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.
216 questions
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Sticks expectation
This was originally a question from interviewstreet.com over a decade ago
You are given an array (or whatever - your choice of input) of positive integers \$y_1,\ldots,y_n\$ that represents \$n\$ line ...
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4
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Identify Last-Layer Perm of a Rubik's Cube
A popular method for solving Rubik's cube consists of:
solving its first two layers, by convention starting with the white side
orienting the last layer's pieces so they face the same direction with ...
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Write two very different programs with the same characters
Your task is to write two programs/functions, in the same language.
Program 1: Verify that two inputs are anagrams of each other.
Program 2: Verify that two inputs differ from each other at every ...
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Triangular Transposition Cipher
A text that can be arranged triangularly in some fashion can be read back in some other fashion effectively enciphering it.
Narrowing down a set of plausible triangular numberings allows to ...
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All possible swaps for the permutation
Given a permutation of {1,2,...,n} named A, do each swap of form swap A[i], A[j] exactly once, where ...
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Unap_peel_ing permutations
Given the height, \$h\$, and width, \$w\$, describing a rectangle of the first \$hw\$ natural numbers in row-major order produce the numbers in the order they are encountered by repeatedly removing a ...
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13
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Meandering over ℤ
The easiest way to understand this task is to look at this
graph,
which you can change interactively.
It defines a sequence n -> a(n) like this:
a(0) = 0; thereafter a(n) is the least integer (in ...
- 1,742
8
votes
6
answers
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Ranking of binary trees
Let N = [0,1,2,...n-1] be the initial segment of the natural
numbers of length n, then all permutations of N can be sorted
lexicographically, starting with the identity. The index into this
sorted ...
- 1,742
6
votes
3
answers
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Implement any rotation-invariant function on colored dodecahedrons
Each of a regular dodecahedron's 12 faces can be painted either red or blue. Your task is to implement a function \$f\$ that takes a painted dodecahedron (as 12 booleans, in whatever order and format ...
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7
votes
12
answers
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Counting constrained permutations
Challenge:
Write a program or function that, given positive integers n, t, b, c, counts permutations of 1..n where:
Exactly t numbers are in their original position
Exactly b numbers are higher than ...
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3
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4
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Create 251610 matrices as quickly as possible
There are 251610 6 by 6 binary matrices that are inequivalent. We say two matrices are equivalent if there is some permutation of their rows and/or columns that makes them equal.
For example:
...
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votes
9
answers
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Reorder a string of length \$2^n\$ by permuting the \$n\$ binary digits of every index
Given a binary string \$s\$ of length \$2^n\$ and a permutation \$\sigma\$ of \$\{1,\dots,n\}\$, generate the binary string \$u\$ of length \$2^n\$ which is a reordering of \$s\$ such that \$u[i^\...
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8
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Lexicographically earliest permutation of the initial segment of nonnegative integers subject to divisibility constraints
The challenge is simple: Reorder the first integers {0, 1, 2, ..., n} into an ordered list so that the following three conditions are met:
If k is the last element in the list, then all of its prime ...
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18
answers
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Check if two lists are permutations of each other [duplicate]
Challenge
Given two lists of equal length, find if one of them is a permutation of the other. Output truthy or falsy values, or 1 or 0.
Test case Examples
...
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Find the child anagrams of a word
Select any word from https://websites.umich.edu/~jlawler/wordlist with length greater than 1. For each letter on that word, remove it and check if any rearrangement of the remaining letters is present ...
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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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votes
8
answers
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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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answer
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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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votes
14
answers
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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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12
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18
answers
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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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3
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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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12
answers
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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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14
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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 ...
- 103k
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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
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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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25
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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 ...
- 103k
28
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30
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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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4
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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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votes
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answers
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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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0
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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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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 <...
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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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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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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 ...
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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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