Reversing Factorial

Factorial is a very impotent one when it comes to Computer Science and Programming. Teachers choose factorial as a good example to teach recursion. But reverse factorial (or some people say, reverser engineering factorial and some say, reverse factorial lookup) is also a good tool to solver particular problems when come to make some search algorithms and some algorithms with permutation calculations.

For this given scene, many people suggest to go with a generic algorithm like below, its a brute-force approach

 ```1 2 3 4``` ```Set X=1. Generate F=X! Is F = the input? If yes, then X is N. If not, then set X=X+1, then start again at #2. ```

But this is not a good approach for a good programmer you know. Even we can optimize this optimize by using the previous result of F to compute the new F (new F = new X * old F). So I have written a function in C# like below

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```static int reverse_factorial(int factorial) { int in_scope_fact = factorial; int reverse_factorial_number = 1; while (true) { if (in_scope_fact / reverse_factorial_number == 1) return reverse_factorial_number; in_scope_fact = in_scope_fact / reverse_factorial_number; reverse_factorial_number = reverse_factorial_number + 1; } return reverse_factorial_number; } ```

If you go through the code you can easily understand what I have done. And get full code for the program below

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; namespace InverseFactorial { class Program { static void Main(string[] args) { Console.Write(reverse_factorial(int.Parse(args[0]))); Console.ReadLine(); } static int reverse_factorial(int factorial) { int in_scope_fact = factorial; int reverse_factorial_number = 1; while (true) { if (in_scope_fact / reverse_factorial_number == 1) return reverse_factorial_number; in_scope_fact = in_scope_fact / reverse_factorial_number; reverse_factorial_number = reverse_factorial_number + 1; } return reverse_factorial_number; } } } ```

Output is

One thought on “Reversing Factorial”

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