A graph search algorithm. When searching for a path through a graph from a given initial node to a solution node with some desired property, a depth-first search may never find a solution if it enters a cycle in the graph. We can either add an explicit check for cycles so that we never extend a path with a node it already contains or we can use iterative deepening where we explore all paths up to length (or "depth") N, starting from N=0 and increasing N until a solution is found.