Questions tagged [set-partitions]
For challenges related to the subdivision of a set into smaller disjoint sets. This also includes the subdivision of ordered collections like lists, and non-discrete sets like intervals. Challenges should carefully define the partition concept being used.
64 questions
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Half Price for Every Second Pizza
PizzaTata is a popular restaurant specializing in pizza delivery. Customers can order pizzas by phone. And each order is charged by the sum of pizza prices and the delivery fee.
Pizza Prices: The ...
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Solve the "word break problem" in a single line of code
Challenge
Solve this problem in the fewest number of bytes of code possible.
Write code that takes a string \$str\$ and a dictionary-list of words \$d\$ and finds all combinations of words from \$d\$ ...
- 475
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Night hike partitioning
We want to go on a night hike with the youth group, but of course not everyone has their torch, even though we told them we planned to split up. What options are there for group formation if n teens ...
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Find the fairest partition of a list
Given a list of positive integers, partition the list into two sublists such that the absolute value of the difference of the sums over the two sublists is minimal.
The output of the program should be ...
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Help, I can't bloody well memorize this number!
The Brits aren't exactly known for being good at memorizing stuff. That's why scientists need newspaper articles to find those who are, and that's why it shouldn't be a surprise that they forget more ...
- 637
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Write a set as a union of ranges
In this challenge, we define a range similarly to Python's range function: A list of positive integers with equal differences between them. For example, ...
- 46.2k
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Minimum partition with non-empty intersections
Given a set of intervals \$\mathcal{I} = \{I_1, \ldots, I_m\}\$, where each interval \$I_j\$ is represented by its bounds \$(a_j, b_j)\$, find a partition \$\mathcal{T}\$ of \$\mathcal{I}\$ of minimal ...
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Is this substring list ambiguous?
Given a set of substrings, such as [ca, ar, car, rd], it's possible to create infinitely many strings by concatting them together. Some examples of this for the ...
- 19.3k
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Incomparable partitions
A partition of a list \$A\$ is a way of splitting \$A\$ up into smaller parts, concretely it is list of lists that when concatenated gives back \$A\$.
For example ...
- 103k
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Cut along the lines
In this challenge you will take as input a non-empty list of binary values (these can be booleans or integers on the range 0-1), you should output all the ways to partition the list into non-empty ...
- 103k
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Divisible subset sums
Inspired by the recent 3Blue1Brown video
Consider, for some positive integer \$n\$, the set \$\{1, 2, ..., n\}\$ and its subsets. For example, for \$n = 3\$, we have
$$\emptyset, \{1\}, \{2\}, \{3\}, \...
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There's more than one way to skin a set
Given a set of positive integers \$ S \$, output the set of all positive integers \$ n \$ such that \$ n \$ can be made by summing a subset of \$ S \$ in more than one different way, i.e., that are ...
- 25.3k
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answers
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Third Stirling numbers of the second kind
\$\left\{ n \atop k \right\}\$ or \$S(n, k)\$ is a way of referring to the Stirling numbers of the second kind, the number of ways to partition a set of \$n\$ items into \$k\$ non-empty subsets. For ...
- 50.9k
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Square chunk my matrix
Your challenge is to write a function/program that takes a matrix of integers m and a number n as input and:
Splits m into n by n chunks
Replaces each chunk with the most common value in that chunk (...
- 46.2k
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The number of tilings of a grid
Setup:
A block is any rectangular array of squares, specified by its dimensions \$(w,h)\$. A grid is any finite ordered list of blocks. For example, \$\lambda = ((3,2),(3,1),(1,2))\$ defines a grid.
...
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Topologically distinct ways of dissecting a square into rectangles
I was asked by OEIS contributor Andrew Howroyd to post a Code Golf Challenge to extend OEIS sequence A049021.
Would be super great to get a couple more terms for [...] A049021. Kind of thing [...] ...
- 8,165
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Is it a vampire number?
Repost and improvement of this challenge from 2011
A vampire number is a positive integer \$v\$ with an even number of digits that can be split into 2 smaller integers \$x, y\$ consisting of the ...
- 50.9k
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Split a number in every way possible way within a threshold
Task
Given a positive integer number and a threshold, split into every possible way without generating any numbers above the threshold.
Examples
Input: 15008
Threshold: 400
Valid Output:
...
- 253
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Split a number in every possible way
You task here is very simple:
Given a positive integer n without leading zeroes as input, split it in all possible ways
Examples
Input->Output
...
- 25.5k
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(RGS 5/5) Computing the set of all set partitions with fixed sizes
Task
Given a set of n unique elements and a multiset l of positive numbers that add up to n,...
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Counting the number of restricted forests on the Möbius ladder of length n
OEIS sequence A020872 counts the number of restricted forests on the Möbius ladder Mn.
The Challenge
The challenge is to write a program that takes an integer as an input ...
- 8,165
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votes
2
answers
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Partition a square grid into parts of equal area
This challenge is based on the following puzzle: You are given an n by n grid with n cells ...
- 8,165
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votes
15
answers
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Split a list into sized chunks, but not counting items failing predicate
Motivation: Sometimes certain items in a list don't count towards your totals. For example, counting plane passengers in rows, where babies sit on a parent's laps.
Challenge: write a program to split ...
- 443
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Partition it into as few disjoint contiguous increasing subsequences as possible [closed]
Specification
This challenge is simple to state: your input is a non-empty array of nonnegative integers, and your task is to partition it into as few substrings as possible, such that each substring ...
14
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Decomposing into primes
Given an integer n, return the number of ways that n can be written as a list of prime numbers. For example, 2323 can be written ...
- 1,543
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Advent Challenge 6: Transport Dock Relabeling!
<< Prev Next >>
Thanks to the PPCG community, Santa managed to sort his presents into the correct order for moving into the transportation dock. Unfortunately, the transportation dock signs are ...
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Let's divide a lattice
Let's say we have a n × n lattice; we can then divide the lattice into two sections by drawing a line through the lattice. Everything to one side of the line is in one set and everything else in ...
- 103k
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How many partitions contain only perfect squares?
Given a non-negative integer or a list of digits, determine in how many ways can the number be formed by concatenating square numbers, which may have leading zeroes.
Examples
...
- 42.8k
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Cover a set with multiples
Lets take a set of integers greater than 1 and call it X. We will define S(i) to be the set of all members of X divisible by i where i > 1. Would like to choose from these subsets a group of sets ...
- 103k
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Rectangular difference
In this challenge, you are given two overlapping rectangles, and you need to calculate the rectangles created by removing one from the other.
For example, if you remove the red rectangle from the ...
- 14.5k
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Find Subset Factors
Let's imagine we have a finite set of positive integers. This set can be represented as a line of dots where each integer present in the set is filled in like a scantron or punch card. For example ...
- 103k
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Generate all Sublist Partitions
Given a non-empty list of integers, output every possible partitioning of the list where each partition is a non-empty sublist.
So for the list [1, 2, 3, 4] the ...
- 23.6k
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Count occurences of a set in a list
Given a non-empty set of strings and a list of strings, find out how many times the set occurs in the list, i.e. how many times you could create the set with items from the list. Every element from ...
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Split a grid into a grid
Introduction
There is a small village with nothing but a few houses and empty fields.
The local bureaucrats want to divide the village into lots so that each lot contains exactly one house, and the ...
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List all multiplicative partitions of n
Given a positive number n, output all distinct multiplicative partitions of n in any convenient format.
A multiplicative partition of n is a set of integers, all greater than one, such that their ...
- 39.4k
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Dobble/SpotIt card generator
Introduction
Dobble/SpotIt is a card game, where people have to spot same symbol on pair of cards in shortest time, indicate it and move to next pair. Each card has multiple symbols (8 in normal ...
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Smallest number of contiguous monotonic subsequences
A monotonic subsequence is a sequence of numbers \$a_1, a_2, ..., a_n\$ such that
$$a_1 \le a_2 \le ... \le a_n \\
\text{or} \\
a_1 \ge a_2 \ge ... \ge a_n$$
...
- 5,722
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Arranging arbitrary rectangles to fill a space
Can these rectangles fill a rectangular space?
Given a bunch of rectangles, you are asked whether or not they can be arranged to fill a rectangular space.
Specs
Given a bunch of arbitrary ...
- 42.8k
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votes
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Solve Grid-Tangram
The Tangram is a dissection puzzle made from seven shapes: Five differently sized triangles, a parallelogram and a square. Given a shape, the goal is recreating the shape using all the pieces and ...
- 44.1k
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Partial factorisations of a positive integer
A collection of positive integers d_1 d_2 ... d_k is a factorisation of a positive integer n if
...
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Interquartile Mean
Task
Given (by any means) a sorted floating point dataset, return (by any means and within 1‰ of the correct value) the interquartile mean.
One possible algorithm
Discard the lowest and highest ...
- 31.8k
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Largest Distinctly Sum-Free Partition
related and inspired by -- Finding sum-free partitions
A set A is defined here as being distinctly sum-free if
1) it consists of at least three elements, ...
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Ravenity of Cube Distance Numbers
Inspired by this Numberphile entry
Background
The cube distance numbers of an integer n are defined here as the set of integers that are x³ distance away for a given x. For a simple example, with <...
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Partition a list!
In this challenge, you need to partition a list, where partitions have a max size, a min size, and a preferred size. I'll be using the notation (min,pref,max) to ...
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votes
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Count the ASCII hamantaschen!
Today is Purim on which one custom is to give out triangle-shaped cookies with filling called hamantaschen (singular: hamantasch). Another custom is to drink heavily.
I'm not the most perfect baker.....
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Enumerate rhyme schemes
A "rhyme scheme" is a string of letters a to z, such that the first occurrences of the characters are in ascending order (...
- 198k
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The absent-minded linguist
Background
Your friend, a linguist, has recorded and analyzed some simple conversation snippets in various languages.
Being quite absent-minded, they have forgotten which language each snippet was in....
- 43.2k
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Remove letters while keeping strings unique
Inspired by this wonderful (based on the number of views and votes) challenge, which, in my humble opinion, has way too few answers.
Given (by any means) a list of strings, return (by any means) a ...
- 31.8k
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Find the Intersection of 2 Sets in Unioned Interval Notation
Find the Intersection of 2 Sets in Unioned Interval Notation
Given two sets of real numbers described as the union of intervals, output a description of the intersection of these two sets as a union ...
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Partition into increasing subsequences
Specification
This challenge is simple to state: your input is a non-empty array of nonnegative integers, and your task is to partition it into as few increasing subsequences as possible.
More ...
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