Comment by danbruc
6 hours ago
And the claimed algorithm solves the counting problem, i.e. determining the number of different solutions, which in many cases is much harder than just determining whether a solution exists or finding one of the solutions.
Knowing the count also gives you a O(n) way of finding a solution.
No.
The number of valid permutations of 10 things is 10!. Reviewing all 10! Things is clearly exponential or even worse than exponential.
We can get the count of 10! pretty easily, far easier than trying all combinations manually.