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

initially calling the algorithm as ReverseArray(A), we call it initially as
ReverseArray(A,0,n−1). In general, if one has difficulty finding the repetitive
structure needed to design a recursive algorithm, it is sometimes useful to work
out the problem on a few concrete examples to see how the subproblems should
be defined.
Tail Recursion
Using recursion can often be a useful tool for designing algorithms that have
elegant, short definitions. But this usefulness does come at a modest cost. When
we use a recursive algorithm to solve a problem, we have to use some of the
memory locations in our computer to keep track of the state of each active
recursive call. When computer memory is at a premium, then, it is useful in some
cases to be able to derive nonrecursive algorithms from recursive ones.
We can use the stack data structure, discussed in Section 5.1, to convert a
recursive algorithm into a nonrecursive algorithm, but there are some instances
when we can do this conversion more easily and efficiently. Specifically, we can
easily convert algorithms that use tail recursion. An algorithm uses tail recursion
if it uses linear recursion and the algorithm makes a recursive call as its very last
operation. For example, the algorithm of Code Fragment 3.32 uses tail recursion
to reverse the elements of an array.
It is not enough that the last statement in the method definition include a recursive
call, however. In order for a method to use tail recursion, the recursive call must
be absolutely the last thing the method does (unless we are in a base case, of
course). For example, the algorithm of Code Fragment 3.31 does not use tail
recursion, even though its last statement includes a recursive call. This recursive
call is not actually the last thing the method does. After it receives the value
returned from the recursive call, it adds this value to A [n − 1] and returns this
sum. That is, the last thing this algorithm does is an add, not a recursive call.
When an algorithm uses tail recursion, we can convert the recursive algorithm
into a nonrecursive one, by iterating through the recursive calls rather than calling
them explicitly. We illustrate this type of conversion by revisiting the problem of
reversing the elements of an array. In Code Fragment 3.33, we give a
nonrecursive algorithm that performs this task by iterating through the recursive
calls of the algorithm of Code Fragment 3.32. We initially call this algorithm as
IterativeReverseArray (A, 0,n − 1).
Code Fragment 3.33: Reversing the elements of an
array using iteration.
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