What is the time complexity of Find Palindrome With Fixed Length?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Find Palindrome With Fixed Length?

This problem uses Array, Math. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Find Palindrome With Fixed Length?

Insight 1: Palindromes can be constructed from their first half. For even length palindromes, the first half is mirrored to create the second half. For odd length palindromes, the first (n+1)/2 digits determine the entire palindrome. Insight 2: We can determine the smallest and largest possible palindrome for a given length `intLength`. This enables us to quickly check if the `queries[i]`-th palindrome exists without generating all possible palindromes.

Which companies ask LeetCode 2217. Find Palindrome With Fixed Length in interviews?

This problem is frequently asked at VMware.

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Find Palindrome With Fixed Length - LeetCode 2217 Solution

Find Palindrome With Fixed Length - Complete Solution Guide

Find Palindrome With Fixed Length is LeetCode problem 2217, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given an integer array queries and a positive integer intLength , return an array answer where answer[i] is either the queries[i] th smallest positive palindrome of length intLength or -1 if no such palindrome exists . A palindrome is a number that reads the same backwards and forwards. Palindromes cannot have leading zeros. Example 1: Input: queries = [1,2,3,4,5,90], intLength = 3 Output: [101,111,121,131,141,999] Explanation: The first few palindromes of length 3 are: 101, 111, 121, 131, 141,

Detailed Explanation

The problem asks us to find the `queries[i]`-th smallest palindrome of a given length `intLength`. If the palindrome exists, we return it; otherwise, we return -1. A palindrome is a number that reads the same forward and backward, and cannot have leading zeros. The input is an array of integers `queries` and an integer `intLength`. The output is an array of integers where each element is the `queries[i]`-th smallest palindrome of length `intLength`, or -1 if it doesn't exist.

Solution Approach

The solution constructs the `queries[i]`-th palindrome by first determining the base number and then calculating the first half of the palindrome. If the `queries[i]`-th palindrome exists, its first half is `base + queries[i] - 1`. We convert the first half to a string, and mirror the necessary part of it to create the second half of the palindrome. These two halves are then concatenated and converted to an integer to form the final palindrome.

Step-by-Step Algorithm

Step 1: Calculate the length of the first half of the palindrome: `half_length = (intLength + 1) // 2`.
Step 2: Calculate the base number for the first half of the palindrome. This is simply 10 raised to the power of `half_length - 1`. This value will be used as the starting point when calculating our palindrome.
Step 3: Determine the total count of possible palindromes of length `intLength`. The count is `9 * (10 ** (half_length - 1))`. This allows us to check if a given `query` will generate a valid palindrome without needing to calculate it.
Step 4: Iterate through the `queries` array. For each `query`, check if it exceeds the `count`. If it does, append -1 to the `answer` array.
Step 5: If the `query` is valid (i.e., it does not exceed `count`), calculate the first half of the palindrome using `first_half_num = base + query - 1`.
Step 6: Convert the `first_half_num` to a string `first_half_str`.
Step 7: Determine the second half of the palindrome by reversing the necessary portion of `first_half_str`. The length of this substring is `intLength // 2`.
Step 8: Concatenate `first_half_str` and `second_half_str` to form the complete palindrome string `palindrome_str`.
Step 9: Convert the `palindrome_str` to an integer and append it to the `answer` array.
Step 10: Return the `answer` array.

Key Insights

Insight 1: Palindromes can be constructed from their first half. For even length palindromes, the first half is mirrored to create the second half. For odd length palindromes, the first (n+1)/2 digits determine the entire palindrome.
Insight 2: We can determine the smallest and largest possible palindrome for a given length `intLength`. This enables us to quickly check if the `queries[i]`-th palindrome exists without generating all possible palindromes.
Insight 3: Efficiently generate the i-th palindrome by constructing its first half directly, avoiding an exhaustive search through all numbers.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Math.

Companies

Asked at: VMware.

Find Palindrome With Fixed Length | LeetCode 2217

Medium

Array Math

Time: O(n)Space: O(n)

Solution Code

Available in:

class Solution {
    public long[] kthPalindrome(int[] queries, int intLength) {
        int n = queries.length;
        long[] answer = new long[n];
        
        int halfLength = (intLength + 1) / 2;
        long base = (long)Math.pow(10, halfLength - 1);
        
        long count = 9 * (long)Math.pow(10, halfLength - 1);
        
        for (int i = 0; i < n; i++) {
            int query = queries[i];
            if (query > count) {
                answer[i] = -1;
            } else {
                long firstHalfNum = base + query - 1;
                String firstHalfStr = String.valueOf(firstHalfNum);
                
                String secondHalfStr = new StringBuilder(firstHalfStr.substring(0, intLength / 2)).reverse().toString();
                
                String palindromeStr = firstHalfStr + secondHalfStr;
                answer[i] = Long.parseLong(palindromeStr);
            }
        }
        
        return answer;
    }
}

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Problem Info

Description

Problem 2217: Find Palindrome With Fixed Length - Detailed explanation and solution approaches.

Topics

Array Math

Companies

VMware

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2217

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

10 steps

1
Step 1: Calculate the length of the first half of the palindrome: `half_length = (intLength + 1) // 2`.
2
Step 2: Calculate the base number for the first half of the palindrome. This is simply 10 raised to the power of `half_length - 1`. This value will be used as the starting point when calculating our palindrome.
3
Step 3: Determine the total count of possible palindromes of length `intLength`. The count is `9 * (10 ** (half_length - 1))`. This allows us to check if a given `query` will generate a valid palindrome without needing to calculate it.
4
Step 4: Iterate through the `queries` array. For each `query`, check if it exceeds the `count`. If it does, append -1 to the `answer` array.
5
Step 5: If the `query` is valid (i.e., it does not exceed `count`), calculate the first half of the palindrome using `first_half_num = base + query - 1`.
6
Step 6: Convert the `first_half_num` to a string `first_half_str`.
7
Step 7: Determine the second half of the palindrome by reversing the necessary portion of `first_half_str`. The length of this substring is `intLength // 2`.
8
Step 8: Concatenate `first_half_str` and `second_half_str` to form the complete palindrome string `palindrome_str`.
9
Step 9: Convert the `palindrome_str` to an integer and append it to the `answer` array.
10
Step 10: Return the `answer` array.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The dominant operation is the loop iterating through the `queries` array. Constructing the palindrome for each query involves string manipulations that take constant time because intLength is constrained to a maximum value of 15. The space used is primarily for the answer array, which has the same size as the queries array.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Pre-compute Palindromes

Generate all palindromes of length `intLength` up to a certain limit and store them in a list. Then, for each query, return the `queries[i]`-th element from the list, or -1 if it doesn't exist.

Time: O(m + n), where m is the time to generate all palindromes up to the limit, and n is the number of queries.Space: O(m), where m is the number of pre-computed palindromes stored.

Trade-offs: This approach might be faster if the number of queries is very large, but requires a significant amount of memory to store the pre-computed palindromes. The main solution is generally more efficient when the number of palindromes to compute is much larger than the number of queries.

✨

Key Insights

1Insight 1: Palindromes can be constructed from their first half. For even length palindromes, the first half is mirrored to create the second half. For odd length palindromes, the first (n+1)/2 digits determine the entire palindrome.
2Insight 2: We can determine the smallest and largest possible palindrome for a given length `intLength`. This enables us to quickly check if the `queries[i]`-th palindrome exists without generating all possible palindromes.
3Insight 3: Efficiently generate the i-th palindrome by constructing its first half directly, avoiding an exhaustive search through all numbers.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Edge case 1: `query` is larger than the maximum number of palindromes for a given `intLength`. The solution correctly returns -1.
Edge case 2: `intLength` is 1. The solution correctly handles this case as the base is 1 and the count is 9, representing the single-digit palindromes 1 to 9.
Edge case 3: Even and odd values of `intLength`. The solution appropriately constructs palindromes by adjusting the length of the reversed second half.
Edge case 4: Extremely large queries values that, when added to the base, could overflow. This is implicitly handled by checking the count of available palindromes and returning -1 if the query is out of bounds, which prevents the calculation altogether.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly calculating the base number for the first half of the palindrome. It should be `10**(half_length - 1)`.

✗Common mistake 2: Not handling the case where the `query` is larger than the maximum possible number of palindromes for the given `intLength`, leading to incorrect output.

✗Common mistake 3: Errors in string manipulation, especially when creating the second half of the palindrome, such as off-by-one errors in substring extraction or incorrect reversing.

✗Common mistake 4: Integer overflow when constructing the palindrome string from large numerical values. The code should use `long` (Java) or `long long` (C/C++) to store palindrome strings to prevent overflows.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Data validation and generation. Palindromes can be used as simple checksums or identifiers in situations where data integrity or uniqueness is important.

🏦Real-world scenario 2: Educational tools for teaching number patterns, string manipulation, and algorithmic thinking. Constructing and identifying palindromes can serve as an interesting coding exercise.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: July 28, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 13

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 6

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Find Palindrome With Fixed Length"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether math techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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