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Task 2. Rats

Available Marks: 9

RATS (in this context) stands for Reverse, Add, Then Sort, applied to a positive decimal integer. It's the generating algorithm for an integer sequence that either diverges, or enters a reasonably short cycle. Consider the integer 180. Reversing the digits gives 081, or just 81. 180 + 81 = 261. Sorting the digits gives 126.

Continuing, 

  126 +   621 =    747, sorted = 477
  477 +   774 =   1251, sorted = 1125
 1125 +  5211 =   6336, sorted = 3366
 3366 +  6633 =   9999, sorted = 9999
 9999 +  9999 =  19998, sorted = 18999
18999 + 99981 = 118980, sorted = 011889
11889 + 98811 = 110700, sorted = 000117
  117 +   711 =    828, sorted = 288
  288 +   882 =   1170, sorted = 117
So the sequence ends in a cycle of period 2 (the period of a cycle is the number of different values it contains).

Only a small number of different cycles can occur, we want to find them.

Your task

Write a program that identifies all cycles that occur for starting numbers less than 10000 (or 1000 for fewer marks). If any sequence element exceeds 1012, you may assume the sequence diverges. Complete answers depend on your computer using 64-bit arithmetic. In the event that your calculations use 32-bit arithmetic and overflow occurs, you will not be penalised provided the other cycles are reported correctly.

Your program's output should consist of one cycle on each line, ordered by period and then by the smallest member of the cycle. Each line should show three data items:

For example, say you discovered that 100 starting values lead to the cycle above, your program's output should include the line 
Period: 2, occurs 100 times, cycle: 117 288

Assessment

Full marks will be awarded for correctly identifying all cycles and displaying the details according to the requirements.

Deductions apply for incorrect identification, or if you don't cover all 9999 starting values, or for not displaying the data in the required order.

Step 0

Refresh the browser window  if the page has been idle for some time.

Step 1

Paste the output of your program for the long test case into the box below.

Step 2

Paste the source code for your program into the box below.

Step 3

When you are sure all the data has been entered correctly on the form press the submit button below.

You may submit multiple times. Only your most recent submission for each question will be marked.

Reference: Weisstein, Eric W. RATS Sequence. From MathWorld--A Wolfram Web Resource.

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