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  • Jesse Sakari Hyttinen

About lexicographic order - Jesse Hyttinen

Updated: Apr 21, 2021


Hi and welcome to the Matladpi blog! In this post I will talk about the lexicographic order the tree generation algorithm is at least partially utilizing.

I think a good way to get a grasp of the order is to look at some examples, without the different possible forms a branch could have.

For example, the rooted tree sum form

1 + 1×7

would have the following forms in tree generation algorithm's lexicographic order, if we exclude the different forms a branch can have:

1 + 2 + 1×5

1 + 2×2 + 1×3

1 + 2×3 + 1

1 + 3 + 1×4

1 + 3 + 2 + 1×2

1 + 3 + 2×2

1 + 3×2 + 1

1 + 4 + 1×3

1 + 4 + 2 + 1

1 + 4 + 3

1 + 5 + 1×2

1 + 5 + 2

1 + 6 + 1

1 + 7

Now, if we look at the forms a branch can have, we see similar behaviour:

1 + 5

1 + (1 + 2 + 1×2)

1 + (1 + 2×2)

1 + (1 + 3 + 1)

1 + (1 + (1 + 2) + 1)

1 + (1 + 4)

1 + (1 + (1 + 2 + 1))

1 + (1 + (1 + 3))

1 + (1 + (1 + ( 1 + 2)))

Njäf! said.

I am Jesse Sakari Hyttinen and I will see you in the next post! 

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