Find the Longest Balanced Substring of a Binary String

Find the Longest Balanced Substring of a Binary String

What is this problem about?

The Find the Longest Balanced Substring of a Binary String coding problem defines a "balanced" substring as one where all '0's appear before all '1's, and the number of '0's is equal to the number of '1's. For example, "0011" is balanced, but "0101" is not (because a '0' comes after a '1'). You need to find the length of the longest such balanced substring within a given binary string.

Why is this asked in interviews?

Amazon and other companies use this "Easy" problem to test basic string parsing and state tracking. It evaluations your ability to handle contiguous segments of data and apply simple geometric or mathematical constraints. It’s a test of whether you can correctly count consecutive characters and identify the transition points between '0' and '1' blocks.

Algorithmic pattern used

This is a Linear Scan problem.

1. Iterate through the string and group consecutive identical characters.
2. Keep track of the length of the current block of '0's and the current block of '1's.
3. Whenever you finish a block of '1's that was immediately preceded by a block of '0's, a balanced substring can be formed.
4. The length of this balanced substring is $2 imes \min( ext{count of 0s}, ext{count of 1s})$.
5. Maintain a global maximum of these calculated lengths.

Example explanation

String: "00011"

1. Count '0's: 3.
2. Count '1's: 2.
3. Balanced substring length: $2 imes \min(3, 2) = 4$. (The substring is "0011"). String: "010011"
4. First group: "01". $\min(1, 1) imes 2 = 2$.
5. Second group: "0011". $\min(2, 2) imes 2 = 4$. Max length: 4.

Common mistakes candidates make

• Counting non-contiguous blocks: Thinking "0101" is balanced because it has two 0s and two 1s.
• Resetting incorrectly: Failing to clear the '0' count when a new block of '0's starts after a block of '1's.
• Off-by-one: Miscalculating the length when the string ends with a valid balanced sequence.

Interview preparation tip

For binary string problems, always think about the "transitions" between 0 and 1. Tracking the counts of consecutive identical characters is a standard String interview pattern that simplifies many contiguous subarray problems.