Questions tagged [permutations]
Permutations are arrangements of the numbers $1,\ldots,n$ in an arbitrary order.
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1answer
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Determining runtime of a theoretical program (question of extraordinary complexity)?
I apologize in advance, as I don't have a clue to which stackexchange to post this question! I beg you to not delete this question, as I have chronic pain and it is very important to me!!! I actually ...
3
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1answer
51 views
Iteratively enumerating all permutations of $N$ objects using a generating set
The group theory of $S_n$ shows that all permutations of $n$ objects can be generated from the $n$-cycle $a:=(1 2 3 .. n)$ and the transposition $b:=(1 2)$. (See Theorem 2.5 at https://kconrad.math....
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2answers
66 views
Memory-efficient list of N unique integers from 0..N-1 with fast lookup
We want to represent a list of $n$ unique integers between $0$ and $n-1$ in a memory-efficient way. The only operation we need to support is looking up the $n\text{-th}$ element.
What are some of the ...
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58 views
Sequential Tasks with Greedy Algorithm
We have N tasks that need to be scheduled for processing. Each task consists of two parts that need to executed in order. The first one is guarded by a mutex and therefore only one task can be ...
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1answer
168 views
Counting number of swaps to make two strings equal in linear time
The input to our problem is a pair of strings, say $x$ and $y$. We treat our alphabet size as a constant, i.e., our input is effectively a pair of arrays with the values therein bounded by a constant.
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1answer
77 views
Faster algorithm for specific inversion count (part 2)
Following the issue from Faster algorithm for a specific inversion:
We have a permutation (a derangement actually) $\sigma$ of the set $\{0,1,\dots,n-1\}$ with cardinality $n$.
I want to compute ...
3
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1answer
540 views
Faster algorithm for a specific inversion
There is a permutation (more precisely a derangement) $\sigma$ of the set $\{0,1,\dots,n-1\}$ with cardinality $n$.
I want to compute the following counts (a kind of inversion):
$$K(\sigma )_{i}=\#\{j&...
3
votes
1answer
53 views
Does this algorithm for permuting rows and columns of a matrix converge?
Given a binary matrix, define the magnitude of a row by reading off the numbers in it left to right and similarly for columns, reading the numbers going down. For instance, the row magnitude of the 1-...
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0answers
66 views
Number of permutations with satisfactory triangles
We are given $N$ points($N \leq 40$), where no combination of three or more points is colinear. The values of $x$ and $y$ are bounded by [$0$,$10^4$]. The problem is to find the number of permutations(...
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1answer
102 views
Iterated multiplication of permutation matrices
Given $m$ matrices of size $n\times n$ each of which is promised to be a permutation is it in $\mathit{quasiAC}^0$ or $\mathit{AC}^0$ to multiply the permutations where
$m=\mathit{poly}(n)$
$m=\...
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0answers
41 views
Binary ↔ Gray permutation matrix
Generating a Gray code representation of a binary number can be thought of as mapping one binary number onto another binary number. Therefore, $n$-bit Gray code is a permutation of $2^n$ elements.
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1answer
192 views
number of ways evaluation of expression such that value not changed [closed]
one example:
How many ways we can do possible value-preserving parenthesis the following expression in such a way that value not changed after parenthesis with one constraint that parenthesis among ...
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1answer
87 views
Find Optimal Permutation/Positioning to Minimize the Total Distance for a Given Path
Summary:
A task for picking certain objects is given in the form of an ordered sequence (eg. to pick apple, banana, apple, apple, orange, order matters). The objects have to be preassigned to certain ...
4
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4answers
670 views
Enumerating all partial permutations of given length in lexicographic order
I need to generate all unique tuples of length k chosen from a series of unique, positive integers. In my case n choose k will have n=10, 1 <= k <= 10; and the series I am choosing from is { 0, ...
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1answer
76 views
Find The "Best" Permutation of Inputs to Maximize Sum of Functions (or approximate "best")
The Problem (in words)
I want to sort $N$ items where the value of item $i$ at position $p$ is given by the function $f_i(p)$. The "best" order for these items is the one that maximizes the ...
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1answer
35 views
Given permutation $p$, compute $p^{-2}$
I'm now to problem solving, and I need some help and insight on the following problem from HackerRank:
Given a sequence $p(1),\ldots,p(n)$ of distinct numbers from $1$ to $n$, find numbers $y_1,\...
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1answer
58 views
What's wrong with the following shuffle algorithm?
Suppose I have an array A of size n, with the initial state of:
...
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0answers
56 views
Simple incremental hash funcion
I have permutations:
4 1 2 5 3
4 3 2 5 1
numbers can be order magnitude of 1000 (fits in two bytes)
I want compute 32 bit (or better 64 bit) hashes, it should be ...
2
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0answers
81 views
How do you write a python\pseudo code that generates all pair permutations?
What would be a good pseudo code or Python 3 code for the following permutations problem?
Let us define a n-permutation as a bijective function $\pi: \{0,...,n-1\}\rightarrow \{0,...,n-1\} $ and ...
0
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0answers
39 views
finding the combinatorial solutions of series and parallel nodes
I have n nodes, and I want to find the (non duplicate) number of possible ways in which these nodes can be combined in series and parallel, and also enumerate all the solutions. For example, for n=3, ...
0
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0answers
55 views
Finding index of $p_{k}$ element in the original sorted array if elements were to be removed using a specific condition
Consider a sorted list of numbers $C_{0}=\{0,1,2,3,...,n-1\}$ from where one element will be eliminated at each step. We are also given a value $L$ in $[0, 1)$ and let the indexing start from $0$.
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2
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1answer
96 views
Math behind leetcode problem 47 permutations II
Please tell me why the expression i>0 && nums[i] == nums[i-1] && !used[i-1] works on getting unique permutations. And what is the math behind it?
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1answer
72 views
Given $n$ unique items and an $m^{th}$ normalised value, compute $m^{th}$ permutation without factorial expansion
We know that the number of permutations possible for $n$ unique items is $n!$.
We can uniquely label each permutation with a number from $0$ to $(n!-1)$.
Suppose if $n=4$, the possible permutations ...
0
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1answer
745 views
Greedy sequential/parallel task scheduling
We have N tasks that need to be scheduled for processing. Each task consists of two parts that need to executed in order. The first one is guarded by a mutex and ...
1
vote
1answer
58 views
What is the maximum number of indices one can create on a table with N columns?
Say, I have a database table with $N$ columns. What is the (theoretical) maximum number of indices I can create on that table? For $N = 1,2,3$ it's easy enough to calculate the answer $(1, 4, 15)$, ...
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2answers
30 views
encrypt with permutation ciphers
I came across this question:
You are given a permutation cipher defined by the bijection t: N -> N where,
...
3
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1answer
101 views
Minimize function on permutations
Problem:
Consider $[k] = \{ 1, 2, \dots, k \}$ and function (of two arguments) $f: [k]^{2} \rightarrow \mathbb{N}$ that is defined for all $(n, m) \in [k]^{2}$ (all ordered pairs of numbers from $[k]$...
2
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1answer
44 views
If I walk through list and delete every out-of-order element I come across, on average how many elements will be left?
I have a uniformly randomly permuted list of length $n$. I walk through the list element-by-element, and delete an element if it's out-of-order (compared to the previous in-order elements of the list)....
2
votes
1answer
190 views
Pseudo code of recursive method of printing all permutations of $n$ given integers
I really don't understand this pseudo code. The function prints all permutations of $n$ given integers, assuming that all numbers are different.
Is there a way to explain this code more easily as I ...
1
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0answers
68 views
Is there an algorithm to generate all permutations of a multiset through swaps?
I am currently working on a project where I have to perform a computation over all possible permutations of a multiset $S$. In my setting, each multiset is a list of small positive integers such as $S ...
9
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2answers
509 views
Subset sum problem for permutations
Given permutations $g_1,\,\ldots, g_m \in S_n$ of size $n$ and target permutation $g \in S_n$, decide if there exists a subset of $\{g_1,\, \ldots, g_m\}$, which composition in some order (or, ...
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4answers
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Stack Permutation Algorithm
I was recently designing a Forth stack machine. I have an atomic instruction which rotates the top N elements.
For example if the top of the stack is on the left, then say the N=3 rotate instruction ...
0
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1answer
70 views
Analysis of Pan-cake sorting
i was implementing pan-cake sorting. We can implement it by taking largest element to start and flipping it recursively (Like selection sort).
However it is mentioned that the A[i] has to be a ...
3
votes
0answers
51 views
Generating permutations with a given bubblesort distance
I'm looking for an algorithm to randomly generate permutations on 1:n, which though have a defined bubblesort distance d from 1:n, e.g. (2,3,1) and (3,1,2) are distance 1 from (1,2,3), (2,3,1) and (3,...
2
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1answer
61 views
Combinations and Permutations of M sets of distinct items?
I'm wokring on this problem for a while. I want to know:
The correct name of this problem, so I can look it up in textbooks\online.
Here is the problem descirption:
The (un-ordered) combinations to ...
1
vote
1answer
86 views
Applying subproblem technique to permutations with grouping
I am trying to apply overlapping subproblems and dynamic programming to permutations.
Say, we have a set of $n$ elements in a string. Each of these elements could be a $1$ or a $0$.
Given some ...
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2answers
965 views
number 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 ...
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0answers
34 views
Complexity of Rearranging a Prefix Tree/Alternative Data Structures
Let $S$ be a subset of $[0,1]^l$. Is there some data structure that can represent $S$ and can perform the following operations/queries efficiently*?
$ADD(s \in [0,1]^l)$ - operation which updates $S$ ...
0
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2answers
1k views
How to generate all combinations given an array of elements using backtracking?
Given an array, generate all combinations
For example:
Input: {1,2,3}
Output: {1}, {2}, {3}, {1,2}, {2,1}, {1,3}, {3,1}, {2,3}, {3,2}, {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, {3,2,1}
I am ...
0
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1answer
97 views
Minimize same placed elements in a list of permutations (Heap)
I'm trying to optimize the permutations generated from a set of n elements.
Here is the pitch:
I have a set of 6 elements $\{1,2,3,4,5,6\}$ and I want to create 10 permutations. I could use Heap ...
1
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2answers
367 views
Permute an array in O(n) time with O(1) extra space with a given ordering function?
This question arises from a problem on a problem solving site (https://practice.geeksforgeeks.org/problems/-rearrange-array-alternately/0).
Given a sorted (ascending order) array $A$ of $N$ ...
6
votes
1answer
655 views
Generate all permutations of 1 to n with i stacks
Assume we have i stacks. the possible actions are:
push to first stack form input
pop from stack i and push it to stack i+1
pop from last stack to output
If we have numbers of 1 to n starting from 1 ...
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2answers
208 views
Check if two separate ranges have some number in common
We are given two permutations: A of size N and B of size M. We need to process Q queries, each query is given by two ranges, one subarray range in permutation A and one in B. We should check if there ...
4
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2answers
153 views
Algorithm for factoring elements of permutation groups?
You can solve a Rubik's cube by factoring its permutation into a sequence of "elementary" permutations (a subset of permutations that is sufficient to construct every other permutation in the group). ...
4
votes
1answer
228 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 ...
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2answers
102 views
Lexicographic permutation list
Does anyone have an algorithm for stepping through all permutations of n given arbitrary objects in lexicographic order?
Thanks.
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1answer
27 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
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0answers
26 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
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1answer
291 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
120 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 $...
