Project Euler | Problem 14 | Longest Collatz Sequence

Problem Description:

The following iterative sequence is defined for the set of positive integers:

n → n/2 (n is even)
n → 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following sequence:

13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.

Which starting number, under one million, produces the longest chain?

NOTE: Once the chain starts the terms are allowed to go above one million.

Concept:

This is very simple problem. If you know the way to find even/odd numbers and maximum number then you can easily solve this problem.

Solution of Project Euler Problem 14 - Longest Collatz Sequence

Figure1

Java Program:

package com.javamultiplex.projecteuler; import java.util.ArrayList; import java.util.List; /** * * @author Rohit Agarwal * @category Project Euler Problems * @Problem 14 - Longest Collatz Sequence. * */ public class Problem14 { public static void main(String[] args) { int limit = 1000000; // Limit is one million int size = 0, max = 1, j = 0; for (int i = 2; i < limit; i++) { size = getChainSize(i); if (size > max) { max = size; j = i; } } System.out.println("Starting number, under one million, produces the longest chain is : " + j); } private static int getChainSize(int n) { long num = n; List<Long> list = new ArrayList<>(); int size = 0; while (num != 1) { list.add(num); /* * As per Collatz sequence condition, if num is even then num=num/2 * else num=3*num+1 */ if (num % 2 == 0) { num = num / 2; } else { num = 3 * num + 1; } } size = list.size(); return size; } }

Output:

Answer of Project Euler Problem 14 - Longest Collatz Sequence

Figure2

References:

https://projecteuler.net/problem=14

Thank you friends, I hope you have clearly understood the solution of this problem. If you have any doubt, suggestion or query please feel free to comment below. You can also discuss this solution in our forum.

About Author:

I am simple guy with lot of ambitions. My main motive is to share whatever knowledge I have related to programming. With me you can easily learn how to solve any programming problem in Java.You can connect with me on social networking sites also.

Let's Get Connected: Linkedin | Facebook | Google Plus