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-
-
-## 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