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 = 7337That 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;
}
}
return total;
}
console.log(main());