javascript - How to count all the palindromes in a string using recursion?

Question

I have a recursive function that checks if a string is a palindrome, but my assignment asks me to count the number of palindromes in a string (for example kayak has 2).

I'm really confused about how I can implement a recursive function that counts the number of palindromes. Here's my current code:

function isPalindrome(string) {
  if (string.length <= 1) {
    return true;
  }

  let [ firstLetter ] = string;
  let lastLetter = string[string.length - 1];

  if (firstLetter === lastLetter) {
    let stringWithoutFirstAndLastLetters = string.substring(1, string.length - 1);
    return isPalindrome(stringWithoutFirstAndLastLetters);
  } else {
    return false;
  }
}

Answer 1

When the function gets a palindrome it is easy:

1. Record the input
2. Try again without the edges
3. Stop when input is three characters or less

"kayak" -> "aya"

If the input isn't a palindrome try "both ends" recursively e.g. with "kayam" try with both "kaya" and "ayam" and keep going...

We stop the recursion when a string is 3 (or less) characters. A single character is not a palindrome and checking whether a two or three characters string is a palindrome is trivial.

                      kayam
                        |
                  +-------------+
                  |             |
                 kaya          ayam
                  |             |
              +-------+     +--------+
              |       |     |        |
             kay     aya   aya      yam

---

const reverse =
  ([...xs]) =>
    xs.reverse().join("");

const is_palindrome =
  a =>
      a.length === 1  ? false
    : a.length <= 3   ? a[0] === a[a.length-1]
                      : a === reverse(a);

const find_palindromes = str => {
  const scan =
    (x, xs = []) =>
        x.length <= 3     ? xs.concat(is_palindrome(x) ? x : [])
      : is_palindrome(x)  ? xs.concat
                              ( x
                              , scan(x.slice(1, -1))
                              )
                          : xs.concat
                              ( scan(x.slice(0, -1))
                              , scan(x.slice(1))
                              );

  return [...new Set(scan(str))];
};


console.log(find_palindromes("kayak").join());
console.log(find_palindromes("kayakkayak").join());
console.log(find_palindromes("kayakcanoe").join());
console.log(find_palindromes("kayam").join());
console.log(find_palindromes("appal").join());
console.log(find_palindromes("madamimadam").join());
console.log(find_palindromes("madamimadamkayak").join());