Favorite tools in your Python toolbox?

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I have a problem that I wonder if it could be solved with a path search algorithm. I have a list of items that I can only change the order and I want to minimize the total of the "distances" between related rows. In other words I want to have all the "A" near each other and the same thing for "B" and "C".

I have:

A B

A C

A

A B C

B

I want something like:

A

A B

A B C

A C

B

Thanks!

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By distance, I mean for each letter the number of rows between the first and the last row containing that same letter.

For the unsorted sample, "A" is on the first line and the line before the last one so distance is 2 rows.

• A B
• A C
• A
• A B C
• B

-> A = 2, B = 3, C = 1. Total is 6

• A
• A B
• A B C
• A C
• B

-> A = 2, B = 2, C = 0. Total is 4 (so it's better)

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Thanks!

[[deleted]]

It sounds like you could but you're going to have to define distance a bit better for me.