metka | Rails gem to manage tags with PostgreSQL array columns | Object-Relational Mapping library

There is a table with numbers. See Attachment

The first column acts as an index. It has number 0. It determines which row to jump to. A number is selected in the row. By this number, go to the row with this number. We select a number from a new row and so on.

Limitations. Numbers are not repeated during transition The return to the initial number can only be on the transition number equal to the number of rows in the table.

It is necessary to build the longest possible chain of transitions by numbers in the table. Ideally, loop, that is, when the initial number is equal to the final number, and the number of transitions is equal to the number of rows.

For example, let's start with the number 1. The 1st row contains the only number - 74. Go to 74th row. In the 74th row select the number that is in the first column (column zero is the row numbering index). There is nothing in the first column in 74th row, so we look further in the following columns. In the 2nd column there is a number 46. Go to the 46th row. There is a number 19 in the first column of the 46th row. Go to 19th row. Etc.

If it is impossible to select such a number so that there is no repetition, then output the sequence that turned out to be a file. Then look for other ways to achieve the longest chain of transitions.

It would be nice if the code could go back one, two, ... n steps back and choose a different path. For example, on the first pass, the code choses the first number from the row and hit a dead end, then it comes back and selects the second or third and repeats again. I have little understanding of how to do this in code.

At the best, I would like the code to suggest how to fix the input table to get a complete sequence. That is, the code would suggest in which cell the number should be changed to loop the sequence.

I went through this table manually and found at least two sequences that loop at step 86 (now there are 86 rows in the table), but the attached code gives a maximum of 73 steps.

I wrote VBA code in Excel. You can see it below.

Full xls on Drive.Google.

Tell me, please, how I can solve this problem. If such problem can not solve using VBA give me an advise, please, which programming language I should use.