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Lattice Path

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

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Lattice Path -

Tag(s) : Graph Theory

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Lattice Path

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Path Count Calculator

Between 2 points

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

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 the binomial coefficient $$\binom{a+b}{a}$$

> 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 $$\binom{4}{2} = 6$$