Question

1. For the following recursive function: Derive a recurrence relation, solve the relation, prove the solution is correct, and find its big-O notation.

String f2(String s, char c)

{

   if (s.length() == 0)      return s;

   if (s.charAt(0) == c)

        return f2(s.substring(1), c);

   else

        return s.charAt(0) + f2(s.substring(1), c);

}

Answer 1

recurrence relation:
-----------------------
T(n) = T(n-1) + O(1)
and T(1) = O(1)

solving equation:
------------------
T(n)
= T(n-1) + O(1)
= T(n-2) + O(1) + O(1)
= T(1) + O(1) + ... + O(1)
= O(1) + O(1) + ... + O(1)
= n*O(1)
= O(n)

Big-O:
-------
From above calculation. time complexity is O(n). where n is the length of the string s.