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Recursive Helper Functions

• Sometimes it is easier to find a recursive solution if you change the original problem slightly, then solve the problem using a recursive helper function.
• In our palindrome example, it is inefficient to construct new string objects in every step.
• Rather than creating a new string, this function simply skips over matching letter pairs by adjusting the start and end parameters with each recursive call.

  bool substring_is_palindrome(string s, int start, int end)
  {
     // separate case for substrings of length 0 and 1
     if (start >= end) return true;
  
     if (s[start] == s[end])
        // test substring that doesn't contain the first and last letters
        return substring_is_palindrome(s, start + 1, end - 1);
     else
        return false;
  }
  

• The new function is a helper function that the user of the is_palindrome function doesn't know about.

  bool is_palindrome(string s)
  {
     return substring_is_palidrome(s, 0, s.length() - 1);
  }
  

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