Shunting Yard Algorithm

The shunting yard algorithm transforms a mathematical expression from infix notation into a reversed polish notation (postfix).

An more in depth introduction to this algorithm you can get on Wikipedia.

Implementation details

if used with a string

This implementation of the shunting yard algorithm takes a String in and puts out an array representation in reversed polish notation (RPN). The resulting RPN you can easily processed (using the ShuntingYard.resolveRPN function) to a resulting number.

Note that ShuntingYard.parse will ignore every whitespace of the input string. Strings formatted like '1 100 + 5' will result in the array containing those tokens: [1100, 5, +] – which also allows for nice formatting of bigger number, but could lead to problems if there was meant an operator between 1 and 100.

if used with an input array

Used with an array of tokens, you have some more flexibility, because the operator tokens can be longer then single characters.

In both cases, you have to define which operators will be in your input. That is, because the algorithm has to know the precedence and associativity of the operators. Predefined are those common operators: +, -, *, / and ^.

Beware that your tokens don't contain whitespaces at the beginning or the end, so "+" is not the same as " +".

Example

const shuntingYard = new ShuntingYard();
const rpn = shuntingYard.parse('10+3*3'); // rpn is now: ['10', '3', '3', '*', '+']
const result = shuntingYard.resolveRPN(rpn); // result is now: 19
// or in short:
const result2 = shuntingYard.resolve('10+3*3'); // result is now: 19

If you want, you could also use eval for this string but nobody would like to have eval in their code (considering what eval is doing to your parser and the security implications you have to be aware of).

But the real benefit of this way is when defining your own Operators. Just like that:

const shuntingYard = new ShuntingYard();
shuntingYard.addOperator('o', new Operator('o', 2, 'left', 2, function(a, b) { return a + Math.sqrt(b); }));
var rpn = shuntingYard.parse('10o3*3'); // rpn is now: ['10', '3', '3', '*', 'o']
var result = shuntingYard.resolveRPN(rpn); // result is now: 13

You can also use an array as input:

shuntingYard.addOperator('add', new Operator('add', 2, 'left', 2, function(a, b) { return a + b; }));
var rpn = shuntingYard.parse([5, 'add', 4, '*', 4]); // rpn is now: [5, 4, 4, '*', 'add']
var result = shuntingYard.resolveRPN(rpn); // result is now: 21

And you can define new functions (those do not have to be infix):

shuntingYard.addOperator('sqrt', new Operator('sqrt', 1, function(a) { return Math.sqrt(a); }));
var rpn = shuntingYard.parse([6, '+', 'sqrt', '(', 6, '+', 3 ')']); // rpn is now: ['6', '6', '3', '+', 'sqrt', '+']
var result = shuntingYard.resolveRPN(rpn); // result is now: 9

TODOs

For resolveRPN:

• change tokenizer from '' to whitespace for example
• change operators

MIT License

Copyright (C) 2013-2020 Georg Tavonius

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