Consider the following algorithm to generate a sequence of numbers. Start with an integer n. If n is even, divide by 2. If n is odd, multiply by 3 and add 1. Repeat this process with the new value of n, terminating when n is equal to 1. For example, the following sequence is generated for n = 22:
22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
It is conjectured (but not yet proven) that this algorithm will terminate at n is equal to 1 for every integer n. The conjecture holds for integers up to at least 1,000,000.
For an input n, the cycle-length of n is the number of numbers generated up to and including the 1. In the example above, the cycle length is 16.
Write a C++ program that repeatedly prompts the user for two numbers, Start and End, and determines the maximum cycle length over all numbers between Start and End, including both endpoints. Assume all inputs are integers less than 1,000,000 and greater than 0. If a negative number is entered for the start, then the program should end immediately.
Sample Command Line Interface: (Bold Signifies User Input)
Start: 1
End: 10
Max: 20
Start: 100
End: 200
Max: 125
Start: 201
End: 210
Max: 89
Start: -3