Branching factor is the number of children or successor states available from a node. In breadth-first search, the maximum branching factor b helps estimate how many states may be generated before reaching depth d: O(b^d). For example, b=2 and d=3 gives up to 2^3=8 traversed nodes, including the start node. section 3.3.1
A larger branching factor rapidly increases both runtime and memory because BFS retains every generated node. It therefore connects graph structure to algorithm scalability, even when a search finds a route without considering optimality. section 3.3.1
Path planning and the 8-puzzle
A robot’s FIFO search expands neighboring grid nodes until it reaches a destination, while a Python BFS example solves an 8-puzzle and reports explored states, processing time, and memory use.
