Problem 803. Twist 'n' Match

This problem has some issues because some pairs (n,m) do not have a solution. For instance, it is impossible to find a matrix such that m = n^2 -1 since a rotation pivot does not move. Moreover, there are floor((n^2)/4) cycles of numbers, and when we match the cycle beginning with its end, it creates two matches. It is possible to do some manipulations to have an m greater than n^2 - floor((n^2)/4), but not always.

can you give an example of a matrix before and after?

This is a great problem that suffers from poor test cases.
Solutions tend to fall into three categories:
Random
Approaches that fail for some n and m
Approaches that are correct

The random problem could be fixed with a large array (n>500) and moderate m value (100,000). This would also eliminate a lot of the inefficient O(n^4) solutions. (Really they are O(m*n^2), but m can vary between 0 and n^2.)

The second problem could be solved with a test case that steps through a variety of m values, like n=100, m=[1:5000].

For reference, my own code runs n=10000;m=9000000; in about 5 seconds, as it is O(m). It also runs n=100, m=[1:5000] in about 5 seconds without failing. I really wish I could easily compare it to other solutions but the answers are simply full of bad solutions.