Find the Longest Balanced Substring of a Binary String

Find the Longest Balanced Substring of a Binary String - Problem

String Easy

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
The number of zeroes is equal to the number of ones

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.

Input & Output

Example 1 — Basic Pattern

$ Input: s = "01000111"

› Output: 6

💡 Note: The longest balanced substring is "000111" with 3 zeros followed by 3 ones, giving length 6

Example 2 — Multiple Patterns

$ Input: s = "00111"

› Output: 4

💡 Note: We have 2 zeros and 3 ones in pattern. The longest balanced part is "0011" with length 4

Example 3 — No Valid Pattern

$ Input: s = "111"

› Output: 0

💡 Note: No zeros present, so no balanced substring is possible

Constraints

1 ≤ s.length ≤ 50
s consists only of '0' and '1'

Visualization

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Asked in

a Amazon 25 M Microsoft 18

The key insight is that a balanced substring must have the pattern '00...0011...11' with equal counts. Best approach is the optimized single-pass solution that identifies consecutive zero-one patterns. Time: O(n), Space: O(1)

Common Approaches

✓ Brute Force - Check All Substrings

⏱️ Time: O(n³) Space: O(1)

For each starting position, examine all possible substrings. A substring is balanced if it has equal zeros and ones, with all zeros appearing before all ones.

Single Pass Optimization

⏱️ Time: O(n) Space: O(1)

Scan the string once and track consecutive zeros followed by consecutive ones. When we find such a pattern, calculate the maximum possible balanced length.

Brute Force - Check All Substrings — Algorithm Steps

Step 1: For each starting position i, check all substrings starting at i
Step 2: For each substring, verify it's balanced (equal counts, zeros before ones)
Step 3: Track the maximum length found

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Check all possible starting and ending positions

Validate Balance

Count zeros and ones, ensure zeros come before ones

Track Maximum

Keep track of the longest balanced substring found

Code -

solution.c — C

#include <stdio.h>
#include <string.h>
#include <stdbool.h>

int solution(char* s) {
    int n = strlen(s);
    int maxLength = 0;
    
    // Check all possible substrings
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            // Check if substring from i to j is balanced
            int zeros = 0, ones = 0;
            bool onesStarted = false;
            bool valid = true;
            
            for (int k = i; k <= j; k++) {
                if (s[k] == '0') {
                    if (onesStarted) {
                        valid = false;
                        break;
                    }
                    zeros++;
                } else {
                    onesStarted = true;
                    ones++;
                }
            }
            
            if (valid && zeros == ones) {
                int length = j - i + 1;
                if (length > maxLength) {
                    maxLength = length;
                }
            }
        }
    }
    
    return maxLength;
}

int main() {
    char s[1001];
    fgets(s, sizeof(s), stdin);
    s[strcspn(s, "\n")] = 0;
    
    int result = solution(s);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Three nested loops: start position, end position, and validation check

⚠ Quadratic Growth

Space Complexity

O(1)

Only using variables to track counts and maximum length

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - Check All Substrings — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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