Minimum Insertion Steps to Make a String Palindrome

Given a string s. In one step you can insert any character at any index of the string.

Return the minimum number of steps to make s palindrome.

A Palindrome String is one that reads the same backward as well as forward.

Example 1:

Input: s = "zzazz"
Output: 0
Explanation: The string "zzazz" is already palindrome we don't need any insertions.

Example 2:

Input: s = "mbadm"
Output: 2
Explanation: String can be "mbdadbm" or "mdbabdm".

Example 3:

Input: s = "leetcode"
Output: 5
Explanation: Inserting 5 characters the string becomes "leetcodocteel".

Constraints:

• 1 <= s.length <= 500
• s consists of lowercase English letters.

SOLUTION:

class Solution:
    def minIns(self, s, i, j):
        if i == j:
            return 0
        if i == j - 1:
            if s[i] == s[j]:
                return 0
            return 1
        if (i, j) in self.cache:
            return self.cache[(i, j)]
        if s[i] == s[j]:
            curr = self.minIns(s, i + 1, j - 1)
            self.cache[(i, j)] = curr
            return curr
        else:
            curr = 1 + min(self.minIns(s, i + 1, j), self.minIns(s, i, j - 1))
            self.cache[(i, j)] = curr
            return curr

    def minInsertions(self, s: str) -> int:
        self.cache = {}
        return self.minIns(s, 0, len(s) - 1)