Arithmetic expression evaluation in java

Computing the value of arithmetic expressions like this one:
                                               ( 1 + ( ( 2 + 3 ) * ( 4 * 5 )

Which means multiply 4 by 5, add 3 to 2, multiply the result, and then add 1, you get the value 101.
But how does the Java system do this calculation?

We can address the essential ideas by writing a Java program that can take a string as input (the expression) and produce the number represented by the expression as output.

Dijkstra's Two stack Algorithm for Expression Evaluation


public class ExpressionEvaluation
{
public static void main(String args[]){

Stack<String> ops = new Stack<String>();

Stack<Double> ops = new Stack<Double>();



String s= "( 1 + ( ( 2 + 3 ) * ( 4 * 5 ) ) )";

for(char c : s){
     if(c+"".equals("("))                  ;
else if(c+"".equals("+"))  ops.push(c+"")  ;
else if(c+"".equals("-"))  ops.push(c+"")  ;
else if(c+"".equals("*"))  ops.push(c+"")  ;
else if(c+"".equals("/"))  ops.push(c+"")  ;
else if(c+"".equals(")")) {

String op=ops.pop();
double v=vlas.pop();

if(c+"".equals("("))                  ;
else if(op.equals("+"))  v=vals.pop+v ;
else if(op.equals("-"))  v=vals.pop-v ;
else if(op.equals("*"))  v=vals.pop*v ;
else if(op.equals("/"))  v=vals.pop/v ;
vals.push(v);

}
else vals.push(Double.parseDouble(s));
}
System.out.println(vals.pop());
}

}


The algorithm computes the same value for all of these expressions:

( 1 + ( ( 2 + 3 ) * ( 4 * 5 ) ) )
( 1 + ( 5 * ( 4 * 5 ) ) )
( 1 + ( 5 * 20 ) )
( 1 + 100 )
101