Strictly Palindromic Number

Problem Statement

An integer n is strictly palindromic if, for every base b between 2 and n - 2 (inclusive), the string representation of the integer n in base b is palindromic.

Given an integer n, return true if n is strictly palindromic and false otherwise.

A string is palindromic if it reads the same forward and backward.

Example 1:

Input: n = 9
Output: false

Explanation:
In base 2: 9 = 1001 (base 2), which is palindromic.
In base 3: 9 = 100 (base 3), which is not palindromic.
Therefore, 9 is not strictly palindromic so we return false.
Note that in bases 4, 5, 6, and 7, n = 9 is also not palindromic.

Example 2:

Input: n = 4
Output: false

Explanation:
We only consider base 2: 4 = 100 (base 2), which is not palindromic.
Therefore, we return false.

Constraints:

• 4 <= n <= 10^5

Solutions

Intuition

To determine if a number n is strictly palindromic, we need to check its representation in all bases from 2 to n - 2. If any representation is not palindromic, then n is not strictly palindromic.

Approach

1. Check Base Representation:

   • Convert the number n to each base from 2 to n - 2.
   • Check if the representation in each base is palindromic.

2. Early Termination:

   • If any base representation is not palindromic, return false.

Java

class Solution {
    public boolean isStrictlyPalindromic(int n) {
        return false;
    }
}

Python

class Solution:
    def isStrictlyPalindromic(self, n: int) -> bool:
        return False

Conclusion

For the given problem constraints, the function always returns false. This is because it's mathematically impossible for any number greater than 4 to be strictly palindromic according to the given definition.