What is the time complexity of the longest common subsequence problem using dynamic programming?
Practice Questions
1 question
Q1
What is the time complexity of the longest common subsequence problem using dynamic programming?
O(n)
O(m)
O(n*m)
O(n^2)
The longest common subsequence problem can be solved using a dynamic programming approach with a time complexity of O(n*m), where n and m are the lengths of the two sequences.
Questions & Step-by-step Solutions
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Q
Q: What is the time complexity of the longest common subsequence problem using dynamic programming?
Solution: The longest common subsequence problem can be solved using a dynamic programming approach with a time complexity of O(n*m), where n and m are the lengths of the two sequences.
Steps: 6
Step 1: Understand the problem - The longest common subsequence (LCS) problem involves finding the longest sequence that appears in the same order in both sequences, but not necessarily consecutively.
Step 2: Identify the sequences - Let's say we have two sequences, A and B, with lengths n and m respectively.
Step 3: Use dynamic programming - We create a 2D table (array) where the rows represent the characters of sequence A and the columns represent the characters of sequence B.
Step 4: Fill the table - We fill this table based on whether the characters from both sequences match or not. If they match, we take the value from the diagonal cell and add 1. If they don't match, we take the maximum value from the left or above cell.
Step 5: Determine the size of the table - The table will have n+1 rows and m+1 columns (including the base case for empty sequences).
Step 6: Calculate time complexity - Filling each cell in the table takes constant time, and since there are n*m cells, the overall time complexity is O(n*m).
