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What is the space complexity of the dynamic programming solution for the Longest

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Question: What is the space complexity of the dynamic programming solution for the Longest Increasing Subsequence problem?

Options:

  1. O(n)
  2. O(n^2)
  3. O(log n)
  4. O(1)

Correct Answer: O(n^2)

Solution: 

The space complexity of the dynamic programming solution for the Longest Increasing Subsequence problem is O(n) due to the storage of intermediate results.

What is the space complexity of the dynamic programming solution for the Longest

Practice Questions

Q1
What is the space complexity of the dynamic programming solution for the Longest Increasing Subsequence problem?
  1. O(n)
  2. O(n^2)
  3. O(log n)
  4. O(1)

Questions & Step-by-Step Solutions

What is the space complexity of the dynamic programming solution for the Longest Increasing Subsequence problem?
  • Step 1: Understand the Longest Increasing Subsequence (LIS) problem. It involves finding the longest subsequence in a sequence of numbers where each number is greater than the previous one.
  • Step 2: Know that a dynamic programming solution is used to solve this problem efficiently by storing intermediate results.
  • Step 3: Realize that to store these intermediate results, we typically use an array (or list) that keeps track of the lengths of the longest increasing subsequences found so far.
  • Step 4: The size of this array is directly related to the number of elements in the input sequence, which we denote as 'n'.
  • Step 5: Since the array can grow to a size of 'n', we say that the space complexity is O(n), meaning it grows linearly with the input size.
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