What is the time complexity of Zigzag Conversion?

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

What data structures are used to solve Zigzag Conversion?

This problem uses String. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Zigzag Conversion?

Insight 1: The core idea is to simulate the zigzag writing process by traversing the rows in a down-and-up manner. Insight 2: We need to keep track of the current row and the direction of movement (downwards or upwards).

Which companies ask LeetCode 6. Zigzag Conversion in interviews?

This problem is frequently asked at Adobe, Amazon, Apple, BitGo, Bloomberg and 17 more companies.

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Zigzag Conversion - LeetCode 6 Solution

Zigzag Conversion - Complete Solution Guide

Zigzag Conversion is LeetCode problem 6, 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

The string "PAYPALISHIRING" is written in a zigzag pattern on a given number of rows like this: (you may want to display this pattern in a fixed font for better legibility) P A H N A P L S I I G Y I R And then read line by line: "PAHNAPLSIIGYIR" Write the code that will take a string and make this conversion given a number of rows: string convert(string s, int numRows); Example 1: Input: s = "PAYPALISHIRING", numRows = 3 Output: "PAHNAPLSIIGYIR" Example 2: Input: s = "PAYPALISHIRING", numRows =

Detailed Explanation

The problem requires converting a given string into a zigzag pattern based on a specified number of rows. Imagine writing the string diagonally downwards and upwards across the rows, like a zigzag. After writing the string in this pattern, we need to read the characters row by row and return the resulting string. The input consists of the string to be converted and the number of rows in the zigzag pattern. The output is the converted string read row by row.

Solution Approach

The solution uses an array (or list of stringbuilders in Java, or an array of strings in C++) to represent the rows of the zigzag pattern. It iterates through the input string, appending each character to the appropriate row based on the current row index and direction of movement. The direction changes when the current row reaches the top (0) or the bottom (numRows - 1). Finally, the rows are concatenated to form the resulting string.

Step-by-Step Algorithm

Step 1: Handle edge cases: If numRows is 1 or greater than or equal to the string length, return the original string.
Step 2: Initialize an array (or list of stringbuilders in Java, or an array of strings in C++) to store the rows. The size of the array will be numRows.
Step 3: Initialize the current row to 0 and the direction (step) to -1 (initially upwards, which will become downwards after the first row is handled).
Step 4: Iterate through the input string, character by character.
Step 5: Append the current character to the string/stringbuilder at the current row index.
Step 6: If the current row is 0 or numRows - 1, change the direction (multiply the step by -1).
Step 7: Update the current row by adding the step (which will be either 1 or -1).
Step 8: After iterating through the entire string, concatenate the strings in the rows array to form the result string.
Step 9: Return the resulting string.

Key Insights

Insight 1: The core idea is to simulate the zigzag writing process by traversing the rows in a down-and-up manner.
Insight 2: We need to keep track of the current row and the direction of movement (downwards or upwards).
Insight 3: The direction changes when we reach the top or bottom row.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: String.

Companies

Asked at: Adobe, Amazon, Apple, BitGo, Bloomberg, Cisco, ConsultAdd, Goldman Sachs, Intuit, Meta, Microsoft, Microstrategy, Mitsogo, Oracle, PayPal, PayPay, ServiceNow, Uber, Yahoo, Zoho, Zopsmart, carwale.

Zigzag Conversion | LeetCode 6

Medium

String

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

Solution Code

Available in:

class Solution {
    public String convert(String s, int numRows) {
        if (numRows == 1 || numRows >= s.length()) {
            return s;
        }
        
        StringBuilder[] rows = new StringBuilder[numRows];
        for (int i = 0; i < numRows; i++) {
            rows[i] = new StringBuilder();
        }
        
        int current_row = 0;
        int step = -1;
        
        for (char c : s.toCharArray()) {
            rows[current_row].append(c);
            if (current_row == 0 || current_row == numRows - 1) {
                step *= -1;
            }
            current_row += step;
        }
        
        StringBuilder result = new StringBuilder();
        for (StringBuilder row : rows) {
            result.append(row);
        }
        
        return result.toString();
    }
}

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Problem Info

Description

Problem 6: Zigzag Conversion - Detailed explanation and solution approaches.

Topics

String

Companies

AdobeAmazonAppleBitGoBloombergCiscoConsultAddGoldman Sachs

Stats

Difficulty:Medium

Languages:4

Companies:22

Problem #:6

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

9 steps

1
Step 1: Handle edge cases: If numRows is 1 or greater than or equal to the string length, return the original string.
2
Step 2: Initialize an array (or list of stringbuilders in Java, or an array of strings in C++) to store the rows. The size of the array will be numRows.
3
Step 3: Initialize the current row to 0 and the direction (step) to -1 (initially upwards, which will become downwards after the first row is handled).
4
Step 4: Iterate through the input string, character by character.
5
Step 5: Append the current character to the string/stringbuilder at the current row index.
6
Step 6: If the current row is 0 or numRows - 1, change the direction (multiply the step by -1).
7
Step 7: Update the current row by adding the step (which will be either 1 or -1).
8
Step 8: After iterating through the entire string, concatenate the strings in the rows array to form the result string.
9
Step 9: Return the resulting string.

💡

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 algorithm iterates through each character of the input string once. The space complexity is determined by the storage required for the rows. In the worst case, the number of rows will hold close to n characters in total, thus O(n).

📖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

Mathematical Approach

Instead of simulating the zigzag pattern, we can directly calculate the index of each character in the resulting string based on mathematical formulas derived from the zigzag pattern. This avoids the need to store the intermediate rows.

Time: O(n)Space: O(1)

Trade-offs: This approach can be more complex to implement and understand, but it offers better space complexity if the code quality and maintainability are not negatively impacted. This approach might be faster due to less memory operations. It is preferred in systems with memory constraints.

✨

Key Insights

1Insight 1: The core idea is to simulate the zigzag writing process by traversing the rows in a down-and-up manner.
2Insight 2: We need to keep track of the current row and the direction of movement (downwards or upwards).
3Insight 3: The direction changes when we reach the top or bottom row.

📚

Key Terms Explained

For Students

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: numRows = 1. The function correctly returns the original string because there is no zigzag pattern in this case.
Edge case 2: numRows >= s.length(). The function correctly returns the original string as well because it degenerates into just placing the characters vertically.
Edge case 3: Empty string. The solution handles empty strings gracefully. It won't cause errors.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly handling the direction change. Forgetting to reverse the direction when reaching the top or bottom row can lead to an incorrect zigzag pattern.

✗Common mistake 2: Not handling the edge cases of numRows = 1 or numRows >= s.length() can lead to incorrect output or runtime errors.

✗Common mistake 3: Off-by-one errors when calculating row indices or iterating through the string.

✅

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 encryption. Zigzag conversion can be used as a simple transposition cipher for encrypting data. While not robust, it illustrates the principle.

🏦Real-world scenario 2: Text compression. In niche cases, reordering characters in a zigzag pattern might improve the efficiency of certain compression algorithms that rely on adjacent character patterns.

🎮Real-world scenario 3: Image processing. Similar zigzag patterns are used to scan images for efficient compression or processing, although the pattern would be much more complex for a 2D image.

💡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

String problems often involve sliding windows or two pointers. Consider if the character set is limited (lowercase letters = only 26 possibilities).

🎯 Interview Tip

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

⚠️ Watch Out

Mutating strings directly in languages where strings are immutable. Use StringBuilder or arrays.

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: June 7, 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

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 13

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

@InterviewProJul 6

❓

Frequently Asked Questions

How do I handle string manipulation efficiently?

In languages with immutable strings (Java, Python, C#), use StringBuilder/list to avoid O(n) concatenation cost. Consider using character arrays for in-place modifications. For pattern matching, consider KMP or Rabin-Karp for O(n+m) complexity.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Zigzag Conversion"?

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

🤖 Need help with this problem?