Questions tagged [graph-theory]

For challenges regarding graphs, mathematical structures used to model relations between objects.

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7
votes
3answers
371 views

Edge Elimination Number

From Erich Friedman's Math Magic, (problem #2 on that page) your challenge is to find the edge elimination number of a connected graph. A single edge elimination is the removal of an edge from a graph,...
24
votes
7answers
2k views

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 ...
14
votes
9answers
610 views

Find a set of maximal matching edges

Consider a connected undirected graph. A matching set of edges on this graph is defined as a set of edges such that no two edges in the set share a common vertex. For example, the left figure denotes ...
7
votes
8answers
576 views

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, ...
22
votes
3answers
1k views

Map of Islands (and a river)

Introduction For many centuries, there has been a certain river that has never been mapped. The Guild of Cartographers want to produce a map of the river, however, they have never managed to succeed -...
8
votes
14answers
5k views

Find all reachable nodes in a graph

You are given a directed graph in an adjacency dictionary format. This can be whatever format is most natural for your language. For instance, in python, this would be a dictionary with keys of nodes ...
22
votes
10answers
3k views

Can the maze be solved?

Task Print 0 if an n*m maze cannot be solved Print 1 if an n*m maze can be solved (in 1 or more ways) (so I'm not asking for ...
2
votes
0answers
170 views

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 ...
14
votes
4answers
545 views

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, ...
9
votes
11answers
777 views

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 ...
50
votes
3answers
3k views

Help, I'm trapped in a Sierpinski triangle!

Drawing the Sierpinski triangle has been done to death. There's other interesting things we can do with it though. If we squint hard enough at the triangle, we can view upside-down triangles as nodes ...
12
votes
1answer
378 views

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, <...
22
votes
3answers
646 views

Follow incomplete directions

A friend of yours has given you directions to the best restaurant in town. It's a series of left and right turns. Unfortunately, they forgot to mention for how long you need to go straight ahead ...
20
votes
14answers
2k views

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 ...
29
votes
4answers
924 views

Arranging Bubbles

Note, challenge copied from question asked at math.stackexchange. Recently, I attained quite some skill at blowing bubbles. At first I would blow bubbles like this: But then things started getting ...
13
votes
1answer
382 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\$ ...
19
votes
7answers
1k views

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 \$ \...
4
votes
0answers
182 views

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 ...
3
votes
0answers
222 views

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 ...
13
votes
5answers
1k views

Is it bipartite?

A bipartite graph is a graph whose vertices can be divided into two disjoint set, such that no edge connects two vertices in the same set. A graph is bipartite if and only if it is 2-colorable. ...
19
votes
1answer
885 views

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: ...
22
votes
7answers
2k views

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 ...
11
votes
2answers
380 views

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\$ ...
13
votes
10answers
960 views

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 ...
19
votes
3answers
653 views

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 ...
1
vote
0answers
100 views

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 ...
15
votes
26answers
3k views

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 ...
20
votes
14answers
2k views

Check if all non-zero elements in a matrix are connected

Input: A matrix containing integers in the range [0 - 9]. Challenge: Determine if all non-zero elements are connected to each other vertically and/or horizontally. Output: A truthy value if all ...
16
votes
2answers
377 views

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 ...
23
votes
1answer
809 views

Determine if a Graph is Toroidal

A simple graph is toroidal if it can be drawn on the surface of a torus without any edges intersecting. Your task is to take a simple undirected graph via any reasonable method (adjacency matrix, ...
13
votes
7answers
432 views

Cutpoints in a maze

A maze is given as a matrix of 0s (walls) and 1s (walkable space) in any convenient format. Each cell is considered connected to its 4 (or fewer) orthogonal neighbours. A connected component is a set ...
14
votes
11answers
1k views

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 ...
8
votes
3answers
223 views

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 ...
16
votes
5answers
1k views

Minimum operations to get from one number to another

Let's define a simple language that operates on a single 8-bit value. It defines three bitwise operations (code explanation assumes 8-bit value variable): ...
20
votes
1answer
346 views

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. ...
12
votes
5answers
533 views

Get Two from One

As we saw in this question complex logical statements can be expressed in terms of the simple connectives of generalized Minesweeper. However Generalized minesweeper still has redundancies. In order ...
6
votes
1answer
494 views

Hamilton is coming to town

It's almost Christmas, so Santa has to plan his route. You're helping him, for reasons unknown. Santa needs help planning the route and wants you to give him a solution, but since you're all ...
9
votes
2answers
208 views

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 ...
-2
votes
1answer
505 views

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 ...
2
votes
0answers
91 views

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). ...
17
votes
12answers
766 views

Is this Sequence Graphic?

A graphic sequence is a sequence of positive integers each denoting the number of edges for a node in a simple graph. For example the sequence 2 1 1 denotes a ...
1
vote
3answers
248 views

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 ...
12
votes
4answers
318 views

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 ...
19
votes
2answers
3k views

Mastermind strategy

I could only find code-golf challenges for Mastermind, so here's a code-challenge version that I would have liked to take on myself. An optimal strategy for the normal Mastermind game, MM(4,6), was ...
14
votes
3answers
1k views

Solve the Trolley Problem

Philosophers have long pondered the Trolley problem. Unfortunately, no human has solved this problem yet. Luckily, as programmers we can use computers to solve the problem for us! Input Your program ...
13
votes
3answers
392 views

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 ...
15
votes
16answers
5k views

Determine if a relation is transitive

Challenge description Let's start with some definitions: a relation is a set of ordered pairs of elements (in this challenge, we'll be using integers) For instance, ...
51
votes
18answers
4k views

Can my 4-note music box play that song?

I have a crank-operated music box that can play a series of four notes. When I turn the crank, it plucks one of four strings, depending on the position of the crank and the direction of the turn. When ...
21
votes
23answers
3k views

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 ...
9
votes
3answers
272 views

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 ...