Collatz | Topcoder Archive

Problem Statement

The Collatz Problem asks whether the following function will reach 1 for all positive k if we keep applying it:

      { if k is odd    :   3*k +1 
f(k)= {
      { if k is even   :    k/2

For example, lets say you were given k = 20:

f(20) = 10     First application
f(10) = 5      Second application
f(5)  = 16     Third application
f(16) = 8      Fourth application
f(8)  = 4      Fifth application
f(4)  = 2      Sixth application
f(2)  = 1      Seventh application

So for k = 20 this function required 7 applications of the function to reach 1. Given an int k return the number of applications required to reach 1. Topcoder has ensured that the number of applications will be less than 1000 and that any temporary value will not overflow a 32-bit integer.

Definition

Class:: Collatz
Method:: numSteps
Parameters:: int
Returns:: int
Method signature:: int numSteps(int k)
(be sure your method is public)

Constraints

k will be between 2 and 100000 inclusive.
The return value will be less than 1000.

Examples

```
20
```
```
Returns: 7
```
The example from above
```
2
```
```
Returns: 1
```
Just a single application required
```
5
```
```
Returns: 5
```
5*3+1 = 16 16/2 = 8 8/2 = 4 4/2 = 2 2/2 = 1
```
99999
```
```
Returns: 226
```
```
77671
```
```
Returns: 231
```

This problem statement is the exclusive and proprietary property of Topcoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of Topcoder, Inc. is strictly prohibited. (c)2024, Topcoder, Inc. All rights reserved.