What is the time complexity of Lexicographically Smallest String After Substring Operation?

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

What data structures are used to solve Lexicographically Smallest String After Substring Operation?

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

What are the key insights for solving Lexicographically Smallest String After Substring Operation?

Insight 1: The key is to realize that we want to change characters to their preceding characters ('b' -> 'a', 'c' -> 'b', etc.) as much as possible, but strategically. Converting a character to 'a' is optimal. Converting 'a' to 'z' is undesirable except for a special case. Insight 2: We should prioritize changing characters to 'a' from left to right. The first non-'a' character should be the start of our substring to be converted.

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Lexicographically Smallest String After Substring Operation - LeetCode 2734 Solution

Q: Which companies ask LeetCode 2734. Lexicographically Smallest String After Substring Operation in interviews?

This problem is frequently asked at Agoda, IBM.

Lexicographically Smallest String After Substring Operation - Complete Solution Guide

Lexicographically Smallest String After Substring Operation is LeetCode problem 2734, 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 a string s consisting of lowercase English letters. Perform the following operation: Select any non-empty substring then replace every letter of the substring with the preceding letter of the English alphabet. For example, 'b' is converted to 'a', and 'a' is converted to 'z'. Return the lexicographically smallest string after performing the operation . Example 1: Input: s = "cbabc" Output: "baabc" Explanation: Perform the operation on the substring starting at index 0, and ending at index

Detailed Explanation

The problem asks us to find the lexicographically smallest string that can be obtained from a given string `s` by applying a specific operation. The operation involves selecting any non-empty substring and replacing each character in that substring with its preceding letter in the English alphabet (e.g., 'b' becomes 'a', and 'a' becomes 'z'). The goal is to minimize the string lexicographically, meaning we want to make it as close to 'a' as possible from left to right. The input is a string `s` of lowercase English letters, and the output is the lexicographically smallest string after performing the described operation.

Solution Approach

The solution uses a greedy approach to find the lexicographically smallest string. It iterates through the string from left to right. The algorithm attempts to find the first character that is not 'a'. Once it finds such a character, it starts converting the subsequent characters to their preceding characters until it encounters an 'a' or the end of the string. If the entire string consists of 'a' characters, it changes the last character to 'z'.

Step-by-Step Algorithm

Step 1: Convert the input string `s` into a character array (or equivalent data structure for string manipulation) to allow in-place modification.
Step 2: Iterate through the character array from the beginning to find the first character that is not 'a'.
Step 3: If all characters are 'a' (i.e., the loop completes without finding a non-'a' character), change the last character to 'z' and return the modified string.
Step 4: If a non-'a' character is found at index `i`, start from that index and continue changing characters to their preceding character until an 'a' is encountered or the end of the string is reached. The conversion is done by subtracting 1 from the ASCII value of each character.
Step 5: Convert the character array back into a string and return the result.

Key Insights

Insight 1: The key is to realize that we want to change characters to their preceding characters ('b' -> 'a', 'c' -> 'b', etc.) as much as possible, but strategically. Converting a character to 'a' is optimal. Converting 'a' to 'z' is undesirable except for a special case.
Insight 2: We should prioritize changing characters to 'a' from left to right. The first non-'a' character should be the start of our substring to be converted.
Insight 3: If the entire string consists of 'a' characters, we only change the last character to 'z' because that will be the smallest possible string in that scenario. This handles an important edge case.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: String, Greedy.

Companies

Asked at: Agoda, IBM.

Lexicographically Smallest String After Substring Operation | LeetCode 2734

Medium

String Greedy

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

Solution Code

Available in:

class Solution {
    public String smallestString(String s) {
        char[] chars = s.toCharArray();
        int n = chars.length;
        
        int i = 0;
        while (i < n && chars[i] == 'a') {
            i += 1;
        }
        
        if (i == n) {
            chars[n - 1] = 'z';
            return new String(chars);
        }
        
        int j = i;
        while (j < n && chars[j] != 'a') {
            chars[j] = (char)(chars[j] - 1);
            j += 1;
        }
        
        return new String(chars);
    }
}

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Problem Info

Description

Problem 2734: Lexicographically Smallest String After Substring Operation - Detailed explanation and solution approaches.

Topics

String Greedy

Companies

AgodaIBM

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:2734

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

5 steps

1
Step 1: Convert the input string `s` into a character array (or equivalent data structure for string manipulation) to allow in-place modification.
2
Step 2: Iterate through the character array from the beginning to find the first character that is not 'a'.
3
Step 3: If all characters are 'a' (i.e., the loop completes without finding a non-'a' character), change the last character to 'z' and return the modified string.
4
Step 4: If a non-'a' character is found at index `i`, start from that index and continue changing characters to their preceding character until an 'a' is encountered or the end of the string is reached. The conversion is done by subtracting 1 from the ASCII value of each character.
5
Step 5: Convert the character array back into a string and return the result.

💡

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 time complexity is linear because the algorithm iterates through the string a maximum of two times, each taking O(n) time. The space complexity is O(n) due to the creation of a character array or vector to represent the string. In the C code, `malloc` is used to create a copy of the string, hence O(n) space.

📖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

Brute Force

Generate all possible substrings, apply the operation on each substring, and then find the lexicographically smallest string among all results. This involves generating all substrings and modifying the string which is very inefficient.

Time: O(n^3)Space: O(n)

Trade-offs: This approach is highly inefficient due to the generation of all possible substrings. The main solution is much faster and more suitable.

✨

Key Insights

1Insight 1: The key is to realize that we want to change characters to their preceding characters ('b' -> 'a', 'c' -> 'b', etc.) as much as possible, but strategically. Converting a character to 'a' is optimal. Converting 'a' to 'z' is undesirable except for a special case.
2Insight 2: We should prioritize changing characters to 'a' from left to right. The first non-'a' character should be the start of our substring to be converted.
3Insight 3: If the entire string consists of 'a' characters, we only change the last character to 'z' because that will be the smallest possible string in that scenario. This handles an important edge case.

📚

Key Terms Explained

For Students

Greedy Algorithm

Making the best choice at each step without looking ahead.

String

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

Edge Cases

Edge case 1: The input string consists entirely of 'a' characters (e.g., "aaaa"). In this case, the solution correctly changes the last character to 'z'.
Edge case 2: The input string contains a single character which is 'a'. In this case, the solution correctly changes the single character to 'z'.
Edge case 3: The input string contains no 'a' character. In this case, the solution correctly changes all characters until the end of the string to their preceding character in the alphabet.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the edge case where the string consists entirely of 'a' characters. This will lead to incorrect results.

✗Common mistake 2: Incorrectly implementing the character replacement logic. It's crucial to remember that 'a' should be replaced with 'z'.

✗Common mistake 3: Modifying the original string directly without creating a copy or using a character array, especially in languages where strings are immutable.

✅

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: String compression or optimization algorithms where transforming strings lexicographically can aid in reducing storage space or improving search efficiency.

🏦Real-world scenario 2: Cryptographic applications involving string manipulation and transformation, where variations of this algorithm could be used as part of more complex encryption schemes.

🎮Real-world scenario 3: Text editors and IDEs that offer features like automatic code formatting or refactoring, where manipulating strings to achieve a desired lexicographical order may be required.

💡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

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ 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: July 5, 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

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

@TechLeadJul 14

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 7

❓

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.

How do I verify if a greedy approach is correct?

Prove the greedy choice property: the locally optimal choice leads to globally optimal solution. Use exchange argument: show that swapping any element with the greedy choice doesn't improve the solution. If you can't prove it, test extensively or consider DP.

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 "Lexicographically Smallest String After Substring Operation"?

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 greedy techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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