How do you solve Find the Largest Palindrome Divisible by K on LeetCode?

Find the Largest Palindrome Divisible by K (LeetCode #3260) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Palindromes can be efficiently constructed by manipulating their half.

What is the brute force solution for Find the Largest Palindrome Divisible by K?

The brute force approach for Find the Largest Palindrome Divisible by K is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible n-digit palindromic numbers and checking if they are divisible by k. This is straightforward but inefficient for larger values of n. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Find the Largest Palindrome Divisible by K?

Always clarify the constraints and edge cases before jumping into coding. Think about how you can reduce the problem size or complexity through clever manipulations. Practice generating palindromic numbers to get comfortable with the concept.

What are common mistakes when solving Find the Largest Palindrome Divisible by K?

Not considering leading zeros when generating palindromes. Overlooking the need to check both palindrome and divisibility conditions.

#3260

Find the Largest Palindrome Divisible by K

Hard

MathStringDynamic ProgrammingGreedyNumber TheoryGreedyString Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

Instead of generating all n-digit numbers, we can construct palindromes directly by manipulating their half. This reduces the number of checks significantly and allows us to focus on valid candidates only.

⚙️

Algorithm

4 steps

1Step 1: Calculate the largest half palindrome based on n (for odd/even n).
2Step 2: Generate the full palindrome from the half.
3Step 3: Check if the palindrome is divisible by k.
4Step 4: If not, decrement the half and repeat until a valid palindrome is found.

solution.py11 lines

1# Full working Python code
2
3def largest_palindrome_divisible(n, k):
4    half_length = (n + 1) // 2
5    start = 10**half_length - 1
6    end = 10**(half_length - 1)
7    for half in range(start, end - 1, -1):
8        palindrome = str(half) + str(half)[-1 - (n % 2):][::-1]
9        if int(palindrome) % k == 0:
10            return palindrome
11    return ""

ℹ

Complexity note: The time complexity is O(n) because we only generate half of the palindrome and check for divisibility, which is much more efficient than checking all n-digit numbers.

1Palindromes can be efficiently constructed by manipulating their half.
2Divisibility checks can be integrated into the palindrome generation process.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.