What is the optimal time complexity of solving Multiply Strings?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Multiply Strings?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Multiply Strings?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Multiply Strings?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Multiply Strings

Learn how to solve the 'Multiply Strings' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.

Note: You must not use any built-in BigInteger library or convert the inputs to integer directly.

Implement a function multiply(num1: str, num2: str) -> str.

Constraints

•1 <= num1.length, num2.length <= 200
•num1 and num2 consist of digits only
•Both num1 and num2 do not contain any leading zero, except the number 0 itself

Examples

Example 1

Input

"2", "3"

Output

"6"

Explanation

2 * 3 = 6.

Example 2

Input

"123", "456"

Output

"56088"

Explanation

123 * 456 = 56088.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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