Question

The length of a hailstone sequence is the number of terms it contains. For example, the hailstone sequence in example 1 (5, 16, 8, 4, 2, 1) has a length of 6 and the hailstone sequence in example 2 (8, 4, 2, 1) has a length of 4. Write the method hailstoneLength(int n), which returns the length of the hailstone sequence that starts with n.

Answer 1

Answer:

1. #include <iostream>
2. using namespace std;
4. int hailstoneLength(int n){
5.    int term = 1;
6.    while(n != 1){
7.        if(n % 2 == 0){
8.            n = n / 2;
9.            term++;
10.        }
11.        else{
12.            n = n * 3 + 1;
13.            term++;
14.        }
15.    }
16.    return term;
17. }
19. int main()
20. {
21.    cout<<hailstoneLength(8);
23.    return 0;
24. }

Explanation:

Hailstone sequence is a list of number that is generated by following the rules as below:

1. Given a starting number (e.g. 5)
2. If the number is even, divide it by 2
3. If the number is odd, multiply it by 3 and then add 1
4. the starting number will either be repeatedly divided or multiplied until the final n reaches 1

So, we can create a function called hailstoneLength that takes one input number, n, as starting number (Line 4).

In the function initialize the variable term with value of 1 (Line 5).  Create a while loop and set the condition to enable the loop running until the n become 1 (Line 6). In the loop, keep checking the n value if it is currently even or odd using modulus operator (Line 7 - 14). If it is even, divide n by 2 and increment the term by one (Line 7 - 10). If it is odd, multiple it by 3 and add 1 (Line 11 - 14). At last, return term value as output (Line 16).

In the main program, test the function by passing 8 as argument. We shall get the output of 4 (Line 21).