What is the time complexity of the dynamic programming solution for the edit distance problem?
Practice Questions
1 question
Q1
What is the time complexity of the dynamic programming solution for the edit distance problem?
O(n*m)
O(n^2)
O(n log n)
O(2^n)
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.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the time complexity of the dynamic programming solution for the edit distance problem?
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.
Steps: 7
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).
