Questions tagged [graph-theory]
For challenges regarding graphs, mathematical structures used to model relations between objects.
186
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Convert between graph representations
What?
Let's say I have this graph:
1
\
\
2 3
\ /
\ /
4
I can represent it in 2 ways:
A list of connected vertices. ...
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21
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1
answer
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Can you draw this in one stroke?
Related | Related
Given an ASCII art with |, _, and , check if you can draw the art in one ...
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8
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Chromatic polynomial of a graph
Given a undirected graph \$G\$ and a integer \$k\$, how many \$k\$-coloring does the graph have?
Here by a \$k\$-coloring, we mean assigning one of the \$k\$ colors to each vertex of the graph, such ...
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8
votes
4
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Your trees need to be rerooted
In graph theory a tree is just any graph with no cycles. But in computer science we often use rooted trees. Rooted trees are like trees except they have one specific node as the "root", ...
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Who Is Kevin Bacon?
You may know the game The Six Degrees of Kevin Bacon, based on the conjecture that every actor in Hollywood can be connected to Kevin Bacon by no more than 6 "co-star" relations, so Kevin ...
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AoCG2021 Day 19: To Hire or To Fire
Part of Advent of Code Golf 2021 event. See the linked meta post for details.
The story continues from AoC2018 Day 7, Part 2.
Why I'm pxeger, not Bubbler
As soon as you and a few Elves successfully ...
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12
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9
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AoCG2021 Day 13: Defrag in action!
Part of Advent of Code Golf 2021 event. See the linked meta post for details.
The story continues from AoC2017 Day 14.
To recap: The disk is a rectangular grid with \$r\$ rows and \$c\$ columns. Each ...
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13
votes
2
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Is this an interval graph?
Background
An interval graph (Wikipedia, MathWorld, GraphClasses) is an undirected graph derived from a set of intervals on a line. Each vertex represents an interval, and an edge is present between ...
- 62.1k
10
votes
4
answers
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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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Classify a graph
Challenge
Given a graph (a structure consisting of nodes and vertices), classify it according to a few categories.
Specifically, you will be given an unweighted directed graph, which is a set of nodes ...
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0
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NP-complete reduction: (grid-)Hamiltonian circuit
Background
Hamiltonian circuit problem is a decision problem which asks whether a given graph has a Hamiltonian circuit, i.e. a cycle that visits every vertex exactly once. This problem is one of the ...
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Taking the long route
Challenge
Your goal is to find the furthest point on a graph (from a provided start node). Your code doesn't need to handle cycles in the graph properly, but it might pose a fun challenge. For this ...
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3
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Radio station hopping
Introduction
You are listening to a car radio. You are pressing seek up/down, moving you to the next frequency some radio station broadcasts on, to avoid all this pointless music and listen to all the ...
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7
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Find the Best Set of Adapters
I'm trying to plug this really old phone into my computer but the phone seems to use a very obscure plug. Luckily I have some adapters. Unfortunately, I can't figure out which of them to use to ...
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1
answer
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Is this Game of Go configuration fully alive?
Background
This challenge is about the Game of Go. Here are some rules and terminology relevant to this challenge:
Game of Go is a two-player game, played over a square board of size 19x19.
One of ...
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18
votes
5
answers
953
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Count all binary relations
A binary relation on a set \$X\$ is simply a subset \$S \subseteq X \times X\$; in other words, a relation is a collection of pairs \$(x,y)\$ such that both \$x\$ and \$y\$ are in \$X\$. The number of ...
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A graph and its seven closures
Background
A little while ago, someone posted an interesting puzzle on Math.SE:
What is the smallest digraph (directed graph) G where the following eight graphs are all distinct:
G, the original ...
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votes
7
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Are these states connected?
With the US election going on right now, I noticed that there is one (completely meaningless, but still) thing which Trump can still achieve and which is out of reach for Biden: Having the won states ...
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votes
8
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Count Euler's Tours
Leonhard Euler wants to visit a few friends who live in houses 2, 3, ..., N (he lives in house 1). However, because of how his city is laid out, none of the paths between any houses form a loop (so, ...
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votes
0
answers
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Solve the Trolley Problem with Multitrack Drifting [closed]
Introduction
Programmers have already solved the trolley problem (a classical problem in philosophy). In the usual trolley problem, we have a directed graph and each edge is weighted by the number of ...
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4
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Find the maximum flow
Given a directed network, with a single source and a single sink, it is possible to find the maximum flow through this network, from source to sink. For example, take the below network, \$G\$:
Here, ...
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10
votes
11
answers
802
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Counting King's Hamiltonian Paths through 3-by-N grid
Background
A Hamiltonian path is a path on a graph that steps through its vertices exactly once. On a grid, this means stepping through every cell exactly once.
On a square grid, a Chess King can move ...
- 62.1k
12
votes
1
answer
494
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Scoring Quantum Tic-Tac-Toe
In the description of this challenge, the following board will be used as a reference for positions:
ABC
DEF
GHI
For instance, in a game of ordinary tic-tac-toe, <...
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14
answers
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Get to the Zone!
You are playing a famous game called \$1\text{D Array BattleGround}\$. In the game, the player can be stationed in any position from \$0\$ to \$10^5\$.
You are a Paratrooper in the game and have the ...
20
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7
answers
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Break The Chain
You are given an \$ 25 \times 25 \$ square lattice graph. You are to remove certain nodes from the graph as to minimize your score, based on the following scoring system:
Your score will be the \$ \...
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5
votes
0
answers
321
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Hamming distance traveling salesman problem
The Hamming distance between two strings is the number of positions they differ at.
You are given a set of binary strings. The task is to find the length of the shortest route that visits all of them ...
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5
votes
1
answer
249
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How annoying is my Euler diagram?
Challenge
Premise
Euler diagrams consist of simple closed shapes in a 2-D plane that each depict a set or category. How or whether these shapes overlap demonstrates the relationships between the ...
11
votes
2
answers
407
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Spanning paths in a tournament on n nodes
The goal of this challenge is to extend the On-Line Encyclopedia of Integer Sequences (OEIS) sequence A038375.
Maximal number of spanning paths in tournament on n nodes.
A tournament on \$n\$ ...
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1
vote
0
answers
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Minimum Hop Count in Directed Graph based on Conditional Statement [closed]
A directed graph G is given with Vertices V and Edges E, representing train stations and unidirectional train routes respectively.
Trains of different train numbers move in between pairs of Vertices ...
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3
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All roads lead to Rome
"All roads lead to Rome" is a saying that essentially means there are plenty of different ways of achieving an objective.
Task
Your task is to write a program that finds a set of link connections ...
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23
votes
32
answers
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Drawing one-liner
CodeDrawing one-liner
Teaser
Behold this formidable drawing:
Can you draw this in a single stroke? Give it a try.
Can you do this one, now:
Give it a try.
How it works
These "make this drawing ...
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13
votes
1
answer
400
views
Gossipping ladies
Problem description
Vertices \$V\$ of directed graph \$G=(V,E)\$ represent gossipping ladies; edge \$(u,v) \in E\$ signifies that lady \$u\$ knows of lady \$v\$ (which does not imply that lady \$v\$ ...
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10
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Random spanning tree of a rectangular grid
Significantly harder version of Spanning tree of a rectangular grid.
Background
A spanning tree (Wikipedia) of an undirected graph is a subgraph that is a tree which includes all of the vertices of ...
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16
votes
2
answers
451
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Calculate Coefficient of Inbreeding
Your task is, given a family tree, to calculate the Coefficient of Inbreeding for a given person in it.
Definition
The Coefficient of Inbreeding is equal to the Coefficient of Relationship of the ...
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2
answers
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Can this Scottish village have a wedding?
This is the exact same question I asked earlier, but without the annoying Cyrillic factor which many found superfluous. I hope this is a better puzzle!
The quaint hamlet of North Codetown in the ...
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3
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Can this village have a wedding?
The quaint hamlet of Кодгольф in the Russian far east has a problem: their population is low (below 66), and no new people have arrived for years. Moreover, after centuries of near-isolation, just ...
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11
answers
1k
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Spanning tree of a rectangular grid
Background
A spanning tree (Wikipedia) of an undirected graph is a subgraph that is a tree which includes all of the vertices of the original graph. The following is an example of a spanning tree of ...
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8
votes
3
answers
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Multigraphs with a given degree sequence
This challenge will give you an input of a degree sequence in the form of a partition of an even number. Your goal will be to write a program that will output the number of loop-free labeled ...
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19
votes
1
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Gerrymander North Carolina
The challenge
How well can you gerrymander North Carolina into 13 voting districts?
In this challenge, you use the following files to draw different maps for Republicans and Democrats.
File 1: ...
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votes
1
answer
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Complete the grid-filling meander
A grid-filling meander is a closed path that visits every cell of a square \$N \times N\$ grid at least once, never crossing any edge between adjacent cells more than once and never crossing itself. ...
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9
votes
2
answers
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Reroute the Path
Given a grid of directions and a start and end position, determine the minimum number of substitutions in the direction grid that needs to be made to complete the path between the two points. The grid ...
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votes
1
answer
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Pandemic Outbreak Calculator [closed]
In the board game Pandemic, an outbreak occurs when a city contains more than 3 disease cubes. When the outbreak occurs, any disease cubes in the city in excess of 3 are removed, and each city ...
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0
answers
95
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Finding row wise sum of transpose of hv-convex binary matrix [closed]
I'm stuck on a problem involving the Gale-Ryser Theorem. The problem's input gives me the row-wise sum of an hv-convex binary matrix(n*m).
...
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1
vote
3
answers
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Havel-to-da-Hakimi [duplicate]
It was a dark and stormy night. Detective Havel and Detective Hakimi arrived at the scene of the crime.
Other than the detectives, there were 10 people present. They asked the first person, "out of ...
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votes
7
answers
2k
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Surface of the 3x3x3 cube as a graph
Your task is to generate a graph with 54 vertices, each corresponds to a facet on a Rubik's cube. There is an edge between two vertices iff the corresponding facets share a side.
Rules
You may ...
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12
votes
4
answers
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Ambassadors and Translators
Two ambassadors at a UN conference want to speak to each other, but unfortunately each one only speaks one language- and they're not the same language. Fortunately, they have access to several ...
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3
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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 ...
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9
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3
answers
463
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Minimum-cost flow problem
A flow network is a directed graph G = (V, E) with a source vertex s ϵ V and a sink vertex ...
user45941
22
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23
answers
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Pointer jumping
Suppose we have an array \$\texttt{ps}\$ of length \$n\$ with pointers pointing to some location in the array: The process of "pointer jumping" will set every pointer to the location the pointer it ...
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Order of Elements of the Rubik's Cube [duplicate]
Introduction
All the possible moves and their combinations of a Rubik's Cube form a group. A group in general is a set with some binary operation defined on it. It must contain a neutral element with ...
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