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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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 ...
13 votes
13 answers
567 views

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, ...
11 votes
17 answers
402 views

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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15 votes
9 answers
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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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15 answers
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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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3 answers
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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 ...
9 votes
7 answers
880 views

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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11 votes
12 answers
796 views

Permutations summing to permutations

Given an integer \$N\$ consider a permutation \$p=p_1,p_2,p_3,\ldots\$ of \$1,\ldots,N-1\$. Let \$P = p_1 , p_1+p_2 \bmod N, p_1+p_2+p_3 \bmod N, \ldots\$ be its prefix sums modulo \$N\$. Sometimes \$...
11 votes
14 answers
681 views

Increasing permutation trees

For this challenge a "binary tree" is a rooted tree where each node has 0 children (leaf) or 2. The children of a node are unordered, meaning that while you might draw the tree with left ...
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15 votes
13 answers
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Count alternating permutations

An alternating permutation is a permutation of the first \$ n \$ integers \$ \{ 1 ... n \} \$, such that adjacent pairs of values in the permutation alternate between increasing and decreasing (or ...
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13 answers
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Shuffle an array, a little bit

Given some input array a = [a1, a2, ..., an] and a positive integer k, shuffle the input array ...
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7 votes
13 answers
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Complex permutation

Given an array of integers as input(including negative integers), find all (can include duplicates) permutations that do not have the same number next to each other, then print them all out. If no ...
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8 votes
20 answers
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Give the inverse permutation

Task Given a finite permutation output its inverse. You may take input and output in any reasonable format equivalent to a list of natural numbers. You may choose to use 0 indexing or 1 indexing. ...
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15 votes
8 answers
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Is it a sub-permutation?

A finite-permutation is a function which takes an \$n\$-tuple and produces an \$n\$-tuple such that every element of the input is present in the output, and the ordering does not rely on the values of ...
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22 votes
23 answers
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How many laps around the permutation?

Your input is an array of numbers: a permutation of \$\{1, 2 \dots n\}\$ for some integer \$n \geq 2\$. How many times must you repeat this list before you can "pick out" the numbers \$[1, 2 ...
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16 answers
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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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28 votes
28 answers
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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 ...
8 votes
17 answers
806 views

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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10 votes
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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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16 answers
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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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14 answers
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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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3 answers
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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 ...
3 votes
0 answers
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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 <...
22 votes
20 answers
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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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20 answers
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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 ...
9 votes
6 answers
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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 ...
3 votes
7 answers
255 views

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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19 answers
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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 ...
20 votes
11 answers
4k views

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 ...
18 votes
18 answers
2k views

Plain Hunt Bell-Ringing

Your task is to create a plain hunt (a bell ringing pattern) with n bells. An example with 6 bells: ...
14 votes
11 answers
849 views

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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14 answers
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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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22 votes
9 answers
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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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21 votes
12 answers
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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 ...
9 votes
4 answers
649 views

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&...
14 votes
16 answers
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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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23 answers
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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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3 answers
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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. ...
15 votes
11 answers
1k views

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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14 votes
6 answers
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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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28 votes
13 answers
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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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10 answers
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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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3 answers
147 views

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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7 answers
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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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10 votes
5 answers
550 views

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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23 votes
23 answers
4k views

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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8 votes
1 answer
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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 ...
8 votes
5 answers
834 views

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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