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

102 Solutions
26 Solvers

Last Solution submitted on Oct 30, 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

Show comments

Problem Recent Solvers26

Problem Tags

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 Solvers26

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 Solvers26

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Players