# Questions tagged [graph-theory]

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

177 questions
Filter by
Sorted by
Tagged with
6k views

### Your car only turns right!

Introduction You have the misfortune of being stuck in a runaway car on an obstacle course. All of the car's features are non-responsive, save for the steering system, which is damaged. It can ...
3k views

### Find the Chromatic Number

Surprisingly, we haven't had any challenges on graph colouring yet! Given an undirected graph, we can give each vertex a colour such that no two adjacent vertices share the same colour. The smallest ...
3k views

### How to slow down a drunkard on his way home

Consider a square n by n grid graph that looks like this. It is important to notice that this graph is 11 by 11. At any given point a man stands at an intersection and he only ever moves vertically ...
829 views

### Growing Manhattan Ameobas

An ***ameoba graph**** is a type of tree whose nodes all have values from 0 to some non-negative integer N, and any particular node with value x < N connects to x+1 distinct nodes with values x+1. ...
2k views

### Family Tree Solver

This is one of several challenges left for the community by Calvin's Hobbies. Take a "family tree describing" file with lines of the form: ...
685 views

### How strong are nonary numbers?

You are given a nonary (base 9) non-negative integer consisting of the digits 0 through 8 as usual. However the number of digits in this number (with no leading zeros) is a prefect square. Because of ...
491 views

### Swing Through Trees with Your Grappling Hook

You have found the path through the forest and now plan on travelling along it. However, just before you start on your journey, the ground turns into lava. You manage to scurry up the nearest tree (...
2k views

### Extreme Whitewater Canoeing

You are paddling a canoe down a fairly fast whitewater river. Suddenly, your paddles explode, and you find yourself in a dangerous situation hurtling down a river rapid without any paddles. Luckily, ...
907 views

### Horror Movie Search Party

Plot: Jimmy is missing; we have to find him. We should split up. Plot twist: Jimmy is already dead. But, our cast doesn't know that, so they need to search the whole area anyway. There is an N ...
703 views

### Racketeer Taxi Driver

The Scenario You are a taxi driver in your city. You picked up a passenger from the airport and he told you the place he'd like to go. To earn more money, you need to drive as much as you can. ...
5k views

### To Vectory! – The Vector Racing Grand Prix

User CarpetPython posted a new take on this problem which puts a much bigger focus on heuristic solutions, due to an increased search space. I personally think that challenge is much nicer than mine, ...
3k views

### Are you in the biggest room?

Introduction You have recently accepted a job offer at a Pretty Good Software Company. You're pretty content with the size of your office, but do you have the biggest office? Its kinda hard to tell ...
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 ...
714 views

### Count the terminal cycles of a directed graph

Task You must write a program or function in the language of your choice which accurately counts the number of terminal cycles of a simple directed graph. This particular kind of directed graph is ...
6k 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 ...
369 views

### Wireless Keyboard Inteference

Initech are setting up an office of 36 employees in a soul-crushingly efficient square of cubicles, 6 desks long and 6 desks deep. Management has bought wireless keyboards in bulk from a cheap, ...
815 views

### Alex the Truck Driver

Alex is a Truck Driver who wants to find the quickest way to deliver goods to multiple cities. He knows the distances between his destinations, but you need to write a program to help him find the ...
538 views

### Determine number of connected components

You are given a graph represented through an adjacency list. For example, the input 1-2 2-3 3-4 4-1 would correspond to the graph with nodes 1, 2, 3 and 4, where ...
3k views

### Score a game of Go

Scoring a Go game is a task that is not all too easy. In the past there have been several debates about how to design rules to cover all the strange corner cases that may occur. Luckily, in this task ...
2k views

### City names game

If you like, write a program which sorts cities according to the rules of city name game. Each name of the city should start from the last letter in the previous city name. E.g. ...
2k views

### Calculate Network Average Clustering Coefficient

The clustering coefficient of a graph (or network) is a: measure of degree to which nodes in a graph tend to cluster together The Wikipedia article gives a much better description of how network ...
728 views

### Shortest route through a one-way system

My home town, Rhyl, has a one-way traffic system which seems to have been designed to keep people away from their destination for as long as possible. Your task, should you choose to attempt it, is to ...
244 views

### BWInf 2011, question 5: Twin towns

This is a challenge that was originally a tas for the German Bundeswettbewerb Informatik (federal competition of computer science [?]), a competition for highschool students. As opposed to the ...
2k views

Choose Your Own Adventure books are a form of interactive literature where the reader must make decisions that affect the outcome of the story. At certain points in the story, the reader has multiple ...
2k views

### Traffic light synchronization problem [closed]

I'm not a 100% sure if this qualifies under this stack exchange; however, I asked this question on the stats stackexchange with no answers. I wonder if you can solve it: Traffic light synchronization ...
2k views

### Help Mr Jones to enjoy his bicycle round-trip

Mr Jones wants to do a round-trip on his bicycle. He wants to visit several cities in arbitrary order, but his route must not cross it self, since he hates to be at the same place twice in his ...
993 views

### Shortest path in a graph

Write a program to take a graph (from either standard input or a file, your choice) and find a shortest path in the graph. Graphs are specified using the following format: ...