Editing Iterative deepening depth-first search (section)

==Example==
For the following graph:

[[Image:graph.traversal.example.svg|200px]]

a depth-first search starting at A, assuming that the left edges in the shown graph are chosen before right edges, and assuming the search remembers previously-visited nodes and will not repeat them (since this is a small graph), will visit the nodes in the following order: A, B, D, F, E, C, G.  The edges traversed in this search form a [[Trémaux tree]], a structure with important applications in [[graph theory]].

Performing the same search without remembering previously visited nodes results in visiting nodes in the order A, B, D, F, E, A, B, D, F, E, etc. forever, caught in the A, B, D, F, E cycle and never reaching C or G.

Iterative deepening prevents this loop and will reach the following nodes on the following depths, assuming it proceeds left-to-right as above:

*0: A
*1: A, B, C, E
(Iterative deepening has now seen C, when a conventional depth-first search did not.)
*2: A, B, D, F, C, G, E, F
(It still sees C, but that it came later. Also it sees E via a different path, and loops back to F twice.)
*3: A, B, D, F, E, C, G, E, F, B

For this graph, as more depth is added, the two cycles "ABFE" and "AEFB" will simply get longer before the algorithm gives up and tries another branch.