Let's say a positive integer is a super-palindrome if it is a palindrome, and it is also the square of a palindrome.
Given two positive integers left and right represented as strings, return the number of super-palindromes integers in the inclusive range[left, right].
Example 1:
Input: left = "4", right = "1000"
Output: 4
Explanation: 4, 9, 121, and 484 are superpalindromes.
Note that 676 is not a superpalindrome: 26 * 26 = 676, but 26 is not a palindrome.
Example 2:
Input: left = "1", right = "2"
Output: 1
Constraints:
1 <= left.length, right.length <= 18
left and right consist of only digits.
left and right cannot have leading zeros.
left and right represent integers in the range [1, 1018 - 1].
left is less than or equal to right.
Solutions
Solution 1: Preprocessing + Enumeration
According to the problem description, we assume that the super palindrome number $x = p^2 \in [1, 10^{18})$, where $p$ is a palindrome number, so $p \in [1, 10^9)$. We can enumerate the first half of the palindrome number $p$, then reverse it, and concatenate it to get all palindrome numbers, which are recorded in the array $ps$.
Next, we traverse the array $ps$. For each $p$, we calculate $p^2$, check whether it is in the interval $[L, R]$, and also check whether $p^2$ is a palindrome number. If it is, the answer is incremented by one.
After the traversal, return the answer.
The time complexity is $O(M^{\frac{1}{4}} \times \log M)$, and the space complexity is $O(M^{\frac{1}{4}})$. Where $M$ is the upper bound of $L$ and $R$, and in this problem, $M \leq 10^{18}$.