Suppose a step in an algorithm must examine every possible (nonempty) subset or combination of n nodes. Show that the complexity of this step is O (2 n ). Suppose a step in an algorithm must examine...

Suppose a step in an algorithm must examine every possible (nonempty) subset or combination of n nodes. Show that the complexity of this step is O (2ⁿ).

Suppose a step in an algorithm must examine every possible permutation of n nodes. Show that the complexity of this step is O (n!).