What is the Longest Increasing Subsequence problem and how do you solve it?
This problem asks for the length of the longest subsequence where elements are in increasing order. It tests DP or patience sorting.
Why Interviewers Ask This
Interviewers use this to test LIS algorithm knowledge. They want to see if you can derive the O(n^2) DP solution or the O(n log n) patience sorting approach. It demonstrates sequence analysis skills.
How to Answer This Question
Explain the O(n^2) DP approach where dp[i] is the length of LIS ending at i. For each i, check all j < i. Also mention the O(n log n) approach using a tails array and binary search. Walk through the logic of extending or replacing elements in the tails array.
Key Points to Cover
- DP state definition
- Nested loop logic
- Patience sorting alternative
- Binary search optimization
Sample Answer
The standard solution uses dynamic programming where dp[i] stores the length of the longest increasing subsequence ending at index i. For each element, I check all previous elements; if the current element is greater, I…
Common Mistakes to Avoid
- Confusing subsequence with substring
- Incorrect binary search bounds
- Not returning the maximum value
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