# 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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### Numbers with distinct decimal digits

Write a program or function that outputs all positive integers with distinct decimal digits (OEIS: A010784) Examples: ...
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### First odd then even indices

Your task is to find out how often you need to "shuffle" a given list with the following operation until you get back the original list. ...
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### Count N-Rich Permutations of an Integer Sequence

Given a sequence of integers with length $L$ and an integer $1 \le N \le L$, an "$N$-rich" permutation is one whose the longest strictly increasing contiguous subsequence has length ...
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### How many sorting networks?

Below on the left is a picture of a sorting network that can sort 4 inputs. On the right you can see it sorting the input 3,2,4,1. A sorting network of size ...
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### Find Unique Anagrams

Challenge Description: An anagram is a word or phrase formed by rearranging the letters of another word or phrase. For example, "listen" and "silent" are anagrams. In this ...
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### Generate all possible equations from a list of numbers [closed]

This is my first codegolf post so let me know if I have missed anything. Thanks :) Description You are given a list of numbers with 2 < n <= 6 length i.e. [1, ...
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### Decoding a non injective bit matrix encoding

The problem Someone has created an encoding format for square bit matrices, however they have found it isn't perfect! One encoding may not decode to exactly one matrix, or it may not even be possible ...
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### Generate a permutation from the high-water marks

Given a permutation, we can define its high-water marks as the indices in which its cumulative maximum increases, or, equivalently, indices with values bigger than all previous values. For example, ...
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### Normal Subgroups of $S_4$

Objective Given a permutation of 4 distinct items, classify the permutation by the normal subgroup(s) it belongs. Input/Output Format You gotta choose the followings as the hyperparameters for your ...
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### CGAC2022 Day 6: Shuffles with specific "magic number"

Part of Code Golf Advent Calendar 2022 event. See the linked meta post for details. On the flight to Hawaii for vacation, I'm playing with a deck of cards numbered from 1 to $n$. Out of curiosity, ...
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### Character insertion on letterboards

You know those letterboards outside old-style cinemas which show upcoming films - perhaps you have a miniature one in your home? If you've operated one, you'll know that you can normally add letters ...
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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 [email protected], [email protected], and [email protected] 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 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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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 ...