What is the space complexity of the dynamic programming solution for the Longest Increasing Subsequence problem?
Practice Questions
1 question
Q1
What is the space complexity of the dynamic programming solution for the Longest Increasing Subsequence problem?
O(n)
O(n^2)
O(log n)
O(1)
The space complexity of the dynamic programming solution for the Longest Increasing Subsequence problem is O(n) due to the storage of intermediate results.
Questions & Step-by-step Solutions
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Q
Q: What is the space complexity of the dynamic programming solution for the Longest Increasing Subsequence problem?
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.
Steps: 5
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.
