Problem Statement: String Transformation

You are given two strings $s1$ and $s2$. Your task is to determine the minimum number of operations required to transform $s1$ into $s2$. You can use the following three operations:

1. Insert a character into the string.
2. Delete a character from the string.
3. Substitute one character in the string with another character.

Each operation has a cost of 1 unit, and your goal is to achieve the transformation with the minimum cost possible.

Input

• Two strings, $s1$ and $s2$, where:
  • $1 <= len(s1), len(s2) <= 500$
  • Both strings consist of only lowercase English letters.

Output

• A single integer representing the minimum number of operations required to transform $s1$ into $s2$.

Example

Input: s1 = "kitten", s2 = "sitting"
Output: 3

Explanation

- kitten -> sitten (substitute 'k' with 's')
- sitten -> sittin (substitute 'e' with 'i')
- sittin -> sitting (insert 'g')

Objective

Implement an efficient algorithm to calculate the minimum number of operations needed to convert $s1$ into $s2$ and return the cost.

Submission

Think you’ve cracked it? Submit your solutions here and wait a few days to get it verified.

Note

• This technique, often called Edit Distance or Levenshtein Distance, is of particular interest in bioinformatics. Biologists use similar methods to measure differences between DNA, RNA, or protein sequences, helping to identify evolutionary relationships, mutations, and functional similarities. Such comparisons play a critical role in areas like gene editing, where understanding and calculating minimal sequence transformations can guide precise modifications to genetic material.

Solution

The solution to the problem can be found at Solution 1.