How to adapt a-star algorithm to a 2D platformer game where character cannot jump?

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I have been working on creating a pathfinding solution similar to that in the game Craft the World (https://youtu.be/59z-TTeetAg?t=359), according to the tip from the dev team, the pathfinding algorithm is based on a-star, but a-star official document says it's not compatabile with 2D platformer game, so they must have made some important changes. The character in the game can climb wall/ladder, find its path to any place without the need of jumping in a 2D platformer level.

I've checked many documents and tutorial about 2D platformer pathfinding, but the gameplays are different, and some solution are AI-based which is not the way Craft the World does.

I'm wondering if I can have some tips on how to make such pathfinding solution.

Thanks very much.

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