How do you solve Greatest Common Divisor of Strings on LeetCode?

Greatest Common Divisor of Strings (LeetCode #1071) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The GCD of strings relies on the property of concatenation.

What is the time complexity of Greatest Common Divisor of Strings?

The optimal solution for Greatest Common Divisor of Strings runs in O(n) time and uses O(1) space. The time complexity is O(n) due to the string concatenation and GCD calculation, which is efficient compared to the brute-force method.

What is the brute force solution for Greatest Common Divisor of Strings?

The brute force approach for Greatest Common Divisor of Strings is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check all possible prefixes of the shorter string and see if they can divide both strings. This approach is straightforward but inefficient as it checks each prefix exhaustively. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Greatest Common Divisor of Strings?

Greatest Common Divisor of Strings uses the following concepts: Math, String. The recommended patterns to study are: String Manipulation, Mathematical GCD.

What are the interview tips for Greatest Common Divisor of Strings?

Always clarify the problem and constraints before diving into coding. Think about edge cases, such as strings of different lengths or completely different strings. Explain your thought process clearly while coding; it shows your understanding and can help you catch mistakes.

What are common mistakes when solving Greatest Common Divisor of Strings?

Not checking the concatenation condition first, which can lead to incorrect results. Assuming that any common prefix is a valid divisor without verifying.

#1071

Greatest Common Divisor of Strings

Easy

MathStringString ManipulationMathematical GCD

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

We can use the properties of the greatest common divisor (GCD) to find the largest string that divides both. If the concatenation of the two strings in both orders is equal, the GCD string is the prefix of either string up to the GCD of their lengths.

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Algorithm

3 steps

1Step 1: Check if str1 + str2 is equal to str2 + str1. If not, return an empty string.
2Step 2: Calculate the GCD of the lengths of str1 and str2.
3Step 3: Return the substring of str1 from the start to the GCD length.

solution.py8 lines

1# Full working Python code
2import math
3
4def gcdOfStrings(str1, str2):
5    if str1 + str2 != str2 + str1:
6        return ""
7    gcd_length = math.gcd(len(str1), len(str2))
8    return str1[:gcd_length]

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Complexity note: The time complexity is O(n) due to the string concatenation and GCD calculation, which is efficient compared to the brute-force method.

1The GCD of strings relies on the property of concatenation.
2If two strings can be formed by repeating a common substring, their concatenation in either order must be equal.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.