What is the optimal time complexity of solving Edit Distance?

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 Edit Distance?

The space complexity is O(1) 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 Edit Distance?

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 Edit Distance?

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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Competitive ProgrammingEasy

Edit Distance

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

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Problem Statement

Easy

Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.

You have the following three operations permitted on a word:

1. Insert a character

2. Delete a character

3. Replace a character

Write a function minDistance(word1: str, word2: str) -> int.

Constraints

•0 <= len(word1), len(word2) <= 500
•word1 and word2 consist of lowercase English letters

Examples

Example 1

Input

word1 = "horse", word2 = "ros"

Output

Explanation

horse -> rorse (replace 'h' with 'r') -> rose (remove 'r') -> ros (remove 'e').

Example 2

Input

word1 = "intention", word2 = "execution"

Output

Explanation

intention -> extention -> exention -> exection -> execution. Total 5 operations.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

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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