Talk:Special factorials: Difference between revisions

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Revision as of 17:58, 16 March 2021

Reverse factorial algorithm

I took a stab at translating the reverse factorial algorithm used in the Factor entry to Java. It should be almost as efficient as taking the factorial itself. <lang java>public static int rf(int n) {

   if (n == 1)
     return 0;

   int a = 1;
   int b = 1;
   while (n > a) {
     b++;
     a = a * b;
   }
   if (a == n)
     return b;
   else return -1; //undefined
 }</lang>

--Chunes (talk) 17:06, 16 March 2021 (UTC)

Note that the factorial inverse (or reverse factorial) of unity has two possible answers: zero and unity.

It is normal when searching a series (in this case, the series of factorial products) to use the first match found in the series. -- Gerard Schildberger (talk) 17:37, 16 March 2021 (UTC)

Good catch. I revised the algorithm above and will make a note about it in the task description. --Chunes (talk) 17:58, 16 March 2021 (UTC)

Why is af(0) 0?

Is it that 0 is the additive identity the way that factorial of 0 is 1 is the multiplicative identity? If so why should it be the identity anyway?

I think it's just that the formula literally produces 0 for n = 0.

First run through, i is 1, this produces -1. Second run through, i is 0, this produces 1 and their sum is 0. --Chunes (talk) 17:36, 16 March 2021 (UTC)

@@ Line 2: / Line 2: @@
 I took a stab at translating the reverse factorial algorithm used in the Factor entry to Java. It should be almost as efficient as taking the factorial itself.
 <lang java>public static int rf(int n) {
+    if (n == 1)
+      return 0;
     int a = 1;
     int b = 1;
@@ Line 14: / Line 17: @@
 --[[User:Chunes|Chunes]] ([[User talk:Chunes|talk]]) 17:06, 16 March 2021 (UTC)
 : Note that the &nbsp; ''factorial inverse'' &nbsp; (or &nbsp;''reverse factorial'') &nbsp; of &nbsp; '''unity''' &nbsp; has two possible answers: &nbsp; '''zero''' &nbsp; and &nbsp; '''unity'''.
 : It is normal when searching a series &nbsp; (in this case, the series of factorial products) &nbsp; to use the first match found in the series. &nbsp; &nbsp; -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 17:37, 16 March 2021 (UTC)
+:: Good catch. I revised the algorithm above and will make a note about it in the task description. --[[User:Chunes|Chunes]] ([[User talk:Chunes|talk]]) 17:58, 16 March 2021 (UTC)
 === Why is af(0) 0? ===