the question is: suppose I have an input function like sin(2-cos(3*A/B)^2.5)+0.756*(C*D+3-B) specified with a BNF, I will parse input using recursive descent algorithm, and then how can I use or change Dijkstra’s algorithm to handle this given function? I need to execute it with sin | cos | sqrt | ln, where Dijkstra’s algorithm should do the work.
EDIT: May be I should ask also: What is the best practice or data structure to represent given function?
EDIT: Input set can be acquired as:
C 0.01 .01 .02 .04 .08 .02 .02 .04
A .016 .008 .116 .124 .147 .155 .039 .023
D .012 .025 .05 .1 .1 .1 .025 .012000 .012
B .007 .007 .015 .022 .029 .036 .044 .051 .058 .066 .073 .080
EDIT: Shunting Yard is the algorithm to convert input function to RPN, but how can I extend it to accept another function like sin | cos | sqrt | ln? Does recursive descent provides required extension to Shunting Yard?
I presume you are talking about Dijkstra's Shunting Yard algorithm?
To evaluate the reverse polish notation (output of shunting yard), normally a stack is used.
Shunting Yard was devised to do the parsing in Algol I believe, and I believe it is supposed to work with any functions (either fixed or variable number of arguments).
Here is a blog post which explains it in more detail: http://www.kallisti.net.nz/blog/2008/02/extension-to-the-shunting-yard-algorithm-to-allow-variable-numbers-of-arguments-to-functions/