"use strict";

function BinOperation(a, b) {
    this.a = a;
    this.b = b;

    this.toString = () => this.a.toString() + " " + this.b.toString() + " " + this.operator;
    this.evaluate = (...args) => this.evaluateImpl(this.a.evaluate(...args), this.b.evaluate(...args));
}

function Add(a, b) {
    BinOperation.call(this, a, b);

    this.operator = '+';
    this.evaluateImpl = (a, b) => a + b;
    this.diff = (diffName) => new Add( this.a.diff(diffName), this.b.diff(diffName) );
}

function Subtract(a, b) {
    BinOperation.call(this, a, b);

    this.operator = '-';
    this.evaluateImpl = (a, b) => a - b;
    this.diff = (diffName) => new Subtract( this.a.diff(diffName), this.b.diff(diffName) );
}

function Multiply(a, b) {
    BinOperation.call(this, a, b);

    this.operator = '*';
    this.evaluateImpl = (a, b) => a * b;
    this.diff = (diffName) => new Add(
        new Multiply( this.a.diff(diffName), this.b ),
        new Multiply( this.a, this.b.diff(diffName) )
    );
}

function Divide(a, b) {
    BinOperation.call(this, a, b);

    this.operator = '/';
    this.evaluateImpl = (a, b) => a / b;
    this.diff = (diffName) => new Divide(
        new Subtract(
            new Multiply(this.a.diff(diffName), this.b),
            new Multiply(this.a, this.b.diff(diffName))
        ),
        new Multiply(this.b, this.b)
    )
}

function Negate(a) {
    this.a = a;

    this.toString = () => this.a.toString() + ' negate';
    this.evaluate = (...args) => (-1) * this.a.evaluate(...args);
    this.diff = (diffName) => new Negate(a.diff(diffName));
}

function Const(val) {
    this.val = val;

    this.toString = () => this.val.toString();
    this.evaluate = () => this.val;
    this.diff = () => new Const(0);
}

function Variable(name) {
    this.name = name;

    this.toString = () => this.name;
    this.evaluate = (...args) => {
        if (name === 'x') return args[0];
        if (name === 'y') return args[1];
        if (name === 'z') return args[2];
    }
    this.diff = (diffName) => new Const( this.name === diffName ? 1 : 0 );
}

const operations = [ 'negate', '+', '-', '*', '/' ];
const variables = [ 'x', 'y', 'z' ];

const operationToArity = {
    'negate': 1,
    '+' : 2,
    '-' : 2,
    '*' : 2,
    '/' : 2,
};

const tokenToOperation = {
    'negate': Negate,
    '+' : Add,
    '-' : Subtract,
    '*' : Multiply,
    '/' : Divide
};

const parse = function(expression) {
    let stack = [];
    let tokens = expression.split(' ').filter((word) => word !== '');
    for (let token of tokens) {
        if (operations.includes(token)) {
            let arity = operationToArity[token];
            let args = [];
            for (let i = arity - 1; i >= 0; i--) {
                args[i] = stack.pop();
            }
            stack.push(new tokenToOperation[token](...args));
        } else if (variables.includes(token)) {
            stack.push(new Variable(token));
        } else {
            stack.push(new Const(Number.parseInt(token)));
        }
    }
    return stack.pop();
}