Control over depth-first scan and breadth-first scan

Question

Is there a way to conditionally take control/modify the flow during a depth-first scan or the breadth-first scan ?

Say, for example, if a particular node if found, consider it as a leaf-node and continue with the rest of the processing as usual (meaning do not traverse its child-nodes).

Answer 1

The answer by Mr. Wizard that Daniel linked to is easily hacked to include a stop condition, you simply take the recursive function, but filter the next level depending on your stopping criterion.

stopCondition[element_] := Length[element] > 1;
(Print@#; #0~Scan~Select[#, stopCondition]) &@{{1, {2, 3}, 0}, {4, 5, 2}, 2}