Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

Code Fragment 3.36: Computing the kth Fibonacci
number using linear recursion.
The algorithm given in Code Fragment 3.36 shows that using linear recursion to
compute Fibonacci numbers is much more efficient than using binary recursion.
Since each recursive call to LinearFibonacci decreases the argument k by 1,
the original call LinearFibonacci(k) results in a series of k − 1 additional
calls. That is, computing the kth Fibonacci number via linear recursion requires k
method calls. This performance is significantly faster than the exponential time
needed by the algorithm based on binary recursion, which was given in Code
Fragment 3.35. Therefore, when using binary recursion, we should first try to
fully partition the problem in two (as we did for summing the elements of an
array) or, we should be sure that overlapping recursive calls are really necessary.
Usually, we can eliminate overlapping recursive calls by using more memory to
keep track of previous values. In fact, this approach is a central part of a technique
called dynamic programming, which is related to recursion and is discussed in
Section 12.5.2.
3.5.3 Multiple Recursion
Generalizing from binary recursion, we use multiple recursion when a method may
make multiple recursive calls, with that number potentially being more than two.
One of the most common applications of this type of recursion is used when we
wish to enumerate various configurations in order to solve a combinatorial puzzle.
For example, the following are all instances of summation puzzles:
pot + pan = bib
dog + cat = pig
boy + girl = baby
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