Types of recursion

               Recursion is of two types depending on whether a function calls itself from within itself or whether two functions call one another mutually. The former is called direct recursion and the latter is called indirect recursion. Thus the two types of recursions are:

1.      Direct Recursion.

2.     Indirect Recursion.

               Now before we proceed into the core programming with recursion first of all we will see a brief idea of storage classes (which are in fact necessary to provide solid base in understanding recursion), after which we study necessary conditions for recursion to be implemented correctly.

 Recursion may be further categorized as :

1. Linear Recursion       

2. Binary Recursion                      

3. Multiple Recursion

Linear Recursion

               Linear Recursion begins by testing for a set of base cases there should be at least one. Every possible chain of recursive calls must eventually reach a base case and the handling of each base case should not use recursion.

               In linear recursion we follow:

1.      Perform a single recursive call. This recursive step may involve a test that decides which of several possible recursive calls to make, but it should ultimately choose to make just one of these calls each time we perform this step.

2.      Define each possible recursive call so that it makes progress towards a base case.

Binary Recursion

         Binary recursion occurs whenever there are two recursive calls for each non base case. Example is the problem to add all the numbers in an integer array A.

Algorithm

         Binary sum (A, i, n),

Input

         An Array A and integers I and n

Output

         The sum of integers in A starting at index i.

         If n = 1 then

Return a [i] else

         Return Binary sun [A, I, n/2]+Binary sum[A, I, + n/2, n/2]

Multiple Recursions

In multiple recursions we make not just one or two but many recursive calls. One of the motivating examples is summation puzzles.

                    .pot+pan = bib

                    .dog+cat = pig

                    .boy+girl = baby

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