Largest Palindrome Product

Largest Palindrome Product - Problem

Math Enumeration Hard

Given an integer n, return the largest palindromic integer that can be represented as the product of two n-digit integers.

Since the result can be very large, return it modulo 1337.

For example, if n = 2, we need to find the largest palindrome that is the product of two 2-digit numbers (from 10 to 99). The largest palindrome would be 9009 = 91 × 99.

Note: For n = 1, the answer is 9 since 3 × 3 = 9 is the largest palindromic product of two 1-digit numbers.

Input & Output

Example 1 — Basic Case

$ Input: n = 2

› Output: 906

💡 Note: We need the largest palindrome from products of 2-digit numbers (10-99). The largest is 9009 = 91 × 99. Return 9009 % 1337 = 906.

Example 2 — Single Digit

$ Input: n = 1

› Output: 9

💡 Note: For 1-digit numbers (1-9), the largest palindromic product is 3 × 3 = 9. Since 9 < 1337, we return 9.

Example 3 — Larger Case

$ Input: n = 3

› Output: 123

💡 Note: For 3-digit numbers (100-999), we find the largest palindromic product and return it modulo 1337. The actual palindrome is much larger than 1337.

Constraints

1 ≤ n ≤ 8

Visualization

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Asked in

G Google 12 f Facebook 8 M Microsoft 6

The key insight is to generate palindromes in descending order rather than checking all products. For each palindrome, we verify if it can be factored into two n-digit numbers. The optimized approach uses palindrome generation with factorization checking. Time: O(10^n × √P), Space: O(1).

Common Approaches

✓ Two Pass Hash

⏱️ Time: N/A Space: N/A

Brute Force - Check All Products

⏱️ Time: O(10^(2n)) Space: O(1)

Generate all possible products of two n-digit numbers, check if each product is palindromic, and keep track of the maximum palindrome found. For n-digit numbers, we iterate from the smallest n-digit number to the largest.

Palindrome Generation Approach

⏱️ Time: O(10^n × √P) Space: O(1)

Instead of checking all products, we generate palindromes in descending order and verify if each can be expressed as a product of two n-digit numbers. This is more efficient as there are fewer palindromes than products to check.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Medium Frequency

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Smart Actions

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