Problem 44072. Number of paths on a n-dimensional grid

Created by Jihye Sofia Seo

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>This problem is inspired by</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/1483-number-of-paths-on-a-grid\"><w:r><w:t>&lt;https://www.mathworks.com/matlabcentral/cody/problems/1483-number-of-paths-on-a-grid</w:t></w:r></w:hyperlink><w:r><w:t>&gt; and </w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/44066-number-of-paths-on-a-3d-grid\"><w:r><w:t>&lt;https://www.mathworks.com/matlabcentral/cody/problems/44066-number-of-paths-on-a-3d-grid</w:t></w:r></w:hyperlink><w:r><w:t>&gt;, which you might want to solve first.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Consider n-dimensional grid, and you are moving from one corner to the farthest corner in a minimal number of moves. Each move corresponds to moving to a neighbouring hypercube (among possible up to 2*n neighbours). How many ways are there?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Input format is a row array of size \"d\" (for d dimension) with number of grid points on each direction.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Optional: can you solve it without loops?</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

16 Solutions
15 Solvers

Last Solution submitted on Nov 29, 2020

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 44072. Number of paths on a n-dimensional grid

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Problem 44072. Number of paths on a n-dimensional grid

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Players