Find the Closest Palindrome

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class Solution:
    def nearestPalindromic(self, n: str) -> str:
        length = len(n)
        candidates = set()

        # Add the edge cases
        candidates.add(str(10**length + 1))
        candidates.add(str(10**(length - 1) - 1))

        # Get the prefix and construct the palindromes by mirroring the prefix
        prefix = int(n[:length // 2 + length % 2])
        for i in range(-1, 2):
            candidate_prefix = str(prefix + i)
            candidate = candidate_prefix
            if length % 2 == 0:
                candidate += candidate_prefix[::-1]
            else:
                candidate += candidate_prefix[:-1][::-1]
            candidates.add(candidate)

        # Remove the original number from candidates
        candidates.discard(n)

        # Find the closest palindrome
        closest, min_diff = None, float('inf')
        for candidate in candidates:
            diff = abs(int(candidate) - int(n))
            if diff < min_diff or (diff == min_diff and int(candidate) < closest):
                closest = int(candidate)
                min_diff = diff

        return str(closest)

10 Prerequisite LeetCode Problems

“Find the Closest Palindrome” (LeetCode #564) involves understanding of numbers, string manipulation and the concept of palindrome. Here are 10 problems to prepare:

“Reverse Integer” (LeetCode Problem #7): This problem introduces the concept of reversing digits of an integer, which is crucial in understanding how to manipulate numbers.
“Palindrome Number” (LeetCode Problem #9): You will need to understand what makes a number a palindrome, this problem will introduce this concept.
“Valid Palindrome” (LeetCode Problem #125): This problem extends the concept of palindrome to strings, which will be helpful when you need to consider numbers as strings.
“Longest Palindromic Substring” (LeetCode Problem #5): Understanding how to work with palindromes in a string context is necessary for “Find the Closest Palindrome”.
“Palindromic Substrings” (LeetCode Problem #647): Further practice on finding palindromes within strings.
“Add Strings” (LeetCode Problem #415): This problem introduces the idea of working with numbers as strings which will be helpful in manipulating numeric strings in “Find the Closest Palindrome”.
“Add Binary” (LeetCode Problem #67): Another problem on string manipulation with binary numbers which can enhance your understanding of numeric strings.
“Backspace String Compare” (LeetCode Problem #844): This problem requires understanding how changes in a string can affect the final result, similar to how changes in the digits of a number can affect whether it’s a palindrome.
“Valid Palindrome II” (LeetCode Problem #680): This problem requires understanding how to determine a palindrome when you can modify the string slightly, similar to how you might need to adjust a number to find the closest palindrome.
“Construct K Palindrome Strings” (LeetCode Problem #1400): Further explores the properties of palindromes within strings.

These problems should provide a solid foundation for handling numeric strings and understanding palindromes, preparing you to tackle the “Find the Closest Palindrome” problem.

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class Solution:
    def find_next_palindrome(self, n, additive):
        l = len(n)
        if l == 0:
            return 0
        first_half = str(int(n[:l // 2 + l % 2]) + additive)
        return int(first_half + first_half[(-1 - l%2)::-1])

    def nearestPalindromic(self, n: str) -> str:
        m = int(n)
        candidates = [self.find_next_palindrome(n, additive) for additive in range(-1, 2)]
        candidates.append(self.find_next_palindrome("9"*(len(n)-1), 0))
        candidates.append(self.find_next_palindrome("1" + "0"*len(n), 0))

        ans = None
        for t in candidates:
            if t == m:
                continue
            if ans is None or abs(ans - m) > abs(t - m) or (abs(ans - m) == abs(t - m) and t < m):
                ans = t
        return str(ans)

Problem Classification

This problem is part of the “Mathematics” and “String Processing” domains. It involves concepts related to number manipulation and string processing.

What:

Input: A string ’n’ representing an integer.
Output: The output is the closest integer (excluding the original integer itself), which is a palindrome. If there’s a tie for the closest palindrome, the smaller one should be returned.
Conditions: The notion of “closest” is defined as the smallest absolute difference between two integers.

The problem can be classified as a “Number Theory” problem, as it involves operations related to integers and their properties (in this case, palindrome). It also falls under “String Manipulation” since the given integer is provided as a string and the manipulation of this string might be a part of the solution. The problem could also be viewed as a type of “Search” problem, as we need to find the nearest palindrome number.

Language Agnostic Coding Drills

This Python code is finding the nearest palindrome number for a given number. Let’s break down the steps needed to implement this solution and arrange the learning units in increasing order of difficulty:

Basic Arithmetic Operations and String Manipulation: This is a fundamental skill required to solve the problem. It involves adding or subtracting a number and converting an integer to a string. A drill for this would be to take an integer, add or subtract from it, convert it to a string, and perform string manipulations like slicing and concatenation.
Finding the palindrome of a number: This step involves generating a palindrome from a given number. It’s important to understand how to slice the number into half, add to the first half if necessary, and then concatenate with the reversed half to generate a palindrome. This process could be practiced by writing a function that takes in an integer and generates its palindrome.
Creating multiple possible solutions: The problem approach creates multiple possible solutions and then selects the best one. This involves creating a list of candidates from the original number with a specific range (-1, 0, 1) and adding two specific edge cases. A drill for this could involve creating a list of possible solutions for a problem and then implementing logic to select the best solution.
Selecting the nearest palindrome: This is the final step where it involves finding the nearest palindrome, except for the original number itself. This involves a comparison of the absolute difference between the original number and the candidate numbers, and also when the difference is the same, taking the smaller one.

The aim of these drills is to focus on smaller parts of the problem, which can be then combined to solve the entire problem. By focusing on these parts, one can understand the underlying logic better and it helps in debugging and writing the final solution.

Targeted Drills in Python

Here are the drills for each concept, implemented in Python:

Basic Arithmetic Operations and String Manipulation:

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def basic_operations(num, additive):
    num += additive
    num_str = str(num)
    print(num_str)

basic_operations(123, 2)

The function basic_operations performs addition on the input number and converts it into a string.

Finding the palindrome of a number:

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def generate_palindrome(num, additive):
    num_str = str(num + additive)
    length = len(num_str)
    first_half = num_str[:length // 2 + length % 2]
    palindrome = first_half + first_half[(-1 - length%2)::-1]
    print(palindrome)

generate_palindrome(123, 1)

This function generate_palindrome generates a palindrome by adding to the first half of the number and then concatenating it with its reverse.

Creating multiple possible solutions:

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def generate_candidates(num):
    candidates = [num + additive for additive in range(-1, 2)]
    candidates.append(int("9" * (len(str(num)) - 1)))
    candidates.append(int("1" + "0" * len(str(num))))
    print(candidates)

generate_candidates(123)

The function generate_candidates generates a list of candidate solutions by creating palindromes around the number and adding two specific edge cases.

Selecting the nearest palindrome:

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def find_nearest(num, candidates):
    closest = None
    for candidate in candidates:
        if candidate == num:
            continue
        if closest is None or abs(closest - num) > abs(candidate - num) or (abs(closest - num) == abs(candidate - num) and candidate < num):
            closest = candidate
    print(closest)

find_nearest(123, [121, 125, 129, 99, 1000])

This function find_nearest finds the nearest palindrome from a list of candidate numbers, except for the number itself.

Note: These drills are tailored specifically for the given problem but they can be adapted to any problem with similar concepts.

Problem Classification

Problem Statement: Given a string n representing an integer, return the closest integer (not including itself), which is a palindrome. If there is a tie, return the smaller one. The closest is defined as the absolute difference minimized between two integers.

Example 1:

Input: n = “123” Output: “121”

Example 2:

Input: n = “1” Output: “0” Explanation: 0 and 2 are the closest palindromes but we return the smallest which is 0.

Constraints:

1 <= n.length <= 18 n consists of only digits. n does not have leading zeros. n is representing an integer in the range [1, 1018 - 1].

Analyze the provided problem statement. Categorize it based on its domain, ignoring ‘How’ it might be solved. Identify and list out the ‘What’ components. Based on these, further classify the problem. Explain your categorizations.

Visual Model of the Problem

How to visualize the problem statement for this problem?

Problem Restatement

Could you start by paraphrasing the problem statement in your own words? Try to distill the problem into its essential elements and make sure to clarify the requirements and constraints. This exercise should aid in understanding the problem better and aligning our thought process before jumping into solving it.

Abstract Representation of the Problem

Could you help me formulate an abstract representation of this problem?

Alternatively, if you’re working on a specific problem, you might ask something like:

Given this problem, how can we describe it in an abstract way that emphasizes the structure and key elements, without the specific real-world details?

Terminology

Are there any specialized terms, jargon, or technical concepts that are crucial to understanding this problem or solution? Could you define them and explain their role within the context of this problem?

Problem Simplification and Explanation

Could you please break down this problem into simpler terms? What are the key concepts involved and how do they interact? Can you also provide a metaphor or analogy to help me understand the problem better?

Constraints

Given the problem statement and the constraints provided, identify specific characteristics or conditions that can be exploited to our advantage in finding an efficient solution. Look for patterns or specific numerical ranges that could be useful in manipulating or interpreting the data.

What are the key insights from analyzing the constraints?

Case Analysis

Could you please provide additional examples or test cases that cover a wider range of the input space, including edge and boundary conditions? In doing so, could you also analyze each example to highlight different aspects of the problem, key constraints and potential pitfalls, as well as the reasoning behind the expected output for each case? This should help in generating key insights about the problem and ensuring the solution is robust and handles all possible scenarios.

Identification of Applicable Theoretical Concepts

Can you identify any mathematical or algorithmic concepts or properties that can be applied to simplify the problem or make it more manageable? Think about the nature of the operations or manipulations required by the problem statement. Are there existing theories, metrics, or methodologies in mathematics, computer science, or related fields that can be applied to calculate, measure, or perform these operations more effectively or efficiently?

Problem Breakdown and Solution Methodology

Given the problem statement, can you explain in detail how you would approach solving it? Please break down the process into smaller steps, illustrating how each step contributes to the overall solution. If applicable, consider using metaphors, analogies, or visual representations to make your explanation more intuitive. After explaining the process, can you also discuss how specific operations or changes in the problem’s parameters would affect the solution? Lastly, demonstrate the workings of your approach using one or more example cases.

Inference of Problem-Solving Approach from the Problem Statement

How did you infer from the problem statement that this problem can be solved using ?

Could you please provide a stepwise refinement of our approach to solving this problem?
How can we take the high-level solution approach and distill it into more granular, actionable steps?
Could you identify any parts of the problem that can be solved independently?
Are there any repeatable patterns within our solution?

Solution Approach and Analysis

Thought Process

Explain the thought process by thinking step by step to solve this problem from the problem statement and code the final solution. Write code in Python3. What are the cues in the problem statement? What direction does it suggest in the approach to the problem? Generate insights about the problem statement.

From Brute Force to Optimal Solution

Could you please begin by illustrating a brute force solution for this problem? After detailing and discussing the inefficiencies of the brute force approach, could you then guide us through the process of optimizing this solution? Please explain each step towards optimization, discussing the reasoning behind each decision made, and how it improves upon the previous solution. Also, could you show how these optimizations impact the time and space complexity of our solution?

Coding Constructs

Consider the following piece of complex software code.

What are the high-level problem-solving strategies or techniques being used by this code?
If you had to explain the purpose of this code to a non-programmer, what would you say?
Can you identify the logical elements or constructs used in this code, independent of any programming language?
Could you describe the algorithmic approach used by this code in plain English?
What are the key steps or operations this code is performing on the input data, and why?
Can you identify the algorithmic patterns or strategies used by this code, irrespective of the specific programming language syntax?

Language Agnostic Coding Drills

Your mission is to deconstruct this code into the smallest possible learning units, each corresponding to a separate coding concept. Consider these concepts as unique coding drills that can be individually implemented and later assembled into the final solution.

Dissect the code and identify each distinct concept it contains. Remember, this process should be language-agnostic and generally applicable to most modern programming languages.
Once you’ve identified these coding concepts or drills, list them out in order of increasing difficulty. Provide a brief description of each concept and why it is classified at its particular difficulty level.
Next, describe the problem-solving approach that would lead from the problem statement to the final solution. Think about how each of these coding drills contributes to the overall solution. Elucidate the step-by-step process involved in using these drills to solve the problem. Please refrain from writing any actual code; we’re focusing on understanding the process and strategy.

Targeted Drills in Python

Now that you’ve identified and ordered the coding concepts from a complex software code in the previous exercise, let’s focus on creating Python-based coding drills for each of those concepts.

Begin by writing a separate piece of Python code that encapsulates each identified concept. These individual drills should illustrate how to implement each concept in Python. Please ensure that these are suitable even for those with a basic understanding of Python.
In addition to the general concepts, identify and write coding drills for any problem-specific concepts that might be needed to create a solution. Describe why these drills are essential for our problem.
Once all drills have been coded, describe how these pieces can be integrated together in the right order to solve the initial problem. Each drill should contribute to building up to the final solution.

Remember, the goal is to not only to write these drills but also to ensure that they can be cohesively assembled into one comprehensive solution.

Find the Closest Palindrome

10 Prerequisite LeetCode Problems

Problem Classification

Language Agnostic Coding Drills

Targeted Drills in Python

Problem Classification

Visual Model of the Problem

Problem Restatement

Abstract Representation of the Problem

Terminology

Problem Simplification and Explanation

Constraints

Case Analysis

Identification of Applicable Theoretical Concepts

Problem Breakdown and Solution Methodology

Inference of Problem-Solving Approach from the Problem Statement

Stepwise Refinement

Solution Approach and Analysis

Thought Process

From Brute Force to Optimal Solution

Coding Constructs

Language Agnostic Coding Drills

Targeted Drills in Python

Q&A

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