What is the time complexity of the dynamic programming solution for the edit dis

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Question: What is the time complexity of the dynamic programming solution for the edit distance problem?

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Correct Answer: O(n*m)

Solution:

The time complexity of the dynamic programming solution for the edit distance problem is O(n*m), where n and m are the lengths of the two strings.

What is the time complexity of the dynamic programming solution for the edit distance problem?

What is the time complexity of the dynamic programming solution for the edit distance problem?

Step 1: Understand the edit distance problem. It measures how many operations (insertions, deletions, substitutions) are needed to transform one string into another.
Step 2: Identify the two strings involved. Let's call them String A and String B, with lengths n and m respectively.
Step 3: Recognize that we will use a 2D table (array) to store the edit distances between all prefixes of String A and String B.
Step 4: The table will have (n+1) rows and (m+1) columns. This is because we need to account for the empty prefix of both strings.
Step 5: Filling in this table requires iterating through each cell, which involves a nested loop: one loop for the rows (n) and one for the columns (m).
Step 6: Each cell in the table takes constant time to compute, so the total time taken is proportional to the number of cells, which is (n+1)*(m+1).
Step 7: Simplifying this gives us a time complexity of O(n*m).

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