Question

I need to write a function to satisfy this input -> output list:

0 -> 0
1 -> 1
3 -> 2
4 -> 3
5 -> 5
7 -> 13
9 -> 34

f(x) = ??

Answer 1

Well, that is incredibly easy… if you aren’t concerned about over-fitting, then you can do:

switch(input)
     case 0: report 0
     case 1: report 1
     case 3: report 2
     ...
     default: report whatever

You probably need more constraints on the problem if you want a good solution. You also might consider graphing the function to see if there is any obvious pattern, or maybe show the bits involved. It would also be useful to know if the inputs and outputs are integer-valued or real-valued (is the function supposed to be continuous or discrete?). Without this information, it’s a little bit hard to help.

Edit
Showing the missing numbers helps:

0 -> 0
1 -> 1
2 -> 1
3 -> 2
4 -> 3
5 -> 5
6 -> 8
7 -> 13
8 -> 21
9 -> 34

(It’s the Fibonnaci numbers: f(x) = f(x-1)+f(x-2), where f(0)=0 and f(1)=1).

PS
This is a function for which dynamic programming or memoization is particularly useful.