c++

 

The program explores the properties of the 3n + 1 sequence which has two very simple rules forgenerating its elements: starting with a positive number, if the current number n is odd, the next one is3n + 1; if it is even, the next one is n/2. The number 1 is a special case. If the current number is 1, thesequence terminates and there is no next element. A few examples below with different starting values:- start = 3: 3, 10, 5, 16, 8, 4, 2, 1 has 8 elements- start = 4: 4, 2, 1 has 3 elements- start = 1: 1 has 1 elementIt is conjectured, but never proven, that the 3n+1 sequence always reaches 1 and terminates,regardless of its starting value. We can't check infinitely many start values, but we know how toprogram and we can check quite a few. We plan to see for ourselves.The program asks the user to enter the start and the end of the range for start values to check.We will generate a sequence for each of the values in the given range. When (or if? :) ) the programterminates, we will output the longest sequence we encountered and the number of elements it has.A few sample runs are given below:Sample Run 1Enter the min of the range for the sequence to start 1Enter the max of the range for the sequence to start 5The longest sequence with a start value in the range [1, 5] has 8 elements.3, 10, 5, 16, 8, 4, 2, 1We did not find a non terminating case.Sample Run 2Enter the min of the range for the sequence to start 10Enter the max of the range for the sequence to start 100The longest sequence with a start value in the range [10, 100] has 119 elements.97, 292, 146, 73, 220, 110, 55, 166, 83, 250, 125, 376, 188, 94, 47, 142, 71, 214,107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155,466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668,334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479,1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367,4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650,325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20,10, 5, 16, 8, 4, 2, 1We did not find a non terminating case. Sample Run 3Enter the min of the range for the sequence to start 100Enter the max of the range for the sequence to start 100The longest sequence with a start value in the range [100, 100] has 26 elements.100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10,5, 16, 8, 4, 2, 1We did not find a non terminating case.You will decompose the program into the 4 functions below:getUserInput – takes two parameters start and end and asks the user to enter the min and max of therange to check. It sets start to min and end to max. The function returns nothing.getNextElement – takes a value and returns the next value in the sequence according to the rules. 1shall return 1.generateSequence – takes a start value for the sequence and a sequence string. It returns the length ofthe generated sequence starting with that start value and the sequence string is set to the generatedsequence.longestSequence - takes a start and an end value specifying the range of start values to check and asequence string. It returns the length of the longest sequence encountered with a start value in the range[start, end] and the sequence string is set to the longest sequence encountered.