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Project Euler - problem 014

August 1st, 2007 by Daniel

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.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41

 
#include <iostream>
#include <ctime>
using namespace std;
 
#define max 1000000
 
int numbersOfTerms(int num);
 
int main ()
{
clock_t start = clock();
int res(0), temp(0);
 
for(int i = max; i > 0; i--){
temp = numbersOfTerms(i);
if( temp > res){
res = temp;
cout << res << '\n';
}
cout << i << " ";
}
 
cout << "resultatet er ";
cout << res << "\n";
cout<< ( ( clock() - start ) / (double)CLOCKS_PER_SEC ) <<'\n';
return 0;
}
 
int numbersOfTerms(int num){
int res(1);
while(num != 1){
if(num % 2 == 0){
num /= 2;
} else {
num = 3*num + 1;
}
res ++;
}
return res;
}

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