Question

I need help writing a code in Java or C or python that follows the following requirements.

1. It prompts the user to enter values of the four integers (a, b, c, and M in this order) and prints out the first 100 elements (?0, ?1, ?2, …, ?99) of the sequence produced by the linear congruential random number generator for these parameters. Use a for loop and the following update formula: x = (a * x + b) % M . Print the sequence elements in a table with 10 values per line.

2. The second part of this assignment is to implement Floyd's algorithm (described below) for finding the cycle length. First, you need to find a point on the cycle (Phase (i)). Then, you need to compute the cycle length (Phase (ii)). Output the cycle length.

We can determine the cycle length by using Floyd's algorithm for finding the cycle length or period. Floyd's algorithm consists of two phases: (i) find a point on the cycle, and (ii) compute the cycle length.  Phase (i). To find a point on the cycle, we use the following idea: run two versions of the generator concurrently, one iterating twice as fast as the other, until both versions have the same value. At some point, both of them are on the cycle and we have a race on the cycle, with the gap between the faster one and the slower one shrinking by one on each iteration. Eventually, the faster one catches up to the slower one, and the two generators are at the same point on the cycle. The following table contains an example of the process with a = 22, b = 1, c = 0, and M = 72. In this example, the cycle is 3-67-35-51-43-11-27- 19-59-3, and its length is 9. Somewhat coincidentally, this happens to be equal to the number of steps until the fast and slow generators first meet, but this will not be true in general. The fast generator (denoted by F) happens to be at 51 when the slow one (denoted by S) first hits the cycle at 3. The fast one is six steps behind the slow one, and catches up, one step at a time

Phase (ii). Once we know a value on the cycle, one more trip around the cycle (back to that same value) will give us the cycle length. Continuing the example above, we discovered from Phase I that 27 is in the cycle. After another 9 iterations we are back at 27, so we conclude the cycle length is 9 (as illustrated in the table below)

Sample run 1: Please enter values of a, b, c, and M in this order: 22 1 0 72

The first 100 elements of the sequence:

0 1 23 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27 19 59 3 67 35 51 43 11 27

Cycle length is 9

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Sample run 2:

Please enter values of a, b, c, and M in this order:

123 456 789 1000000

The first 100 elements of the sequence:

789 97503 993325 179431 70469 668143 182045 391991 215349 488383 71565 802951 763429 902223 973885 788311 962709 413663 881005 364071 781189 86703 664925 786231 706869 945343 277645 150791 547749 373583 951165 993751 231829 515423 397485 891111 607109 674863 8605 58871 241589 715903 56525 953031 223269 462543 893245 869591 960149 98783 150765 544551 980229 568623 941085 753911 731509 976063 56205 913671 381989 985103 168125 679831 619669 219743 28845 548391 452549 663983 670365 455351 8629 61823 604685 376711 335909 317263 23805 928471 202389 894303 999725 966631 896069 216943 684445 187191 24949 69183 509965 726151 317029 995023 388285 759511 420309 698463 911405 103271

Cycle length is 50000

Answer 1

Answer:

Note: As per the specifications, the program can be done in either Java or C or Python. So, the program is given in Java.

Program code screen shot: