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

The optimal solution for Find the Longest Balanced Substring of a Binary String runs in O(n) time and uses O(n) space. This complexity is linear because we traverse the string once and use a HashMap to store balance indices, which allows for quick lookups.

What is the brute force solution for Find the Longest Balanced Substring of a Binary String?

The brute force approach for Find the Longest Balanced Substring of a Binary String is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible substring of the binary string to see if it is balanced. This means we will iterate through all pairs of indices to form substrings and validate them. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Longest Balanced Substring of a Binary String?

Find the Longest Balanced Substring of a Binary String uses the following concepts: String. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find the Longest Balanced Substring of a Binary String?

Explain your thought process clearly. Discuss edge cases, like strings with no balanced substrings. Practice writing clean and efficient code.

What are common mistakes when solving Find the Longest Balanced Substring of a Binary String?

Not checking for balance correctly. Overlooking the need to track first occurrences of balances.

#2609

Find the Longest Balanced Substring of a Binary String

Easy

StringHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a HashMap to track the balance of zeroes and ones as we iterate through the string. This allows us to find the longest balanced substring in linear time by leveraging the concept of prefix sums.

⚙️

Algorithm

6 steps

1Step 1: Initialize a HashMap to store the first occurrence of each balance value.
2Step 2: Initialize variables for balance (0) and max_length (0).
3Step 3: Iterate through the string, updating the balance: +1 for '1' and -1 for '0'.
4Step 4: If the balance is seen before, calculate the length of the substring from the first occurrence to the current index.
5Step 5: If the balance is new, store the current index in the HashMap.
6Step 6: Return the max_length found.

solution.py11 lines

1def longestBalancedSubstring(s):
2    balance_map = {0: -1}
3    balance = 0
4    max_length = 0
5    for i, char in enumerate(s):
6        balance += 1 if char == '1' else -1
7        if balance in balance_map:
8            max_length = max(max_length, i - balance_map[balance])
9        else:
10            balance_map[balance] = i
11    return max_length

ℹ

Complexity note: This complexity is linear because we traverse the string once and use a HashMap to store balance indices, which allows for quick lookups.

1Balanced substrings require equal counts of '0's and '1's.
2Using a HashMap can optimize the search for previously seen balances.

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