SIMSCRIPT II.5 Programming Language

SIMSCRIPT II.5 Programming Language
Routine definition:
function POLYN given A, XVAL and K
define A as a 1-dimensional real array
define XVAL as a real variable
define K as an integer variable
if K eq 0
return with 0
otherwise
return with A(K) + XVAL * POLYN(A(*), X, K-1)
end
Notice that the interior call to POLYN uses K-1 as an argument instead of K. To illustrate how the
routine works, the evaluation of the polynomial is described:
3.3x 2 + 2.1x + 9.2 .
Assume that the coefficients 3.3, 2.1, and 9.2 are stored in an array COEF, in the order COEF(1),
COEF(2), and COEF(3), respectively. The polynomial is to be evaluated for the value x = 0.5.
The function is called by the statement:
let VALUE=POLYN(COEF(*), 0.5, 3)
The polynomial is evaluated as:
POLYN(COEF(*), 0.5, 3)
= 9.2 + 0.5 * POLYN(COEF(*), 0.5, 2)
= 9.2 + 0.5 * ( 2.1 + 0.5 * POLYN(COEF(*), 0.5, 1) )
= 9.2 + 0.5 * ( 2.1 + 0.5 * ( 3.3 + 0.5 * POLYN(COEF(*), 0.5, 0) ) )
= 9.2 + 0.5 * ( 2.1 + 0.5 * ( 3.3 + 0.5 * 0.0 ) )
which evaluates to 11.075.
A commonly used data structure in computing is the "tree" structure. One form of such a structure
is a "binary tree," where each node within the tree may have a "left branch" and a "right branch"
that represents links to other nodes in the tree. One node is chosen to represent the root. No node
is directly linked to/from more than one other node. Any node may be reached by starting from the
root and taking successive links at each node encountered. At the end of each possible path are
"leaf" nodes that have no successor links. Binary trees are well suited to processing with recursive
routines, since each node in such a tree may be considered as a "root" for a tree at a lower level within
the hierarchy of nodes.
An example of a recursive routine for destroying all the nodes of binary tree is shown below. The
tree is constructed of two-element, one-dimensional arrays that point to each other. Data storage at
the nodes may be disregarded for this example. To illustrate the tree-building process, the following
program segment forms the root of a binary tree named TREE:
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