> For the complete documentation index, see [llms.txt](https://infi-1.gitbook.io/infi-litepaper/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://infi-1.gitbook.io/infi-litepaper/readme-2.md).

# Pathfinding Algorithm

The core intelligence of InfiRouter lies in its on-chain pathfinding algorithm, implemented primarily within the internal \_findBestPath function. This recursive algorithm systematically explores potential swap routes to identify the one offering the maximum output amount, potentially adjusted for gas costs. It utilizes a recursive depth-first search strategy.

The algorithm operates recursively as follows:

1. **Base Case** - Direct Path Evaluation: The function first considers all possible single-step path. It  iterates through every registered adapter. 
2. **Recursive Step - Multi-Hop Exploration**:<br>

   – The algorithm checks if further exploration is warranted based on the maxSteps constraint. If the current path being built has length ( l ) and ( l <  - 1 ), it proceeds to explore two-step (or longer) paths originating from the current state. \
   \
   – It iterates through each potential intermediary token in the TRUSTED\_TOKENS list.