Search for a tool
Lattice Path

Tool to calculate all paths on a lattice graphe (square grid graph). A path is a series of directions (north, south, east, west) to connect two points on a grid.

Results

Lattice Path -

Tag(s) : Graph Theory

Share
Share
dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our community Discord for help requests!


Thanks to your feedback and relevant comments, dCode has developped the best Lattice Path tool, so feel free to write! Thank you !

Lattice Path

Sponsored ads

Path Count Calculator (North-East - NE)

The information on this page is for a square grid and is not valid on triangular grids (or other non square lattice graphs).

Whole Lattice Graph



Between 2 points





Tool to calculate all paths on a lattice graphe (square grid graph). A path is a series of directions (north, south, east, west) to connect two points on a grid.

Answers to Questions

How to count paths on a lattice graph?

The calculation of the number of paths (of length $ a + b $) on a grid of size (a x b) (limited to a north-south direction and a west-east direction) uses combinatorics tools such as the binomial coefficient $ \binom{a+b}{a} $

The north direction N consists of moving up one unit along the ordinate (0,1).

The east direction E consists of moving one unit to the right along the abscissa (1,0).

Example: To go from the point $ (0, 0) $ to the point $ (2, 2) $ (which corresponds to a 2x2 grid) using only north and east. (N,N,E,E), (N,E,N,E), (N,E,E,N), (E,N,E,N), (E,N,N,E), (E,E,N,N) so 6 paths and is computed $ \binom{4}{2} = 6 $

What is a lattice graph?

A grid graph is the name given to a bounded grid (with borders).

How to enumerate pathways in a lattice graph?

To generate the list of all paths, use the permutation generator.

Example: N,N,N,E has 4 distinct permutations: (N,N,N,E) (N,N,E,N) (E,N,N,N) (N,E,N,N)

Source code

dCode retains ownership of the online 'Lattice Path' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Lattice Path download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developped the best Lattice Path tool, so feel free to write! Thank you !


Source : https://www.dcode.fr/lattice-path
© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback