What is the time complexity of Find the Longest Balanced Substring of a Binary String?

The optimal solution has a time complexity of O(n^3).

What data structures are used to solve Find the Longest Balanced Substring of a Binary String?

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

What are the key insights for solving Find the Longest Balanced Substring of a Binary String?

Insight 1: Brute-force approach: The problem can be solved by iterating through all possible substrings and checking if each substring is balanced. This involves checking both the order of 0s and 1s and the equality of their counts. Insight 2: Substring generation: Efficiently generating all substrings is crucial. Nested loops are a straightforward way to do this, though not the most efficient.

Which companies ask LeetCode 2609. Find the Longest Balanced Substring of a Binary String in interviews?

This problem is frequently asked at Tinkoff.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Find the Longest Balanced Substring of a Binary String - LeetCode 2609 Solution

Find the Longest Balanced Substring of a Binary String - Complete Solution Guide

Find the Longest Balanced Substring of a Binary String is LeetCode problem 2609, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given a binary string s consisting only of zeroes and ones. A substring of s is considered balanced if all zeroes are before ones and the number of zeroes is equal to the number of ones inside the substring. Notice that the empty substring is considered a balanced substring. Return the length of the longest balanced substring of s . A substring is a contiguous sequence of characters within a string. Example 1: Input: s = "01000111" Output: 6 Explanation: The longest balanced substring is

Detailed Explanation

The problem asks to find the length of the longest balanced substring within a binary string (containing only '0's and '1's). A balanced substring is defined as a substring where all the '0's appear before all the '1's, and the count of '0's is equal to the count of '1's. The empty string is considered a balanced substring with length 0. The input is a binary string, and the output is an integer representing the length of the longest balanced substring.

Solution Approach

The provided solutions use a brute-force approach. They iterate through all possible substrings of the input string. For each substring, they count the number of '0's and '1's. Then, they check if the substring is balanced by verifying that all '0's precede all '1's and the counts of '0's and '1's are equal. The length of the longest balanced substring encountered is tracked and returned.

Step-by-Step Algorithm

Step 1: Initialize `max_len` to 0. This variable will store the length of the longest balanced substring found so far.
Step 2: Iterate through all possible starting indices `i` of substrings using a nested loop.
Step 3: For each starting index `i`, iterate through all possible ending indices `j` of substrings.
Step 4: Extract the substring `s[i:j]`.
Step 5: Count the number of '0's and '1's in the substring.
Step 6: Check if the substring is balanced (all '0's before '1's and equal counts).
Step 7: If the substring is balanced, update `max_len` to the maximum of `max_len` and the length of the substring.
Step 8: After iterating through all substrings, return `max_len`.

Key Insights

Insight 1: Brute-force approach: The problem can be solved by iterating through all possible substrings and checking if each substring is balanced. This involves checking both the order of 0s and 1s and the equality of their counts.
Insight 2: Substring generation: Efficiently generating all substrings is crucial. Nested loops are a straightforward way to do this, though not the most efficient.
Insight 3: Balanced substring condition: The condition for a balanced substring requires checking two things: (1) all zeros come before all ones and (2) the number of zeros equals the number of ones. The code needs to correctly implement both of these checks.

Complexity Analysis

Time Complexity: O(n^3)

Space Complexity: O(1)

Topics

This problem involves: String.

Companies

Asked at: Tinkoff.

Find the Longest Balanced Substring of a Binary String | LeetCode 2609

Easy

String

Time: O(n^3)Space: O(1)

Solution Code

Available in:

class Solution {
    public int findTheLongestBalancedSubstring(String s) {
        int maxLen = 0;
        for (int i = 0; i < s.length(); i++) {
            for (int j = i + 1; j <= s.length(); j++) {
                String sub = s.substring(i, j);
                int zeros = 0;
                int ones = 0;
                boolean balanced = true;
                boolean oneStarted = false;

                for (int k = 0; k < sub.length(); k++) {
                    if (sub.charAt(k) == '0') {
                        if (oneStarted) {
                            balanced = false;
                            break;
                        }
                        zeros++;
                    } else {
                        ones++;
                        oneStarted = true;
                    }
                }
                if (balanced && zeros == ones) {
                    maxLen = Math.max(maxLen, sub.length());
                }
            }
        }
        return maxLen;
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 2609: Find the Longest Balanced Substring of a Binary String - Detailed explanation and solution approaches.

Topics

String

Companies

Tinkoff

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2609

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

8 steps

1
Step 1: Initialize `max_len` to 0. This variable will store the length of the longest balanced substring found so far.
2
Step 2: Iterate through all possible starting indices `i` of substrings using a nested loop.
3
Step 3: For each starting index `i`, iterate through all possible ending indices `j` of substrings.
4
Step 4: Extract the substring `s[i:j]`.
5
Step 5: Count the number of '0's and '1's in the substring.
6
Step 6: Check if the substring is balanced (all '0's before '1's and equal counts).
7
Step 7: If the substring is balanced, update `max_len` to the maximum of `max_len` and the length of the substring.
8
Step 8: After iterating through all substrings, return `max_len`.

💡

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^3)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(n^3) because there are O(n^2) substrings, and checking if each substring is balanced takes O(n) time in the worst case (iterating through the substring). The space complexity is O(1) because only a constant amount of extra space is used to store variables like `max_len`, `zeros`, and `ones`.

📖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

Two Pointers

Use two pointers to efficiently find balanced substrings. One pointer keeps track of the start and the other the end of a potential substring. Move the pointers and update counts in a way that maintains the balanced substring criterion. This can achieve a linear time complexity.

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

Trade-offs: The two-pointer approach is significantly more efficient than the brute-force approach, especially for larger input strings. The brute-force approach is easier to understand but much less efficient.

✨

Key Insights

1Insight 1: Brute-force approach: The problem can be solved by iterating through all possible substrings and checking if each substring is balanced. This involves checking both the order of 0s and 1s and the equality of their counts.
2Insight 2: Substring generation: Efficiently generating all substrings is crucial. Nested loops are a straightforward way to do this, though not the most efficient.
3Insight 3: Balanced substring condition: The condition for a balanced substring requires checking two things: (1) all zeros come before all ones and (2) the number of zeros equals the number of ones. The code needs to correctly implement both of these checks.

📚

Key Terms Explained

For Students

String

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

Edge Cases

Edge case 1: Empty string. The code correctly handles the empty string case, returning 0 as the length of the longest balanced substring.
Edge case 2: String with only '0's or only '1's. The code correctly identifies that there are no balanced substrings (other than the empty string) and returns 0.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly checking the balanced condition. Forgetting to check that all '0's come before all '1's is a common mistake, leading to incorrect results.

✗Common mistake 2: Off-by-one errors in loop indices when processing substrings. This can result in missing substrings or incorrect substring extraction.

✅

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: Analyzing DNA sequences. Identifying patterns in biological sequences might involve finding balanced substrings based on certain nucleotide combinations.

🏦Real-world scenario 2: Data compression. Finding balanced substrings could be a component of compression algorithms seeking repeating patterns in data streams.

💡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

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ 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: August 29, 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 13

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

@DevExpert92Jul 6

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

@AlgoMasterJun 29

❓

Frequently Asked Questions

What is the sliding window technique for string problems?

Sliding window maintains a "window" of characters with two pointers. Expand the right pointer to include characters, shrink from left when window violates constraints. Useful for substring problems, anagrams, and longest/shortest substring with properties.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

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 the Longest Balanced Substring of a Binary String"?

For this easy-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?