Questions tagged [permutations]
The permutations tag has no usage guidance.
4
votes
1answer
67 views
Indexing Edge Permutations for the Rubik's Cube
I'm working on a Rubik's Cube solver that implements Korf's algorithm, as published in his 1997 paper, Finding Optimal Solutions to Rubik's Cube Using Pattern Databases. His method involves creating ...
1
vote
2answers
40 views
Lexicographic permutation list
Does anyone have an algorithm for stepping through all permutations of n given arbitrary objects in lexicographic order?
Thanks.
1
vote
1answer
18 views
Does “$\forall x\in L, \sigma(\neg x)=\neg \sigma(x)$” hold given that $\sigma(F)\equiv F$ for a CNF formula $F$ built on a set $L$ of literals?
Suppose we have a CNF formula $F$ built on the set of literals $L=\{x_1,\neg x_1,\cdots,x_n,\neg x_n\}$ where each variable is used in at least one clause of $F$. Consider a permutation $\sigma$ of $L$...
0
votes
0answers
22 views
Finding “good” order of elements for the purpose of material minimization
I am working with metallic shapes which are curved and highly irregular. The initial order of them is random and by default they are merely sorted by size, which is simple. However the resulting order ...
2
votes
1answer
109 views
Permutation of n-size array with possible repeated elements. E.g [1, 2, 1]
What would it be a recursive algorithm to get permutations for any list of n elements that might contain or not repeated elements?
For the following 3-element list ...
6
votes
1answer
82 views
Index matching algorithm without hash-based data structures?
I am programming in C, so I do not want to implement a hash-based datastructure such as a hashset or hashmap/dictionary. However, I need to solve the following task in linear time.
Given two arrays $...
9
votes
2answers
165 views
Find an optimal ordering
I came across this problem and am struggling to find a way to approach it. Any thoughts would be greatly appreciated!
Suppose we are given a matrix $\{-1, 0, 1\}^{n\ \times\ k} $, for example,
...
1
vote
0answers
55 views
How to find big-O for an in-place perfect shuffle algorithm
I've found a simple algorithm to interleave two halves of an array in place. It involves swapping the first 1/2 of the items into the correct place, then unscrambling the permutation of the 1/4 of ...
2
votes
2answers
27 views
O(B) algorithm to find positions of all permutations of smaller string in a bigger string with length B - how is this possible?
Context: I've been working through Cracking the Code Interview and on page 70 the book asserts that there is a O(B) solution to this problem.
If
s = little string and S = len(s)
b = big string and ...
3
votes
0answers
73 views
Adjacent Gray code
Gray code is permutation of $\{0,1,2,\dots,2^n-1\}$ such that each of consecutive number is differs only one bit in binary representation.
Example for $n = 3$
$000\\
001\\
011\\
010\\
110\\
111\\
...
0
votes
0answers
16 views
Is there a specific search paradigm for finding pairs in a set?
I'm dealing with a very common problem in computer programming that involves, for example 4 people to be divided into 2 pairs. Mathematically, this is just a permutations problem, and the number of ...
0
votes
1answer
38 views
invite 12 person from 24 that we have 6 men and 6 womens [closed]
i had a question and its
"A man has 5 female and 7 male friends and his wife has 7 female and 5 male friends. In how many ways can they invite 6 males and 6 females if husband and wife are to invite ...
2
votes
0answers
15 views
How can I optimise a 8b10b encoding for maximum alignment?
Imagine you encode an 8 bit symbol as a 10 bit symbol that is sent sequentially over a wire. The goal at the receiver is to detect the byte boundary.
Since there are 4 times more encoded symbols than ...
0
votes
2answers
53 views
Find the cheapest combination of raw foods that fulfill nutritional requirements
I am starting a raw food diet and would like to properly plan it, and thus, would like to create a program that takes a list of available raw food, and finds the best combination of foods (multiples ...
0
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0answers
14 views
Applications of signed permutations to machine learning
Are there some applications of signed permutations to machine learning? I searched on google and only found one paper. Thank you very much.
2
votes
1answer
43 views
Does it hold that $F \equiv \sigma(F)$ for a CNF formula $F$ and a permutation $\sigma$ s.t. $F \vDash \sigma(F)$?
Suppose we have a CNF formula $F$ and a permutation $\sigma$ of its literals such that for any literal $x, \sigma(\neg x)=\neg \sigma(x)$ and $F \vDash \sigma(F)$.
Does it hold that $F \equiv \sigma(...
1
vote
0answers
122 views
which arrangement gets favoured in naive shuffling for a given numbers from 1 to n according to the algorithm given?
algorithm:
a=[1,2,3.....n]
for i in (1,n+1):
j=rand(1,n+1):
swap(a[i],a[j])
let us say that n=3:
132
213
231
these 3 are 5 times possible
and
123
312
321
are 4 times possible....
similarly
...
2
votes
1answer
35 views
Efficient algorithm to find the nth number in a base-k numeral system with only different digits
I am looking for an efficient algorithm for the following problem.
There is a base-k numeral system, and we want to have some k-length numbers, but all of the digits must be different ones.
It would ...
6
votes
1answer
155 views
Chernoff-Hoeffding bounds for the number of nonzeros in a submatrix
Consider a $n \times n$ matrix $A$ with $k$ nonzero entries. Assume every row and every column of $A$ has at most $\sqrt{k}$ nonzeros. Permute uniformly at random the rows and the columns of $A$. ...
5
votes
1answer
122 views
Permutation of words that have matched parentheses
Let $L$ denote the (context-free) language of matched parentheses over the alphabet $\Sigma$. Consider the following problem:
Input: words $x_1,\dots,x_n \in \Sigma^*$
Question: does there exist a ...
5
votes
2answers
75 views
Chernoff-like Concentration Bounds on Permutations
Suppose I have $n$ balls. Among them, there are $m \leq n$ black balls and the other $n - m$ balls are white. Fix a random permutation $\pi$ over these balls and denote by $Y_i$ the number of black ...
5
votes
1answer
57 views
Applying a permutation on a sequence with multiplication
We are given a sequence of $n$ numbers called $\alpha$ and an arbitrary number $x$. Give an algorithm to find a permutation $\pi$ of size $n$ such that $\sum_{i=1}^n{\alpha_i.\pi_i} = x$ or tell if ...
2
votes
1answer
80 views
How to restore diagonal-symmetric matrix that has been shuffled?
I have a square matrix M, which originally looked like this:
133 199 101 121
142 133 199 101
156 142 133 199
108 156 142 133
(so symmetric around the diagonal). ...
0
votes
1answer
86 views
Simulated annealing to find the correct permutation of 20 words
I have 20 words. One permutation of these 20 words is the "correct" one. Assume I have a metric to find the correctness of the permutation.
I'm trying to figure out how to use simulated annealing to ...
0
votes
0answers
28 views
How does the following NP hardness proof work?
It is known that computing Kemeny optimal permutation, given a set of permutations is NP hard even when the given list has just four permutations. This is proved here (see Appendix B) along with all ...
1
vote
0answers
18 views
Splay Tree - Insert Permutation
Let $T$ be a Splay Tree. For a given permutation $\sigma$ on a set $S = \{1,2,3,...n \}$ we defined the following function:
...
0
votes
1answer
150 views
Are there any known implementations of a functional Heap's Algorithm?
TL;DR: Is an implementation of the Heap's Algorithm adhering to the principals of functional programming possible, and are any implementations of it known? And by "adhering to the principals of ...
1
vote
0answers
45 views
All permutations of N numbers with at least K-different positions
I'm trying to generate all permutations of N numbers where any two permutations are different by at least K positions. I would just like a push in the right direction, the trivial method of memorizing ...
0
votes
0answers
118 views
I'm having trouble calculating Big O for this bad permutation algorithm
I wrote this code to print all the permutations of a string. I believe it has time complexity of O(N^2). However, I'm not sure about it. Will inner loop run N! times?
Can you please help me ...
1
vote
1answer
36 views
Algorithm for this problem on generating all permutations
I am trying to come up with an efficient algorithm to solve the following problem but not able to design anything nice. I am encountering this problem for a project I am pursuing. Following is an ...
1
vote
1answer
38 views
number of queries to recover the permutation
Imagine this game. I pick a permutation $p$ of $1..n$ and give you an oracle. When the oracle is queried with any sequence of $n$ numbers $\in 1..n$, it masks each number by applying some unknown ...
1
vote
1answer
153 views
Black-box combinatorial optimization problem over permutations
I am solving general black-box optimization problems like:
x*: f(x) -> min, where x are permutations of length N (N = 50 for example, so brute force search is not possible). Objective function f(x) is ...
1
vote
1answer
54 views
Maximizing the sum of adjacent pairs of elements
I encountered the following interesting problem on stackoverflow:
Given numbers $a(1)<\cdots<a(n)$, find a permutation $\pi$ that maximizes $$\sum_{i=1}^{n-1} a(\pi(i)) a(\pi(i+1)).$$
The ...
3
votes
1answer
27 views
Counting number of permutations respecting partial order
Suppose that we have an array $A$ of $n$ elements with some partial order known, e.g. for example as a $n\times n$ matrix containing $c_{ij} \in \{-1, 0, 1\}$ where $0$ represents unknown and $-1, 1$ ...
2
votes
0answers
160 views
How many similar binary search trees are made from different permutations?
If I have numbers ranging from 1 to n, and I generate all the permutations of these numbers. Now, I create Binary search tree from these permutations. For a value n i want to know how many BSTs would ...
0
votes
1answer
100 views
Minimizing the SUM algorithm
We are given $2n$ positive integers $a_1,a_2\ldots,a_n$ and and $$b_1,b_2,\ldots,b_n$$ as input.
The question is to find a permutation $O$ on $\{1,2,\ldots,n\}$
that minimizes $$\sum_{i=1}^n \left(...
3
votes
2answers
50 views
Indexing a random permutation
I am curious if there exists a method for specifying a permutation $F_k: X \to X$ with a small(ish) $k$.
Something that comes very close to my goal is a block cipher, say AES. But block ciphers have ...
4
votes
2answers
7k views
Using backtracking to find all possible permutations in a string
I came across this algorithm in a book, and have been struggling to understand the basic idea. The books says it uses backtracking to print all possible permutations of the characters in a string. In ...
1
vote
1answer
137 views
Determine if a string is a permutation of another string efficiently [duplicate]
Given two strings of the same length, determine if they are permutations of each other.
I can come up with two solutions, one in O(n log n) time with O(1) extra space, and one in O(n) time with O(n) ...
0
votes
0answers
31 views
Efficient permutation of given ranking that preserves given distance
Ranked Biased Overlap (RBO) is a metric for comparing two rankings and is used when the sizes of the given rankings are different and/or the elements that they carry are not the same. Ranked Biased ...
0
votes
0answers
305 views
Interleaving first and second half of an array of even length in place
If A is an array with the following elements:
$$ a_1,a_2,...,a_n,b_1,b_2,...,b_n $$
How to shuffle A to form:
$$ a_1,b_1,a_2,b_2,...,a_n,b_n $$
with minimal swaps and using no additional space?
I ...
1
vote
1answer
55 views
Finding a subset of triplets of digits 0-9 such that each digit occurs 40 times in each position in the triplets
I am trying to generate a list of digit triplets to specify stimuli in an auditory (speech-in-noise) perception experiment. Each triplet has to have three different digits (i.e., no repetition within ...
1
vote
1answer
67 views
How to find number of permutations of 1-N length, each [1-N] with k values
This imaginary problem involves a vector of length 5, with each value to be selected from a unique range of values.
A real-world example might include 5 different single-digit combination locks.
...
1
vote
1answer
560 views
Space and time complexity of balanced parentheses enumeration algorithm
Consider the following recursive algorithm for printing all balanced strings with $n$ left and right parentheses. It is called with prefix = $\epsilon$ (the empty string):
A(prefix):
If prefix ...
0
votes
1answer
190 views
How to encode a sequence of non-decreasing integers with an integer without redundancy, loops, and recursions
How to encode a sequence of n non-decreasing integer of [0, ..., m] fulfilling the following conditions:
no or minimal redundancy
only use 1 integer variable or k independent integer variables with a ...
3
votes
1answer
348 views
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 ...
4
votes
2answers
318 views
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 ...
3
votes
1answer
77 views
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 ...
1
vote
0answers
52 views
Canonical permutation faster than O(n)
Given a set of permutations $P$ of size $n$, is it possible to create a data structure that, given a sequence $s$, returns $p \cdot s$ where $p \in P$ such that $p \cdot s$ is canonical wrt. $\{\,q \...
3
votes
1answer
50 views
Counting permutations whose elements are not exactly their index ± 1
This is a special case of the question:
Counting permutations whose elements are not exactly their index ± M
The $M=0$ case has already been solved, but no one was sure how to work out the non-...
