Largest palindrome by changing at most K-digits

Summary

Given a non-negative integer num and an integer k, find the largest palindromic number that can be obtained by changing at most k digits in the given number. A palindromic number is a number that remains the same when its digits are reversed.

Detailed Explanation

To solve this problem, we will iterate through all possible combinations of changing up to k digits in the given number and check if each combination results in a palindrome. We can use a recursive approach for this.

Here's a step-by-step breakdown of the solution:

Initialize the maximum palindromic number as the given number.
For each digit position from right to left (i.e., from least significant to most significant):
- If k is greater than 0, change the current digit to all possible values (0-9) and recursively check if any of these combinations result in a palindrome.
  - If a larger palindromic number is found, update the maximum palindromic number.
Return the maximum palindromic number.

Time complexity: O(10^k * n), where n is the number of digits in the given number and k is the number of allowed changes. This is because we are iterating through all possible combinations of changing up to k digits.

Space complexity: O(n), as we need to store the current number and the maximum palindromic number at each recursive step.

Optimized Solutions

Java

View GeeksforGeeks Problem

public class Solution {
    public int largestPalindrome(int n) {
        long num = (long) Math.pow(10, n) - 1;
        for (int i = n - 1; i >= 0; i--) {
            if (k > 0 && i < n - 1) {
                for (int j = 0; j <= 9; j++) {
                    num = num / 10 + j;
                    if (isPalindrome(num)) return (int) (num);
                    num = (long) Math.pow(10, n) - 1;
                }
            } else {
                if (isPalindrome(num)) return (int) (num);
            }
        }
        return -1;
    }

    public boolean isPalindrome(long num) {
        long rev = 0, temp = num;
        while (temp > 0) {
            rev = rev * 10 + temp % 10;
            temp /= 10;
        }
        return num == rev;
    }
}

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891956. Largest palindrome by changing at most K-digits