| ## Page 1 | |
| 100 | |
| The 3n + 1 problem | |
| Problems in Computer Science are often classified as belonging to a certain class of problems (e.g., | |
| NP, Unsolvable, Recursive). In this problem you will be analyzing a property of an algorithm whose | |
| classification is not known for all possible inputs. | |
| Consider the following algorithm: | |
| 1. | |
| input n | |
| 2. | |
| print n | |
| 3. | |
| if n = 1 then STOP | |
| 4. | |
| if n is odd then n ←−3n + 1 | |
| 5. | |
| else n ←−n/2 | |
| 6. | |
| GOTO 2 | |
| Given the input 22, the following sequence of numbers will be printed | |
| 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 | |
| It is conjectured that the algorithm above will terminate (when a 1 is printed) for any integral input | |
| value. Despite the simplicity of the algorithm, it is unknown whether this conjecture is true. It has | |
| been verified, however, for all integers n such that 0 < n < 1, 000, 000 (and, in fact, for many more | |
| numbers than this.) | |
| Given an input n, it is possible to determine the number of numbers printed before and including | |
| the 1 is printed. For a given n this is called the cycle-length of n. In the example above, the cycle | |
| length of 22 is 16. | |
| For any two numbers i and j you are to determine the maximum cycle length over all numbers | |
| between and including both i and j. | |
| Input | |
| The input will consist of a series of pairs of integers i and j, one pair of integers per line. All integers | |
| will be less than 10,000 and greater than 0. | |
| You should process all pairs of integers and for each pair determine the maximum cycle length over | |
| all integers between and including i and j. | |
| You can assume that no operation overflows a 32-bit integer. | |
| Output | |
| For each pair of input integers i and j you should output i, j, and the maximum cycle length for integers | |
| between and including i and j. These three numbers should be separated by at least one space with all | |
| three numbers on one line and with one line of output for each line of input. The integers i and j must | |
| appear in the output in the same order in which they appeared in the input and should be followed by | |
| the maximum cycle length (on the same line). | |
| Sample Input | |
| 1 10 | |
| 100 200 | |
| 201 210 | |
| 900 1000 | |
| ## Page 2 | |
| Sample Output | |
| 1 10 20 | |
| 100 200 125 | |
| 201 210 89 | |
| 900 1000 174 |