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2396. Strictly Palindromic Number

Difficulty Topics

Description

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 <= 105

Solution

strictly-palindromic-number.py
class Solution:
    def isStrictlyPalindromic(self, n: int) -> bool:

        def numberToBase(n, b):
            digits = []

            while n:
                digits.append(n % b)
                n //= b

            return "".join(map(str, digits[::-1]))

        for k in range(2, n - 2 + 1):
            s = numberToBase(n, k)

            if s != s[::-1]:
                return False

        return True