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Asked: 2024-09-24T21:42:08+05:30 In:

You are tasked with finding the next smallest palindrome that is greater than a given integer represented as a string of digits. A palindrome is a number that reads the same forwards and backwards. For instance, given the input “12321”, the next smallest palindrome would be “12421”. If the input consists of all 9’s, like “999”, the output should be “1001”, since it’s the next smallest palindrome in that case. Your goal is to implement a function that takes the string representation of a number as input and returns the smallest palindrome that is larger than the provided number.

So, here’s a fun little puzzle for you—think of it like a brain teaser! Imagine you’re given a number, but it’s not just any number; it’s represented as a string of digits. The challenge is to find the next smallest palindrome that is greater than this number. You know palindromes, right? They’re those wonderful numbers that read the same forwards and backwards, like 121 or 1331.

Now, let’s say you’re given the number “12321.” Your mission—should you choose to accept it—is to figure out what the next palindrome would be. Spoiler alert: it’s “12421.” But here’s where it gets even more interesting! If the digits you’re given are all 9’s, like “999,” you can’t just bump it up by one. You have to get a bit creative and realize the next palindrome would actually be “1001.” Pretty cool, right?

Okay, so I want you to put on your thinking cap for a second and picture how you might tackle this problem. What steps would you take to find that next palindrome? Would you just keep incrementing the number until you stumble across a palindrome, or could there be a smarter way to do it? Maybe you’d think about the structure of the number itself!

Imagine you crafted a function that takes that string as input and effortlessly spits out the smallest palindrome larger than the given number. What would that function look like? What kind of logic or loops do you think you’d need?

I’m really curious to hear how you’d approach this! It’s definitely a puzzle that combines a little bit of math with some string manipulation, and I bet there’s a whole bunch of cool ways to solve it. Would you start from the middle of the string, mess around with the first half, or just dive into brute force mode? Can’t wait to see what you come up with!

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    2 Answers


    1. To find the next smallest palindrome greater than a given number represented as a string, we can adopt a systematic approach that focuses on the structure of palindromes rather than attempting a brute-force method of incrementing the number. First, we would check whether the number consists entirely of the digit ‘9’—if so, the next palindrome is straightforwardly ‘100…001’, where the number of zeros is equal to the length of the input string minus one. For other cases, we can break down the string by finding its midpoint. By mirroring the first half of the string, we can create a candidate palindrome. If this candidate palindrome is greater than the given number, we can return it; if not, we need to increment the left half of the string (including the middle digit if the string length is odd) and create a new palindrome from this modified left half, mirroring it again to ensure it’s still a palindrome.

      In practical terms, this function could be implemented using string manipulation techniques. We would start by checking the special case of all ‘9’s. For other inputs, we would create the palindrome by taking the left half (plus the middle if applicable), reversing that half, and concatenating it with itself to form our candidate palindrome. A simple loop would be used to increment the left half if our generated candidate wasn’t valid. To optimize, we would also check for cases where incrementing would create a carry, necessitating an adjustment in the middle digits. This logic takes advantage of the reflective property of palindromes, minimizing unnecessary iterations and ensuring the result meets our requirements.




    2. Next Smallest Palindrome Puzzle

      Finding the Next Palindrome!

      So, let’s think about this palindrome thing. First, a palindrome is a number that is the same forwards and backwards, like 121 or 1331. If I have a number like “12321,” I need to find the next one that is bigger and still a palindrome.

      Steps to Solve It:

      1. Start with the given number as a string.
      2. Check if it’s all 9’s. If it is, the next palindrome will be 100…001, which is a cool edge case!
      3. If it’s not all 9’s, here’s a simple idea: try to build the next palindrome by looking at the first half of the number.
      4. Reverse that first half and append it to create a new palindrome.
      5. If this new palindrome isn’t bigger than the original number, bump up the first half and do the reverse again.

      Code Example Idea:

              
            function nextPalindrome(numStr) {
                // Check for all 9's
                if (numStr === '9'.repeat(numStr.length)) {
                    return '1' + '0'.repeat(numStr.length - 1) + '1';
                }
                // Process normally (this is just an idea)
                let len = numStr.length;
                let firstHalf = numStr.slice(0, Math.ceil(len / 2));
                let nextPalindrome = firstHalf + firstHalf.split('').reverse().join('').slice(len % 2);
                
                if (nextPalindrome > numStr) {
                    return nextPalindrome;
                }
                // Need to increment the first half
                firstHalf = (BigInt(firstHalf) + 1n).toString();
                nextPalindrome = firstHalf + firstHalf.split('').reverse().join('').slice(len % 2);
                return nextPalindrome; 
            }

      So, pretty much, I’d try to work with the first half of the number to create a palindrome. If it doesn’t work, I would just increment that part and see what happens next.

      Would this work? I want to give it a shot!


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