By Clifford A. Shaffer
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Extra resources for A Practical Introduction to Data Structures and Algorithm Analysis Third Edition (Java Version)
Of course, the function that knows how to compute the factorial of n − 1 happens to be fact itself. But we should not think too hard about this while writing the algorithm. The design for recursive algorithms can always be approached in this way. First write the base cases. Then think about solving the problem by combining the results of one or more smaller — but similar — subproblems. If the algorithm you write is correct, then certainly you can rely on it (recursively) to solve the smaller subproblems.
We might render the objects in full detail. Or we might want a “rough draft” rendering that prints only the bounding boxes of the objects. If we come up with a new activity to apply to the collection of objects, we do not need to change any of the code that implements the existing activities. But adding new activities won’t happen often for this application. 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.
It only confirms when a proposed closed-form solution is correct. 1. The running time for a recursive algorithm is most easily expressed by a recursive expression because the total time for the recursive algorithm includes the time to run the recursive call(s). A recurrence relation defines a function by means of an expression that includes one or more (smaller) instances of itself. A classic example is the recursive definition for the factorial function: Hn ≈ loge n + γ + n! = (n − 1)! · n for n > 1; 1!
A Practical Introduction to Data Structures and Algorithm Analysis Third Edition (Java Version) by Clifford A. Shaffer