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Recursion

A recursive routine is one that invokes itself. Recursive routines often offer elegant solutions to complex programming problems, but they also tend to consume large amounts of memory. They are also likely to be less efficient and less scalable than implementations based on iterative execution.

Most recursive algorithms can be reformulated using nonrecursive techniques involving iteration. Where possible, we should give preference to the more efficient iterative algorithm.

For example, in Example 22-18, the stored procedure uses recursion to calculate the Nth element of the Fibonacci sequence, in which each element in the sequence is the sum of the previous two numbers.

Example 22-18. Recursive implementation of the Fibonacci algorithm
CREATE PROCEDURE rec_fib(n INT,OUT out_fib INT)
BEGIN
DECLARE n_1 INT;
DECLARE n_2 INT;

IF (n=0) THEN
SET out_fib=0;
ELSEIF (n=1) then
SET out_fib=1;
ELSE
CALL rec_fib(n-1,n_1);
CALL rec_fib(n-2,n_2);
SET out_fib=(n_1 + n_2);
END IF;
END

Example 22-19 shows a nonrecursive implementation that returns the Nth element of the Fibonacci sequence.

Example 22-19. Nonrecursive implementation of the Fibonacci sequence
CREATE PROCEDURE nonrec_fib(n INT,OUT out_fib INT)
BEGIN
DECLARE m INT default 0;
DECLARE k INT DEFAULT 1;
DECLARE i INT;
DECLARE tmp INT;

SET m=0;
SET k=1;
SET i=1;

WHILE (i<=n) DO
SET tmp=m+k;
SET m=k;
SET k=tmp;
SET i=i+1;
END WHILE;
SET out_fib=m;
END

Figure 22-9 compares the relative performance of the recursive and nonrecursive ...

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