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 ...
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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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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 \$...
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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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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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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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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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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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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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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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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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