Question

I’m currently making a PHP-program that solves equations. I’ve divided the input equation into an array so that each line in the array contains one term. (So. [0] = “+5x”, [1] = “=”, [2] = “-5”, [3] = “+10”. This is just a basic equation. The script also divides what is in () into sub-arrays. So for example 2x+(5-3x)=3(x+1) [0] = “+2*x”, [1] = array([0] = “+5″….

However, I discovered expression trees that is the perfect thing to use in this equation-solver. I’ve searched the whole internet to learn it, but I can’t find any websites that explain it in PHP (I know PHP OOP.). There are lots of pages explaining them in for example C, but as I only know PHP, that is of no help, because I don’t understand the example code.

Can anyone here explain everything about expression trees in PHP and some practical example code?

Answer 1

Here is the algorithm described. you can implement this in PHP. I don’t think anyone already implemented this in PHP (and distribute it as open source)

An example would be:

2*x+3*5-(6+9) = 0

Where:

• * = priority 2
• + = priority 1
• ( = will increase priority of signs by 10
• + (second +) = priority 11
• ) = will decrease priority of signs by 10
• = = in this case it is showing that there is another expression (0)

The highest priority is the most important – the one you need to do first

Using these rules you can create an expression tree…

So.. a way in which you have to create the expression and then interpret is:

2 x * 3 5 * + 6 9 + -

Explained:

• 2 * x | (1)
• 3 * 5 | (2)
• (1) + (2) | (3)
• 6 + 9 | (4)
• (3) - (4) = final

I don’t remember exactly how to write a tree I did this to a course in Computer Science but it was something like this:

                                     -
                                /         \
                                E         (E)
                                |          +
                                +         / \
                             /    \      6   9
                            E      E        
                            |      |    
                            *      *
                           / \    / \    
                          T   E   T  E
                          |   |   |  |
                          2   T   3  T
                              |      |
                              x      5

Now you have to create your own interpreter for this. You can use the interpreter pattern: PHP Interpreter