# Project Euler #55 – Lychrel numbers

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Problem

If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

Not all numbers produce palindromes so quickly. For example,

349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337

That is, 349 took three iterations to arrive at a palindrome.

Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).

Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.

How many Lychrel numbers are there below ten-thousand?

This code works with NodeJS. It is also using ES6 features.
So no SpiderMonkey nonsense now.

``````\$ node -v
v0.12.7
\$ node --harmony p55.js
249
``````

Any and all feedback is appreciated.

``````// Like Python's range.
function* range(start, stop, step){
if (arguments.length == 0){
start = 0;
stop = null;
}
if (arguments.length == 1){
stop = start;
start = 0;
}
if (arguments.length < 3)
step = 1;

start = parseInt(start);
if (Number.isNaN(start))
start = 0;
stop = parseInt(stop);
if (Number.isNaN(stop))
stop = null;
step = parseInt(step);
if (Number.isNaN(step))
step = 1;

if (stop === null){
while (true){
yield start;
start += step;
}
}else if (step == 0){
while (true){
yield start;
}
}else{
if (step > 0){
for (var number = start; number < stop; number += step){
yield number;
}
}else{
for (var number = start - 1; number >= stop; number += step){
yield number;
}
}
}
}

function is_palindrome(string){
var str_len = string.length - 1;
for (var index of range(string.length / 2)){
if (string[index] != string[str_len - index]){
return false;
}
}
return true;
}

function reverse(string){
var new_string = '';
for (var index of range(string.length, 0, -1)){
new_string += string[index];
}
return new_string;
}

function is_lychrel(number, recursions){
if (recursions == 0)
return false;
if (arguments.length == 1)
recursions = 50;
number += parseInt(reverse(number.toString()));
if (is_palindrome(number.toString()))
return true;
return is_lychrel(number, recursions - 1);
}

function main(){
var total = 0;
for (var number of range(10000)){
if (! is_lychrel(number)){
total += 1;
}
}
}

console.log(main());
``````

Solution

Typically in JavaScript, when calling `isNaN`, it is just typed:

``````isNaN(...);
``````

Not as a call from the `Number` class:

``````Number.isNaN(...);
``````

Also, by calling it the way that you did, you are being inconsistent. If you are going to call `isNaN` through `Number`, then why don’t you also call `parseInt` through `Number`?

The function `parseInt` takes a second parameter `radix` which is the base of the first parameter.

According to the MDN, you should always specify the radix parameter.

Why do you call `parseInt` on the arguments of `range`? In every single point of your code where you are calling this function, you are passing numerical arguments.

Calling this functions is just a waste.

In places like these:

``````if (arguments.length == 0){
``````

and

``````if (arguments.length == 1){
``````

You should be using the `===` comparison operator rather than the `==` comparison operator.

1. It is good JavaScript practice.

2. It may be a little faster.

As shown in this SO post, a much, much simpler way to reverse a string would be to do this:

``````return string.split("").reverse().join("");
``````

This could potentially be faster, too, as this is using JavaScript’s built in functions/methods/features.

Your `is_palindrome` function confuses me a little. A palindrome is defined as a word that is spelled the exact same as it’s reverse. Therefore, why aren’t you using the `reverse` function that you already made?

Now, your `is_palindrome` function becomes this:

``````return string == reverse(string);
``````

This is much more simple than whatever you were doing.

The naming case for JavaScript is `camelCase`, not `snake_case`. You need to change the name of these functions:

``````is_palindrome --> isPalindrome
``````

and

``````is_lychrel --> isLychrel
``````

And, make sure you change the name of some of your variables to `camelCase` too.

You are putting too much work on your `isLychrel` function.

Here, you check to see that if there is no `recursions` specified, set it to 50:

``````if (arguments.length == 1)
recursions = 50;
``````

However, this check is going to happen every single iteration (since the function is recursive).

Is is really that difficult to just pass 50 to it in the initial time you call it in `main`? If you did this and removed the check from the function, this could greatly improve your performance.