Problem 475. Is this group simply connected?

Created by Ned Gulley

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given connectivity information about a graph, your job is to figure out if the graph is fully connected. You are given a list of vertex pairs that specify undirected connectivity (edges) among vertices. Vertex labels are always positive integers.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example 1:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ Input  node_pairs = [ 8 9\n                       8 3 ]\n Output tf is true]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The three nodes of this graph are fully connected, since this graph could be drawn like so:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 3--8--9]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example 2:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ Input  node_pairs = [ 1 2 \n                       2 3\n                       1 4\n                       3 4\n                       5 6 ]\n Output tf is false]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This graph could be drawn like so:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 1--2  5--6\n |  |\n 4--3]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>There are two distinct subgraphs.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

100 Solutions
24 Solvers

Last Solution submitted on May 27, 2022

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Jean-Marie Sainthillier on 11 Jul 2013

Maybe some tests with more than two distincts subgraphs.

Jan Orwat on 29 Feb 2016

Seems the problem became easier with R2015b.

Solution Comments

Solution 58785

1 Comment

1 Comment

Alfonso Nieto-Castanon on 11 Mar 2012

very cool (and efficient) solution

Problem Recent Solvers24

Problem Tags

graph theory

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 475. Is this group simply connected?

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers24

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Problem 475. Is this group simply connected?

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers24

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Players