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By Clifford A. Shaffer

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Simply accept that it will solve it correctly, and use this result to in turn correctly solve the original problem. What could be simpler? Recursion has no counterpart in everyday problem solving. The concept can be difficult to grasp because it requires you to think about problems in a new way. To use recursion effectively, it is necessary to train yourself to stop analyzing the recursive process beyond the recursive call. The subproblems will take care of themselves. You just worry about the base cases and how to recombine the subproblems.

2 Mathematical Preliminaries √ 2πn/en < 1), it grows faster than cn for Permutations: A permutation of a sequence S is simply the members of S arranged in some order. For example, a permutation of the integers 1 through n would be those values arranged in some order. If the sequence contains n distinct members, then there are n! different permutations for the sequence. This is because there are n choices for the first member in the permutation; for each choice of first member there are n − 1 choices for the second member, and so on.

In contrast, there could be many object types, and we might frequently add new object types to our implementation. Unfortunately, adding a new object type requires that we modify each activity, and the subroutines implementing the activities get rather long case statements to distinguish the behavior of the many subclasses. An alternative design is to have each object subclass in the hierarchy embody the action for each of the various activities that might be performed. Each subclass will have code to perform each activity (such as full rendering or bounding box rendering).

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