# Questions tagged [permutations]

A permutation is a particular ordering of some list of objects. Problems tagged with permutation usually involve finding or generating permutations, including anagrams of text.

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### All permutations of range from $1$ to $n$ [duplicate]

Given a positive input $n$, output all permutations of either $\{0,1,\ldots,n-1\}$ or $\{1,2,\ldots,n\}$. Examples Outputting permutations of $\{1,2,\ldots,n\}$. Input Output ...
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### Swap every two elements in the list every possible way

Inspired by this question. Challenge Let L be a list of n distinct elements. Let P be the ...
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### Slater-Velez permutation

Let's build a sequence of positive integers. The rule will be that the next number will be the smallest number which: It hasn't already appeared in the sequence Its absolute difference from the ...
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### Unsort an array

Inspired by this StackOverflow post Given a list where each element appears a maximum of 2 times, we can define it's "sortedness" as the sum of the distances between equal elements. For ...
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### Minimum difference between cartesian product of 3 elements that add up to a certain number

Let's say I've got a list (or array) of: l = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] I want to get the third Cartesian power of the above list, where we take every ...
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### Hamiltonian levencycle of 1-dup permutations

The word "levencycle" is inspired by cyclic levenquine challenge. Definitions A 1-dup permutation of order $n$ is some permutation of $1, \cdots, n$ plus one duplicate number in the ...
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### Is this a Permutation of 1..n

Input a non-empty array with $n$ positive integers. Test if the input array contains every integer in $1\cdots n$. In case you prefer 0-indexed numbers, you may choose to input an array of non-...
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### Largest Number with No Repeating Digit Pairs

Inspired by the problem with the same name on Puzzling SE by our very own Dmitry Kamenetsky. You are to find the largest number that only uses every digit pair once, in a given base. For example, in ...
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### Evaluation order of an APL n-train

From Codidact with permission. Description APL trains are a series of functions, that get applied to an argument in this way: (f g) x = f g x here ...
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### Patterns in Permutations

This fastest-code challenge is based partly on this MSE question and exists to extend some OEIS sequences, and create others. If I extend or create sequences based on this challenge, I'll link to this ...
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### Find the number of parenthesis combinations [duplicate]

For example, given 3 sets of parenthesis, you have: ()()() ((())) ()(()) (())() (()()) = 5 possible combinations. Challenge Program must: • Take 1 number as an ...
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### Sums of permutations of vectors [closed]

I am looking for a more efficient way of computing the following. Let A and B be two vectors of non-negative integers of length <...
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### Verify a Superpermutation

A superpermutation on n symbols is a string which contains every permutation of n symbols in its body. For instance, 123121321 is a superpermutation on three ...
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### Generate Gmail Dot-Aliases

Background You may be aware that periods in between letters in gmail addresses are ignored. Email sent to example@gmail.com, exam.ple@gmail.com, and e.x.a.m.p.l.e@gmail.com all end up in the same ...
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### Pairs of palindromic anagramic dates separated by a palindromic number of days

Definitions: A palindrome is a string which reads the same backward or forward (not counting spaces or special characters), such as "madam" or "Sorel Eros". A date is said to be a palindrome when ...
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### String permutations

Print the biggest-size subset of strings in the input that are all permutations of each other. If there are ties, any one will do. If no strings are permutations of each other (for example, only one ...
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### Super permutations

Super permutations Input: A string The program should loop through all lengths of the input (decrementing one each time), generate all combinations with replacement of the string, then make ...
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### Ethan Finds the Maximum Element

This is a problem that the Hacker Cup team made for the 2018 Facebook Hacker Cup, but we ended up not using it (though Ethan struggles through a variety of other challenges). Normally code size isn't ...
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### Plain Hunt Bell-Ringing

Your task is to create a plain hunt (a bell ringing pattern) with n bells. An example with 6 bells: ...
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### Output Distinct Factor Cuboids

Output Distinct Factor Cuboids Today's task is very simple: given a positive integer, output a representative of each cuboid formable by its factors. Explanations A cuboid's volume is the product ...
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### Permutations in Disguise

Given a $n$-dimensional vector $v$ with real entries, find a closest permutation $p$ of $(1,2,...,n)$ with respect to the $l_1$-distance. Details If it is more convenient, you can use ...
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### I see your BIDMAS and raise you a BADMIS

I see your BIDMAS and raise you a BADMIS Challenge Given a set of numbers with operators between them: "5 + 4 * 9 / 3 - 8", return all the possible results of the expression for every permutation of ...
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### Calculate Landau's function

Landau's function $g(n)$ (OEIS A000793) gives the maximum order of an element of the symmetric group $S_n$. Here, the order of a permutation $\pi$ is the smallest positive integer $k$ such ...
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### Leading and Suffering Numbers

Introduction: In Dutch, the words leading and suffering, being 'leiden' and 'lijden' respectively, are pronounced the same way. One is written with a "short ei", and one with a "long ij&...
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### Dihedral group D4 composition with custom labels

The dihedral group $D_4$ is the symmetry group of the square, that is the moves that transform a square to itself via rotations and reflections. It consists of 8 elements: rotations by 0, 90, 180, ...
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### Enumerate Derangements

Given some positive integer $n$ generate all derangements of $n$ objects. Details A derangement is a permutation with no fixed point. (This means in every derangement number $i$ cannot be in ...
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### Words hidden in my phone number [closed]

Telephones in the United States (and perhaps some other places) have letters associated with some of the numbers. ...
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### Source permutation

A permutation of a set $S = \{s_1, s_2, \dotsc, s_n\}$ is a bijective function $\pi: S \to S$. For example, if $S = \{1,2,3,4\}$ then the function $\pi: x \mapsto 1 + (x + 1 \mod 4)$ is a ...
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### Unique Brick Tilings Within A Rectangle

I was browsing Stackoverflow and saw this question about tiling an MxN rectangle, and I thought it would be great for golfing. Here is the task. Given the dimension M and N, write a program that ...
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### Superpermutations

Introduction You're a criminal tasked with stealing some secret plans from the new tech startup Dejavu. You sneak in over the back wall, but find a door that requires a pin to open it. You recognize ...
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### Hide the buildings

Shorter version of Skyscrapers Challenge Task Given an array of building heights and a positive integer k, find all the permutations(without duplicates) of the ...
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### Doce logf a string swapper [closed]

Challenge Take an input string $s$, and split it into words $w_1, w_2, ..., w_n$. If the amount of words is odd, then return $s$. Otherwise, for each word: Take the second last letter, and swap ...
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### 9erilous 9ermutations

Note: This is an attempt at recycling guest271314's permutation question(s) There's an interesting pattern that forms when you find the differences between lexographically sorted permutations of base ...
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### Amidakuji (阿弥陀籤) simplification

If you have ever had any exposure to Japanese or East Asian culture you will have surely encountered the Amidakuji game: As Wikipedia explains, it is a type of lottery drawn on paper and used to ...
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### Encode - Shuffle - Decode

Challenge Your task is to encode an integer as a string of ASCII characters, then successfully decode it after said string has been randomly shuffled. You will write two programs/functions, which ...
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### What is the simplest reversible circuit that computes conjugacy of transpositions?

Reversible computation refers to computation in which little or no information is deleted. Reversible computation a major component of quantum computation, and reversible computation is potentially ...
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### Permutation Encoding

Write a program which can encode text to avoid reusing characters, and convert back. Both normal and encoded forms are restricted to a particular character set: the space character ...
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### Block Rearrangement

So your task is to take a 3x3 block where -'s mean blank spaces, and *'s mean filled spaces, for example: ...
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### Levi-Civita symbol

The three-dimensional Levi-Civita symbol is a function f taking triples of numbers (i,j,k) each in ...
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### Codegolf the Hafnian

The challenge is to write codegolf for the Hafnian of a matrix. The Hafnian of an 2n-by-2n symmetric matrix ... 942 views

### Conjugate permutations

A permutation of size n is a reordering of the first n positive integers. (meaning each integer appears once and exactly once). Permutations can be treated like functions that change the order of a ...
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