of the algoritm to generate permutations in lexicographic order

The following algorithm generates the next permutation lexicographically after a given permutation. It changes the given permutation in-place. Find the largest index k such that a[k] < a[k + 1]. ...
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### Is greedy minimax permutation rejecting sorting optimal?

I sketch an impractical, theoretical comparison sort. Initialize a list of all $n!$ permutations of size $n$. For each possible pair of indices $i, j$, count how many permutations would get rejected ...
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### Need explanation of Heap's Algorithm

Okay I am trying to understand the Heap's Algorithm from the original research paper published by B.R Heap. The most confusing aspect I found that while Heap says that the example described on the ...
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### How can I reduce a product of transpositions?

I'm looking for an algorithm to solve the following task: Input: a set $T$ of transpositions; a permutation $\pi$ expressed as a product of transpositions from $T$ Desired output: express $\pi$ as ...
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### Permutation on matrix to fill main diagonal with non-zero values

I am currently working on some sparse non-singular matrices. One of the algorithms I use requires divisions by the elements on the main diagonal so I have to ensure that my main diagonal is filled ...
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### How to determine Isomorphism of Non-Symmetric Matrix when Permutation-Set is given?

Consider, two $m \times n$ matrices $A, B$ such that there is a permutation $\kappa$ that such that such that $A^{\kappa}=B$ (Wielandt's notation), i.e. $A, B$ are isomorphic but not equal. Since,...
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### Transitivity of concat comparison

I am trying to solve the problem of finding the permutation, amongst all possible ones, of an array of strings, where the concatenation of them compares smallest lexicographically. I solve it with an ...